Auctions with Interdependent Valuations

Theoretical and Empirical Analysis, in particular of Internet Auctions

Julia Schindler Vienna University of Economics and Business Administration January 2003

Abstract

The thesis investigates a number of auction formats both theoretically and empirically. The effect of different auction rules on the final price and on bidder valuations is analysed. Results from an experimental sale of real goods, testing revenue equivalence of the open and sealed- bid second-price auction do not conform to theoretical predictions: the open auction leading to significantly lower prices than the sealed-bid auction. It turns out that the open auction format allows bidders to satisfy a tendency to “stick together” with their valuations. The empirical results motivate a dynamic bidding model of interdependent valuations, bidders being uncertain about their valuations and learning from the exit-prices of their rivals.

Furthermore, bidding behaviour on the Internet is investigated in the hard close and the automatically extended auction. Late bidding is shown to be a rational strategy in the hard close auction, but not in the automatically extended auction. Theoretical results show that the expected final price and seller revenue is lower in the hard close auction than in the automatically extended auction, where prestige-concerns can lead to an explosive final price. Moreover, Yahoo auction data confirms the strong presence of late bidding in the hard-close auction and the seller’s preference for the automatically extended auction.

2

Introduction ...... 8

PART ONE: Auction Theory...... 10

1. The Four Standard Auction Formats...... 10 1.1 English Auction...... 10 1.2 Dutch Auction ...... 10 1.3 First-Price Sealed-Bid Auction ...... 11 1.4 Vickrey Auction (Second-Price Sealed-Bid Auction) ...... 11 2. The Independent Private Values Model (IPV)...... 11 2.1 Bidding strategies in the IPV Model...... 12 2.1.1 First-Price Sealed-Bid Auction ...... 12 2.1.2 Dutch Auction ...... 15 2.1.3 Second-Price Sealed-Bid Auction...... 15 2.1.4 English Auction...... 16 2.1.5 Extension: Sealed-Bid Higher kth-Price Auctions...... 16 2.2 Results of the Independent Private Values Model ...... 17 2.3 Extension: Uncertainty About the Number of Bidders ...... 17 2.3.1 Effect of the Number of Bidders on the Price...... 18 2.3.2 Effect on the Bidding Strategy...... 18 3. Beyond Standard Assumptions...... 19 3.1 Risk Aversion...... 19 3.2 Asymmetries Between Bidders ...... 19 3.3 Interdependent Values...... 20 3.3.1 The Common Value Model...... 20 3.3.2 The Symmetric Model, the Milgrom-Weber Model ...... 22 3.3.2.1 Affiliation...... 23 3.3.2.2 Bidding Strategies in the Milgrom-Weber Model...... 24 3.3.2.2.1 Second-Price Sealed-Bid Auction...... 24 3.3.2.2.2 English Auction...... 24 3.3.2.3 Results of the Milgrom-Weber Model ...... 26 3.3.2.3.1 Ranking of Expected Prices ...... 26 3.3.2.3.2 Linkage principle...... 26 4. Revenue Ranking According to Theoretical Predictions ...... 26

3 5. Experimental Tests of Bidding Behaviour and Auction Revenue...... 27 5.1 Field Experiments ...... 28 5.1.1 Field Experiments on the Internet ...... 28 5.2 Laboratory Experiments...... 28 6. Theoretical Predictions and Empirical Results...... 30 PART TWO: Dynamic Price Formation in the Japanese Auction

...... 31 1. Introduction ...... 32 2. Experiment...... 35 2.1 Experimental Set-Up...... 36 2.2 The Goods ...... 38 3. Results...... 39 3.1 No Revenue-Equivalence...... 40 3.2 Lower Bid-Variance in Japanese Auction...... 40 3.3 Average Bid Not Significantly Different ...... 40 3.4 Reasons for Lower Bid-Variance in Japanese Auction...... 41 3.5. Learning Effects ...... 41 4. Interpretation...... 41 5. The Model ...... 43 5.1 The First Round...... 44 5.1.1 The First Exit...... 45 5.1.2 Common Value Estimation and the Updating Procedure ...... 46 5.2 The General Procedure...... 48 5.3 Estimation Procedure ...... 49 5.4 The Expected Final Price ...... 49 5.5 Results of the Model ...... 50 6. Conclusion...... 53 7. Appendix ...... 55

PART THREE: Experimental Test of Revenue Equivalence ...... 58

1. Motivation ...... 59 2. Experimental Set-Up...... 59

4 3. Revenue Equivalence Between the Second-Price and the Japanese Auction...... 60 3.1 Breakdown of Revenue Equivalence ...... 60 3.2 Testing the Effect of Revealing Public Information ...... 60 3.2.1 Results ...... 61 4. English Outcry versus Second-Price Sealed-Bid Auction ...... 63 4.1 Results ...... 63 5. Revenue Equivalence: First-Price Sealed-Bid and Dutch Auction ...... 64 5.1 Results ...... 65 6. Comparison: Second-Price Sealed-Bid, First-Price Sealed-Bid and Japanese Auction...... 66 6.1 Results ...... 66 6.2 Interpretation ...... 67 7. Six Results of the Experimental Investigation of Revenue Equivalence. 68 8. Conclusion...... 69

PART FOUR: Internet Auctions and their Framework...... 70

1. Introducing Internet Auctions ...... 70 1.1 Three Business Models: Ebay, Amazon, and Yahoo...... 70 1.1.1 Revenue...... 72 1.2 Network Effects...... 73 1.2.1 Loyalty ...... 74 1.3 The Selling Mechanism...... 74 1.3.1 Auctions and Posted Prices ...... 74 1.4 The Goods ...... 75 1.4.1 Suitable for Auctions...... 75 1.4.2 Goods Sold ...... 75 1.5 The Auction Formats Used ...... 77 1.5.1 The Choice of Auction Format by the Auction House...... 77 2. Internet-Specific Characteristics ...... 78 2.1 Internet Specific Advantages ...... 78 2.2 Internet Specific Problems ...... 79 2.3 Outlook...... 81

5 3. The Internet Auction Rules ...... 81 3.1 Bid Submission and Procedure ...... 81 3.2 Bidder and Seller Registration ...... 82 3.3 Auction-Length ...... 82 3.5 Auction Fees...... 83 3.6 Additional Features ...... 83 4. Some Implications of the Auction Rules ...... 85

PART FIVE: Late Bidding Investigation ...... 88

1. Introduction ...... 89 2. Theoretical Investigation ...... 90 2.1 Theoretical Investigation of Late bidding ...... 91 2.1.1 The Moral Hazard Incentive ...... 91 2.1.2 Interdependent Values...... 92 2.1.3 General Bidding Model...... 92 2.1.3.1 Model of the Hard Close Auction ...... 93 2.1.3.5 Revenue Comparison: Hard Close and Automatically Extended Auction ...... 109 2.1.4 Prestige Value Model...... 109 2.1.4.1 Symmetrical Case...... 110 2.1.4.2 Expert-Amateur Case ...... 114 2.1.4.3 Result of Prestige Value Auctions ...... 117 2.1.4.4 Payoffs in the Automatically Extended Auction...... 117 2.1.5 Payoff Comparison: Hard Close and Automatically Extended Auction...... 118 2.1.6 Milgrom-Weber Model ...... 118 2.1.6.1 Bidding in the hard close auction...... 118 2.1.7 General Prediction for Interdependent Valuations...... 121 2.1.8 Late bidding with Respect to the Ending-Rule ...... 121 2.1.9 Late Bidding According to Good Type...... 121 2.2 Seller’s Choice of Ending-Rule...... 122 3. Empirical Investigation...... 123 3.1 Late Bidding...... 124 3.1.1 Existence of Late bidding...... 124 3.1.1.1 Complete Auction Duration ...... 124 3.1.1.2 Last Twelve Hours ...... 126

6 3.1.2 Late bidding: Dependency on Ending-Rule...... 127 3.1.2.1 Complete Bidding-Path...... 128 3.1.2.2 Last Twelve Hours ...... 130 3.1.2.3 Reasons for Late Bidding in Automatically Extended Auctions ...... 130 3.1.3 Late bidding: According To Type of Good...... 131 3.1.3.1 Art: Strongest Late bidding...... 132 3.1.3.2 Computers: Late bidding Similar For Both Ending Rules ...... 133 3.1.3.3 Late bidding In Car Auctions: Strongly Dependent On Ending-Rule ...... 134 3.1.4 Operational Investigation of Late Bidding...... 135 3.2 Time-Invariance ...... 136 3.3 Winner’s Bidding Behaviour ...... 139 3.3.1 Entry Time of Winner ...... 139 3.3.2 Winning Bid: Single Bid or Proxy Bid?...... 140 3.4 Seller’s Choice of Ending-Rule...... 142 3.4.1 The Preferred Ending-Rule ...... 142 3.5 Successful Matchings...... 144 3.5.1 Average Number of Bids...... 144 3.5.2 Buy-Price...... 145 4. Results of the Empirical Analysis ...... 146 4.1 The Four Main Hypotheses and the Empirical Evidence...... 146 4.2 Further Important Results...... 147 5. Conclusion...... 147

PART SIX: Conclusion ...... 148

Literature ...... 149

7 Introduction

What is an auction? A mechanism that determines the price and allocation of goods by comparing competing bids.

Auctions have been used for selling goods in ancient cultures such as early China, Greece and the Roman Empire. Herodotus reports auctions of women on the annual marriage market as early as 500 B.C. in Babylon. Nowadays, auctions are a widely used selling device for diverse items, such as government bonds, state-owned firms and mineral rights for oil and other natural resources.

Sotheby’s and Christies, founded in the 18th Century in Great Britain, represent a branch of traditional auction houses known for selling exquisite items such as art, antiquities and jewellery, or collectibles, such as coins and stamps to the wider public. Another set of goods frequently sold in auctions are perishable products, such as flowers (in Holland) and fish (in Japan).

Due to the Internet and the consequently low transaction costs, auctions have boomed. Ebay, Amazon and Yahoo auctions enable consumers to buy and sell items on a virtual platform open to bidders around the world. Supplier contracts are auctioned-off online. Whether traditional or online, the seller wants to receive the highest possible price for his good. The question of how buyers form their bids and which auction format realises the highest auction revenue for the seller needs to be answered given the information technology era and its new empirical insights.

The dissertation is set-up as follows:

In part one I present an overview of auction theory.

In part two, an experimental test of revenue equivalence between the second-price sealed-bid and the English auction (also known as the English ascending bid auction) is conducted. The empirical results do not conform to theoretical predictions: the open English auction yields significantly higher revenue than the second-price sealed-bid auction. Furthermore, bids are

8 far more narrowly dispersed in the English than in the second-price sealed-bid auction. The empirical observations call forth a dynamic bidding model of interdependent valuations. Bidders are uncertain about their valuations and follow a boundedly rational-learning rule to update their valuations in the course of the auction.

In part three, further tests of revenue-equivalence are conducted. The sealed-bid format is compared to the open format for the two pairs of strategically equivalent auctions: First-price sealed-bid and Dutch auction, English outcry and second-price sealed-bid auction. The results are tested under the effect of revealing public information.

In part four the rules and framework of the currently existing Internet auctions are presented.

In part five bidding behaviour in Internet auctions is analysed using two models of interdependent valuations: a general and a prestige value model. Late bidding is found to be a rational bidding strategy in the hard-closing auction, lowering the price and seller revenue. On the other hand prestige-effects can lead to exorbitant seller revenue in the automatically extended auction. The theoretical predictions are tested using Yahoo auction data with respect to two ending rules (hard close) and three categories of goods (cars, computers and paintings). Late bidding is found to be strongly present both in terms of the dynamic and operational bidding path as well as the winning bidder’s entry time. The proposed seller’s preference for automatically extended auctions is empirically confirmed.

In part six I conclude.

9 PART ONE: Auction Theory

Auction rules can be chosen with respect to two goals. One goal is maximization of the seller revenue; the second goal is efficiency; efficiency meaning that the good is allocated to the highest-valuing bidder. Efficiency and revenue-maximisation do not necessarily conflict. Here we focus on private goods, where a seller is usually concerned with finding an auction mechanism to maximise his revenue. In the best case, the seller could charge the highest valuing bidder a price exactly equal to this valuation. But, the seller does not know the bidders‘ valuations. The goal of the bidder is to maximise his utility, which is the difference between the valuation of the good and the price he has to pay. Thus, the bidder has no interest in revealing his valuation to the seller.

No auction mechanism can determine prices directly in terms of bidder preferences and information. The seller must choose auction rules that reveal information about the bidders’ preferences. There are a large number of rules a seller could choose when designing his personal auction selling device. Auction theory works with the following four auction formats:

1. The Four Standard Auction Formats

1.1 English Auction

The English auction is an open, ascending bid auction. The price is raised sequentially until only one active bidder remains. The good is allocated to the highest bidder, who has to pay a price equal to the second-highest bid.

1.2 Dutch Auction

The Dutch auction is an open, descending bid auction. A counter showing the current price is lowered continuously until the first bidder cries: „halt“. The Dutch auction is for example used in Holland for selling flowers.

10 1.3 First-Price Sealed-Bid Auction

The first-price sealed-bid auction is a closed auction. Every bidder enters a private bid. The good is awarded to the highest bidder at the price of his own bid.

1.4 Vickrey Auction (Second-Price Sealed-Bid Auction)

The second-price sealed-bid auction is a closed auction. The good is awarded to the highest bidder at the price of the second-highest bid.

2. The Independent Private Values Model (IPV)

In order to analyse which auction format is the revenue maximising choice, we need to make some assumptions about the way bidders form their valuation of the good. One frequently chosen set of assumptions is the independent private values model:

Assumptions: - Risk-neutrality: All bidders are risk-neutral, maximising their expected profits. - Independence: The bidders’ values are private and independently distributed. - Symmetry: The values of the bidders are distributed according to the same distribution function. - No budget constraint: Bidders have the ability to pay up to their respective values.

A risk-neutral seller wants to sell an indivisible object that he himself values with zero1. There are n bidders. Bidder i (i = 1,.., n) draws his valuation xi from the distribution function Fi(xi) independently and identically distributed on the interval [x, x]with the density function fi(xi) fi(x) = f(x) for all x ∈[x, x].

1 This is equivalent to assuming the good has already been produced and the seller’s utility from using it is zero. Jehle and Reny (2001), p.374. 11 Every bidder knows his valuation, but cannot observe the private valuations of the other bidders. The seller does not know the bidder valuations, but he and all bidders know the distribution of the bidder valuations and the number of bidders.

A bidder’s valuation is independent and private, denoting differences in taste. The value of the good depends only upon personal preferences; a bidder’s value is unaffected by the valuations of the other bidders (even if he knew them, his valuation for the good would remain unchanged).

The winning bidder receives the good and has to pay a price p. His payoff is given by: xi – p. If he does not win the good, his payoff is zero.

2.1 Bidding strategies in the IPV Model

Bidding behaviour in an IPV auction is a non-cooperative game. Bidders devise a strategy; i.e. a bidding function β :[0,ω] → ℜ + that maps every possible value bidder i could draw into a non-negative bid. Bidders search for the bidding function that leads to the most desirable outcome, given that all other bidders also form their bid according to that same bidding function.

2.1.1 First-Price Sealed-Bid Auction In a first-price sealed-bid auction the bidder with the highest bid wins and pays a price equal to his bid.

 xi − bi if bi < max j≠i b j  Π i =  0 if bi < max j≠i b j  (xi − bi ) / k, k := {arg maxb j } if bi = max j≠i b j j

In the first-price sealed-bid auction bidders shade their bids; i.e. bid less than their valuation. If a bidder bid his true valuation, he would have to pay a price equal to his valuation in case of winning and receive a payoff of zero.

12 Bidders face a trade-off; shading the bid downwards means lowering the probability of winning but also means increasing the expected gain (when being the winning bidder).

G…distribution function of Y1, where Y1 is the second-highest private signal. g…the density of Y1, g = G’

The expected payoff of the winning bidder is given by: G(β −1 (b))(x − b) Maximising this with respect to b, yields the following first-order condition: g(β −1 (b)) (x − b) − G(β −1 (b)) = 0 β '(β −1 (b))

In a symmetric equilibrium b = β (x) and yields the following differential equation:

G(x)β ' (x) + g(x)β (x) = xg(x) or equivalently, d (G(x)β (x)) = xg(x) dx since β (0) = 0,

1 x β (x) = ∫ yg(y)dy G(x) 0

= E[Y1 Y1 < x]

F The symmetric equilibrium strategy in a first-price auction is: β (x) = E[Y1 Y1 < x]

Proof: Only strictly increasing bidding functions are considered; it is assumed that bidders with higher valuations make higher bids. z denotes the value for which b is the equilibrium bid, z = β −1 (b) , so that β (z) = b .

13 Bidder 1’s payoff from bidding β (z) when his value is x is given by: Π(b, x) = G(z)[x − β (z)]

= G(z)x − G(z)E[Y1 Y1 < z] z = G(z)x − ∫ yg(y)dy 0 z = G(z)x − G(z)z + ∫G(y)dy 0 z = G(z)(x − z) + ∫ G(y)dy 0

z It follows that: Π(β (x), x) − Π(β (z), x) = G(z)(z − x) − ∫G(y)dy ≥ 0 x If all bidders follow the strategy β , a bidder with a value of x will be best off bidding β (x) ; thus β is a symmetric equilibrium strategy.

x G(y) The equilibrium bid can be written as: β F (x) = x − ∫ dy 0 G(x)

This is the symmetric Nash equilibrium of a first-price sealed-bid auction. The bidding function is strictly increasing in x and offers a unique solution.

As can be seen from the expression above, bidders in a first-price auction bid less than their valuation. The degree of bid shading depends on the number of rival bidders, because

N −1 G(y)  F(y) =   G(x)  F(x) 

As the number of bidders increases, the equilibrium bid β F (x) approaches x.

In the case of uniformly distributed valuations on [0,1]: N −1 F(x) = x, then G(x)=xN-1 and β F (x) = x N N −1 The expected seller revenue, i.e. expected price is: E[R F ] = N +1

xN The expected utility of the winning bidder with signal xN is: N

14 2.1.2 Dutch Auction In the Dutch auction a bidder needs to decide at what price to cry “halt”. The winning bidder, has to pay a price equal to his “bid”. The Dutch auction is strategically equivalent to the first- price auction.

2.1.3 Second-Price Sealed-Bid Auction In the second-price sealed-bid auction, the price the winner has to pay is determined by the second-highest bid and is thus independent of the winner’s bid.

 xi − bi if bi < max j≠i b j  Π i =  0 if bi < max j≠i b j  (xi − bi ) / k, k := {arg maxb j } if bi = max j≠i b j j

It is a unique weakly dominant strategy to bid one’s own valuation: β S (x) = x

Proof: •By bidding above his valuation, a bidder runs the risk of winning the auction, in cases where he would make a loss.

Assume that bidder 1 has a valuation x1 and that the highest competing bid is: p1 = max j≠i b j .

By bidding b1 = x1 , bidder 1 will win if b1 > p1 and does not win if b1 < p1 .

In case bidder 1 bids an amount higher than his valuation: b1 > x1 . If b1 > x1 ≥ p1 , then bidder

1 wins with a payoff: x1 − p1 . This is the same payoff he would have received from bidding an amount equal to his valuation. If p1 > b1 ≥ x1 , bidder 1 loses. If b1 > p1 > x1 , bidder 1 wins but makes a loss equal to x1 − p1 , whereas by bidding an amount equal to his valuation he would not have made a loss. It follows that it is never profitable for bidder 1 to bid above his valuation, as this never increases his profit, but may actually decrease his profit.

• By bidding below his valuation, a bidder lowers his chances of winning: he does not win in cases where he could have received a positive payoff. Thus, the pay-off maximising strategy for bidder i is to bid his valuation.

15 Assume bidder 1 has a valuation of x1 and that the highest competing bid is p1 = max j≠i b j .

By bidding b1 = x1 , bidder 1 will win if b1 > p1 and does not win if b1 < p1 .

In case bidder 1 bids an amount smaller than his valuation: b1 < x1 . If x1 > b1 ≥ p1 , then bidder 1 wins with a payoff: x1 − p1 . This is the same payoff he would have received from bidding an amount equal to his valuation. If p1 > x1 ≥ b1 , bidder 1 loses. If x1 > p1 > b1 , bidder 1 loses, but could have won by bidding b1 = x1 . It follows that it is never profitable for bidder 1 to bid below his valuation, because this may decrease his profit.

2.1.4 English Auction In an English auction a bidder has to decide when to drop out of the auction. The English auction differs from the sealed-bid auctions in that bidders observe the exit-prices of the others and have the possibility to revise their valuation – as long as they are active participants.

In an English auction truthful bidding is a weakly dominant strategy. If weakly dominated strategies are eliminated, the bidder with the highest valuation wins and pays a price equal to the second highest valuation.

2.1.5 Extension: Sealed-Bid Higher kth-Price Auctions2 Theoretically it is possible to conduct an auction, where it is neither the highest bid that determines the price the winner has to pay, nor the second-highest bid, but instead the third- highest or fourth-highest bid. Using higher k-th price auctions leads to the following results:

1.) Bids are higher than valuations. 2.) Equilibrium bids increase as k increases. 3.) Equilibrium bids decrease as the number of bidders is increased.

The reason why third-price auctions and higher are generally not found in practice, is because they expose the seller to higher risk than the standard auction formats.

2 Higher k-th price auctions, meaning higher than second-price auctions. 16 2.2 Results of the Independent Private Values Model3

Result 1: The Dutch auction is strategically equivalent to the first-price sealed-bid auction. Two auction formats are strategically equivalent, when the expected seller revenue is equal and an identical bidder would choose the same strategy under both auction formats.

Result 2: The English auction is strategically equivalent to the second-price sealed-bid auction, but in a weaker form than the strategic equivalence of the Dutch and first-price sealed-bid auction - the latter holding even when bidders are uncertain about their valuation.

Result 3: The second price and the English auction lead to an efficient allocation, a Pareto- optimal outcome. The Dutch and first-price sealed-bid auction also lead to an efficient outcome as long as the bidders’ valuations are drawn from a symmetric distribution.

Result 4: The expected seller revenue is equal to the expected value of the second highest bidder.

Result 5: The seller’s expected revenue is equally high in all four auction formats. This is the famous revenue equivalence theorem by Vickrey (1961).

Result 6: The four standard auction forms can be designed so as to produce an optimal outcome by using entry fees or reserve prices. This result is true for many common sample distributions, including the normal, exponential, and uniform distribution.

Result 7: When the seller, the bidders or both are risk-averse, the seller strictly prefers the Dutch or first-price sealed-bid auction to the English or second-price auction.

2.3 Extension: Uncertainty About the Number of Bidders

3 As noted in Milgrom and Weber (1982). 17 It is generally assumed in auction theory that the number of participating bidders is known. In reality bidders often face uncertainty with respect to the number of bidders, for example in Internet auctions, where bidders are allowed to enter until the very last moment.

2.3.1 Effect of the Number of Bidders on the Price In the independent private values model, as the number of bidders increases, the second highest valuation approaches the upper limit of the distribution of valuations, and thus the price tends to the highest possible valuation (Holt 1979). As long as the number of bidders is finite, the price the winning bidder has to pay is smaller than his valuation. A higher number of bidders raises the seller revenue and lowers the bidder revenue in all four auction formats.

2.3.2 Effect on the Bidding Strategy The number of bidders does not influence the bidding strategy in the second-price auction, but does influence it in the first-price auction.

The bidding strategy in the second-price auction is given by: β (x) = x . Uncertainty about the number of participating bidders, and consequently under- or overestimating the number of participating bidders has no effect in the second-price auction.

When values are uniformly distributed x ~U[0,1] the bidding strategy in the first-price N −1 auction is determined by: β (x) = x . The expected seller revenue in the first-price N N −1 auction is equal to and the expected payoff of the winning bidder (with the private N +1 x signal x ) is equal to N . N N

Under- or overestimating the number of participating bidders in the first-price auction affects a bidder’s probability of winning and his expected revenue. Underestimating the number of participating bidders reduces the individual bidder’s probability of winning. If all bidders underestimate the number of participating bidders, the seller’s expected revenue falls. Overestimating the number of bidders increases the individual bidder’s probability of winning, but lowers his expected revenue. The seller’s expected revenue rises when all bidders overestimate the number of participating bidders.

18

3. Beyond Standard Assumptions

The Revenue Equivalence Theorem does not always hold when assumptions of the independent private value model are relaxed.

3.1 Risk Aversion

When either the seller or the buyers are risk-averse, the first-price auctions lead to higher seller revenue than the second-price auctions.

Under risk-aversion the equilibrium bidding strategy in the second-price auction remains unchanged, but changes in the first-price auction. In a first-price auction bidders shade their bid whether they are risk-neutral or risk-averse. Risk-averse bidders in a first-price auction shade their reservation price more heavily than when they are risk-neutral. Risk-neutral bidders shade their bid less, because the increase in expected-payment due to a marginal increase of the bid, is less costly than the reduced probability of not winning the auction due to the lower bid. This raises the seller’s expected revenue and lowers the bidder’s expected payoff4.

With constant absolute risk-aversion the first-price auction produces higher expected revenues than the second-price auction.

3.2 Asymmetries Between Bidders

If the assumption of symmetrical bidder valuations is removed, the first-price auction does not always create an efficient outcome (the good is not always awarded to the highest valuation bidder).

Roughly speaking, the sealed-bid auction generates more revenue than the open auction when bidders have distributions with the same shape (but different supports). In contrast the open

4 Riley and Samuelson (1981). 19 auction generates more revenue than the sealed-bid auction when distributions have different shapes but approximately the same support.

Ex ante asymmetries can discourage participation by lower valuing bidders. Small asymmetries can lead to highly asymmetric equilibria that result in low seller revenues5.

3.3 Interdependent Values

The private value model is often unrealistic, because there are many goods where bidders are uncertain about their valuation and are influenced by the valuations of the other bidders. In the following section the private values assumption is relaxed and instead bidders are assumed to have interdependent values. Interdependent values imply that every bidder has some private information in form of a signal, but a bidder does not perfectly know his valuation for the object. It may now be the case that other bidders possess information that would - if known to the bidder - affect his valuation. This can be due to resale or prestige considerations: a buyer of an old-timer might want to resell the car after some time, thus he will let his valuation be somewhat dependent on the other bidder’s valuations.

Interdependent values do not imply anything about the distribution of the bidders’ signals: signals can be independently distributed or correlated. The best-known model of interdependent values is that of Milgrom and Weber (1982). They assume that bidders’ signals are affiliated, which is a special form of positive correlation (see Part Two Chapter 2.3.1 below).

Milgrom and Weber’s general symmetric model of interdependent valuations can account for the case of strictly private valuations (see above for the IPV model), for the intermediate cases and for strictly common valuations (see below).

3.3.1 The Common Value Model A good having a single objective value is offered for sale. The bidders do not know the value of the object, but every bidder has access to some information on its value, each bidder

5 See Klemperer (1998), p.764. 20 making a different estimate of the good’s value. V is the true value of the good, drawn randomly from a probability distribution (here: a uniform distribution) on the interval: [x, x].

Each bidder receives a private signal xi, i =1,..,N. The private signals are independent draws from the uniform distribution on [V-ε, V+ε]. A first-price auction is considered here:

Bidders do not know the true value V and try to estimate the correct expected value. The expected value of the item conditional on signal xi is: E[V X i ] = xi . In this case every bidder would take his private signal to be the best estimate of the good’s value, knowing that the expected mean signal is equal to the site’s true value. But if every bidder bids his private signal, the winning bidder will be the one with the highest private signal. He will have overbid the true value V most highly, making a loss in turn. This is known as the winner’s curse.

Foreseeing that a bidder will only win when his signal is the highest signal, he bids the expected value conditional on being the high bidder:

N − 1 E[V X = x ] = x − ε max i i N + 1

The expected value conditional on being the high bidder is lower than the expected value conditional on the private signal:

E[V X i = xi ] = xi > E[V X max = xi ] for N > 1

The winner’s curse can be measured as the difference in the two expected values. Avoiding the winner’s curse requires considerable discounting of bids relative to the signal values. The size of the discount is an increasing function of the number of bidders N and the dispersion of the signals around the true value ε. Raising the number of bidders or lowering the precision of the signals leads to a higher winner’s curse (when bidders ignore their judgemental failure).

The symmetric equilibrium bid function is equal to:  2ε   − N   b(xi ) = xi − ε + Y where Y =   exp ()xi − (x + ε)   N +1  2ε  

21 2ε Expected profits for the high bidder are equal to: − Y N +1

Y diminishes rapidly as xi moves beyond x + ε. Ignoring Y, the bidding function is 2ε approximately equal to b(x ) = x − ε and the high bidder’s profit equal to . i i N +1

If bidders ignore the winner’s curse, the bid function under risk neutrality is: 2ε Y b s (x ) = x − + i i N N The model predicts that the high signal holder always wins the auction. This is because all bidders use the same bid function, their only difference being their private information xi regarding the value of the item.

3.3.2 The Symmetric Model, the Milgrom-Weber Model As introduced in Section 3.3 the most prominent model of interdependent valuations is the Milgrom-Weber model (1982). Bidders have some uncertainty about their valuation, due to resale or prestige considerations. Being a general model it can take account of the various degrees of uncertainty ranging from the purely private value model to the purely common value model. For all intermediate cases they assume that private signals are positively correlated by affiliation:

There are n bidders. Bidder i’s value of the object is Vi = u i (S, X). The bidder’s valuation does not only depend upon his private signal, but also upon the other bidders’ private signals.

S = (S1,..., Sm ) is a vector of variables measuring the good’s quality, which influence the value of the object to the bidders. The bidders cannot observe S, but the seller can observe some or all components of S.

X = (X1 ,...,Xn) is a vector of value signals observed by the individual bidders. Let Y1,…,Yn-1 represent the largest to the smallest estimates from among X2,…,Xn. Every bidder observes a private signal about the value of the good. Bidder i, i = 1,..,n observes the private signal Xi about the value of the good.

Bidder 1’s value is: V1 = u1 (S1, …Sm, X1, Y1,…Yn –1)

22 Assumption 1: There is a function u such that for all i, u i (S,X) = u(S,X i,{X j}j ≠i). Thus, all of the bidders’ valuations depend on S in the same way, and each bidder’s valuation is a symmetric function of the other bidders’ signals.

Assumption 2: u is nonnegative, continuous and non-decreasing in its variables.

Assumption 3: For each i, E [Vi] < ∞

When Vi = Xi for all i , the model is reduced to the independent private value model.

When Vi = S1 for all i , the model is reduced to the common value model.

Bidders are risk-neutral and their valuations are in monetary units, so that when bidder i receives the object and has to pay p, his payoff is Vi – p. f(s,x) is the joint probability density of the random elements of the model. Two assumptions are made about the joint distribution of S and X: Assumption 4: f is symmetric in its n last arguments.

Assumption 5: The variables S1,..., Sm, X1 ,..., Xn are affiliated.

E [V1|X1= X, Y1 = Y1…, Yn-1 = Yn-1] is non-decreasing in x.

3.3.2.1 Affiliation Every bidder has some private information about the value of the good. This private information is expressed in the signal he draws. In case of affiliation it is assumed that the bidders’ signals X 1 , X 2 ,..., X n are positively affiliated. Affiliation is a strong form of positive correlation and means that if a subset of the X i take on large values, then the remaining X j also take on large values. Variables are affiliated if large values for some of the variables make the other variables more likely to be large than small. A high value of one bidder’s estimate makes high values of the other bidders’ estimates more likely.

For variables with densities, affiliation can be defined as such: Let z ∨ z’ denote the component-wise maximum of n+m dimensional vectors z and z’ and let z ∧ z’ denote the component-wise minimum. Variables are affiliated if, for all z and z’, f(z ∨ z’)f(z ∧ z’) ≥ f(z)f(z’).

23 Three implications of affiliation6:

1.) Y1,…,Yn-1 are the largest to the smallest estimates from among X2,…, Xn. If the variables

X 1 , X 2 ,..., X n are affiliated, then the variables X 1 ,Y1 ,...,Yn−1 are also affiliated.

2.) G(⋅ x) denotes the distribution of Y1 conditional on X1 = x. X 1 and Y1 being affiliated implies that if x’>x, then G(⋅ x') dominates G(⋅ x) in terms of the reverse hazard rate, that is,

g(y x') g(y x) for all y, ≥ G(y x') G(y x)

3.) If γ is any increasing function, then x’>x implies that:

E[γ (Y1 ) X 1 = x'] ≥ E[γ (Y1 ) X 1 = x]

3.3.2.2 Bidding Strategies in the Milgrom-Weber Model

3.3.2.2.1 Second-Price Sealed-Bid Auction Bidder 1’s decision problem in the second-price sealed-bid auction is to choose a bid b that maximises the expected value minus the price conditional on bidder 1’s signal (when this is the highest signal).

The equilibrium strategy of every bidder is to bid β S (x) = v(x, x) v(x, y) := E[V1 X 1 = x,Y1 = y]. v is non-decreasing. In the case of private values (where v(x,x)=x) the equilibrium strategy is weakly dominant. With general interdependent values however β S is not a dominant strategy.

3.3.2.2.2 English Auction The English auction in the Milgrom-Weber Model is modelled as a Japanese Auction. The auction begins at a price of zero, at which all bidders are active. The auctioneer raises the price and bidders can quit the auction by depressing a button. Bidders who have quit the auction cannot return at a later point in time. Every time a bidder quits the auction, the exit- price is revealed to all remaining bidders.

6 Taken from Krishna (2002), p.86. 24 A bidding strategy in the English Auction must specify for each of his possible valuations, whether he will be active at any given price level, as a function of the bidding activity observed until then.

The exit-prices can be ordered as follows: p1§ … § pk

Bidder i’s strategy can be described by a function bik(xi | p1, …, pk), specifying the price at which bidder i will quit if, at that point, k other bidders have left at the prices p1, …, pk.

Because the price can only rise, bik(xi | p1, …, pk) has to be greater or equal to pk.

The symmetric equilibrium is:

* β 0 (x) = E[]V1 X 1 = Y1 = ... = Yn−1 = x β * (x p ,..., p ) = E[V X = Y = ... = Y = x, k 1 k 1 1 1 n−1 * β k −1 (Yn−k p1 ,..., pk −1 ) = pk ,..., * β 0 (Yn−1 ) = p1 ], k = 1,...,n − 2

* β 0 (x) denotes the optimal bid when all bidders are active,

* β k (x p1 ,..., pk ) the equilibrium bid after k bidders have quit the auction.

3.3.2.2.3 First-Price and Dutch Auction The first-price sealed-bid and the Dutch auction are strategically equivalent and can be treated equally. The equilibrium strategy for a bidder is:

x β F (x) = ∫ v(y, y)dL(y x) 0

 x g(t t)  where, L(y x) = exp− dt   ∫ G(t t)   y 

G(⋅ x) is the distribution function of Y1 , i.e. the second highest signal; under the condition that the highest signal is equal to x. g(⋅ x) is the conditional density function of Y1 .

Milgrom and Weber further prove that the expected seller revenue of the second-price sealed- bid auction is greater or equal to that of the first-price sealed-bid auction.

25 3.3.2.3 Results of the Milgrom-Weber Model 1.) The Dutch and the first-price sealed-bid auction are strategically equivalent. 2.) When bidders are uncertain about their value estimates, the English and the second-price sealed-bid auction are not equivalent. The English auction leads to higher expected prices due to the linkage principle (see below). 3.) When bidders’ value estimates are statistically dependent, the second-price sealed-bid auction generates higher average prices than does the first-price sealed-bid auction. 4.) If the seller has access to a private source of information, his best policy is to commit himself to honesty (always reporting all information completely). This is true for the first- price sealed-bid, Dutch, second-price sealed-bid and the English auction.

3.3.2.3.1 Ranking of Expected Prices English > Second-price sealed-bid > Dutch = First-price sealed-bid

3.3.2.3.2 Linkage principle The linkage principle explains why the English auction yields higher revenue than the second- price sealed-bid auction under affiliation and why revealing public information raises the price. Every bidder receives indirect information about the valuations of the other bidders from their publicised exit-prices. Observing bidding behaviour by others makes bidders more confident and lets them bid higher on average. All measures that increase the information of bidders, for example quality guarantees, are price increasing and advantageous to the seller.

The price is linked to the valuations of the non-winning bidders and the winning bidder. The auction prices depend on the reports the bidders make and on the seller’s information. The Dutch and first-price sealed-bid auction with no linkages to the other bidders’ estimates, yield the lowest expected price. The English auction with linkages to any of the estimates of the non-winning bidders yields the highest expected price. Revealing public information raises the price in all three auctions, by adding a linkage.

4. Revenue Ranking According to Theoretical Predictions

The table below summarises the theoretical predictions about seller-revenue for the independent private values and the affiliated values model (for private and interdependent

26 valuations). As can be seen the first-price sealed-bid and Dutch auction always yield equal revenue. The second-price sealed-bid and the English auction yield equal revenue under the private values assumption, but not when values are interdependent:

Model Revenue Ranking IPV and risk neutral bidders All equal IPV and risk averse bidders Dutch = 1st Price > 2nd Price = English Affiliated, privately known values and risk Dutch = 1st Price < 2nd Price = English neutral bidders Affiliated, privately unknown values7 and risk Dutch = 1st Price < 2nd Price < English neutral bidders Table 1: taken from Lucking-Reiley (1999), p.1065

Returning to our original question of finding the auction format that leads to the highest seller revenue out of the four standard formats, we arrive at the result that when bidders are risk- neutral the revenue of the English auction is greater (affiliated values) or equal (private values) to that of the other auction formats. Under risk-aversion the first-price auctions yield highest seller-revenue.

If the theoretical predictions were trustworthy and the seller were able to know what risk- attitude the buyers have and how the bidder valuations are distributed, then he could choose the auction format accordingly. In the next chapter empirical tests of the theoretical predictions are presented.

5. Experimental Tests of Bidding Behaviour and Auction Revenue

Experimental tests of auction revenue can either be conducted through controlled laboratory experiments or field studies. There are far more laboratory tests comparing auction-revenue than field-studies. One disadvantage of using field-studies for revenue comparisons is that the

7 The bidder is uncertain about his valuation only having received a noisy signal about his value. 27 theoretical revenue predictions rely on assumptions about bidder valuations, however it is difficult (impossible) to control field-data for the type of bidder valuations.

5.1 Field Experiments

There is very little field data comparing auction formats, because real auctions tend to be conducted according to one pre-determined mechanism. One example of data making an empirical comparison of two auction formats possible, is the U.S. Forest Service auction for timber harvesting rights in the Pacific Northwest. Due to a change in federal law, the U.S. Forest Service conducted some of its auctions by a first-price sealed-bid auction and the others by an English auction. Mead (1967) and Johnson (1979) used this data in an empirical study and found that the first-price sealed-bid auction raises significantly higher revenue than the English auction. However, Hansen (1985, 1986) finds that after correcting the data for a bias in the selection method for the timber lots, the lower revenue of the English auction is no longer statistically significant.

The striking part of the results is that timber sales are likely to have strong common value or at least correlated private value elements, which in theory should lead to higher prices in the English auction.

Tenorio (1993) studies multi-unit auctions by using data from Zambian currency auctions. Tenorio finds that multi-unit auctions yield higher revenue when the price is determined by a discriminatory rule than when it is determined by a uniform-pricing rule.

5.1.1 Field Experiments on the Internet Lucking-Reiley (1999) conducted auctions of “Magic Cards” on Ebay to empirically test revenue- equivalence on the Internet. He finds that the Dutch auction leads to thirty percent higher revenue than the English auction and that the second-price sealed-bid and the English auction are roughly revenue-equivalent.

5.2 Laboratory Experiments

Most empirical revenue-comparisons are carried out by controlled laboratory experiments. Bidders are assigned valuations distributed according to the assumptions of the theoretical

28 model tested. Under the assumption of private valuations, the participants in the experiment are told that their valuation for the good is exactly x monetary units. The experiment tests whether the participants can “guess” the rational bidding strategy, in the case of independent private values, whether they realise that they are supposed to bid their valuation in the second- price auctions and are supposed to shade their bid in the first-price auctions.

Laboratory experiments that test the existence of the winner’s curse in the common value model, test whether the participants realise that they are not supposed to bid their private signal, but are supposed to shade their bid to discount for the strategic error of overbidding due to the winner’s curse.

Laboratory experiments testing the private-values assumption show that bids tend to be higher in the sealed-bid than in the open auctions:

Coppinger et al (1980) and Cox et al (1982,1983) find that revenue in the first-price sealed- bid auction is significantly higher than theoretically predicted by the risk neutral Nash equilibrium strategy (RNNE); revenue in the Dutch auction is approximately equal to or slightly below the RNNE prediction.

Kagel et al (1987) and Kagel and Levin (1993) find that revenue in the second-price sealed- bid auction is higher than in the English auction format: bidders bid their valuations in the English auction but bid above their valuation in the second-price format. Results were tested with respect to bidder experience, but the breakdown of revenue-equivalence remains.

Experiment Results Coppinger et al (1980) 1st price > Dutch Cox et al (1982, 1983) 1st price > Dutch Kagel et al (1987) 2nd price > English Kagel and Levin (1993) 2nd price above theoretical predictions Table 2: taken from Lucking-Reiley (1999), p.1066

29 6. Theoretical Predictions and Empirical Results

The theoretical predictions of auction theory strongly rely on assumptions about the distribution of bidder valuations. Auction theory expects revenue-equivalence in the case of private values and expects the English auction to yield highest auction revenue in the case of affiliated values. Contrary to theoretical predictions, experimental laboratory results show that the sealed-bid format leads to higher revenue than the open auction format. Possible explanations for this discrepancy may include important aspects being neglected in auction- models or experiments being carried according to unsuitable methods.

30

PART TWO: Dynamic Price Formation in the Japanese Auction

Overview

A dynamic bidding model is presented in which bidders are uncertain about their own valuation. Bidders learn about their private valuation from the exit prices observed. As a result, the second-price sealed-bid auction produces significantly higher revenue than the Japanese auction: moreover, bids in the Japanese auction are far more narrowly spread than in the second-price sealed-bid auction. The model explains this result by showing that bidders are able to satisfy a tendency to “stick together” in the open Japanese auction, whereas the secret second-price sealed-bid auction offers no such opportunity. Furthermore, the model can explain the results of an experimental sale of real goods.

31 1. Introduction

Sellers want to use the auction mechanism that maximises their expected revenue. In this section we compare two auction formats: the Japanese8 and the second-price sealed-bid auction9. Turning to auction theory, the seller has to make an assumption about the bidders’ valuations, whether bidders have purely private, purely common, or interdependent valuations.

Auction theory predicts that when bidders have private values, a good yields equivalent expected revenue whether sold by an English or second-price sealed-bid auction. This is a result of William Vickrey’s fundamental Revenue Equivalence Theorem10. The second-price sealed-bid auction and the English auction are not only revenue equivalent, but are also strategically equivalent. The dominant strategy of both auction formats is to bid an amount equal to one’s private valuation11.

The assumptions underlying the private value model are stringent and maybe unrealistic, as they impose that bidders value the good independently of the valuations of all other bidders. In many instances bidders are influenced by the values that their rivals assign to a good. Imagine for example art, second-hand objects or collector items where bidders are often subject to reputational concerns. Bidders partly base their valuation on other bidders’ value judgements, believing the good to be more precious when others value the good highly and less valuable when others do not care much for the good.

An important instance when bidders do not act according to the predictions of the private value model can be observed in Internet auctions. Goods - loosely classifiable as private- value goods - hardly receive bids for days until only some hours or minutes before the planned auction end, when all of a sudden bidding activity rises incomparably. Late bidding

8 The Japanese auction is a sub-variant of the English auction and is also called ascending-clock auction. The English auction is an open, ascending-bid auction. 9 The high-bidder wins, but pays only the second highest bid. 10 It states that all four standard auction formats (first-price, second-price, English and Dutch auction) lead to equally high expected seller-revenue under the assumption of independent private valuations. 11 Furthermore, the dominant strategy is unaffected when bidders have private affiliated values, see Kagel and Roth (1995), p.508. 32 occurs despite bidders having the possibility to use a proxy-bidding agent12. When bidders have private values, they are expected to have no incentive to hold back their valuation. A possible explanation could be that the high-valuing bidder believes that by bidding early and publicising his high bid, he will cause low valuing bidders to revise their valuation upwards, raising the price the winner has to pay. Prestige considerations and uncertainty about the true quality of the good could be causes of this behaviour.

At the other extreme of independent private values lie purely common values: the good having an unknown but common value to all bidders. Only few goods are pure common value goods, such as for example oil fields or gold nuggets. Many goods, however, have some uncertainty surrounding their true quality, making them irreconcilable with both the purely independent private value model and the purely common value model.

For most goods it is realistic to relax the private values assumption and instead to assume that values are interdependent13. Interdependent values can be of many a kind, but auction theory focuses almost exclusively on the Milgrom and Weber model of interdependent values. In their general model of symmetric interdependent values they assume that the bidders’ private signals are affiliated14, i.e. positively correlated, and predict that the Japanese auction yields higher expected revenue than the second-price sealed-bid auction.

Laboratory experiments test theoretical predictions based on the models’ assumptions. Theoretical predictions concerning auction revenue strongly rely on assumptions about the distribution of the bidders’ valuations. There are many laboratory experiments testing the private values predictions15 (both for affiliated and independent private values), experiments

12 A bidder can submit his maximum-willingness-to-pay to the proxy-bidding agent, who will then bid on his part, raising the current high-bid by a minimum-increment until he appears as the high-bidder. The proxy- bidding agent will stop bidding once the maximum-willingness to pay is reached. 13 See Part One Chapter 3.3. Interdependent values: Bidders have some uncertainty about their values, their value partly being influenced by private information held by the other bidders. 14Affiliation: Bidders know the value of the item to themselves with certainty, but a higher value of the item for one bidder makes higher values for the other bidders more likely (private values are positively correlated relative to the set of possible valuations)”. Kagel and Roth (1995), p.517. 15 Kagel, Harstad and Levin (1987) test revenue equivalence for affiliated private values. Empirical results show failure of the theoretically predicted strategic-equivalence between the second-price sealed-bid and the Japanese auction. 33 testing the existence of the winner’s curse for common values, but there is a lack of experiments comparing revenue for interdependent valuations16.

Laboratory experiments are conducted by assigning a private value or value estimate to every bidder and observing whether bids and revenue correspond to dominant strategy predictions. This method has the drawback that viewed critically it is merely a test of a bidder’s cognitive ability of guessing the dominant bidding strategy. A seller wanting to know which of the two auction formats yields higher expected revenue, might prefer an experiment that is less controlled but has a set-up that makes its results more meaningful to the practical undertaking.

We designed an experiment to test revenue equivalence of the Japanese and second-price sealed-bid auction in a realistic setting: in the experimental sale of real consumption goods. The experimental results in Chapter Three show that bidding behaviour differs in the two auction formats examined, specifically bids in the open auction being far more clustered than under the sealed-bid format. As a result, the final price in the second-price sealed-bid is higher than in the Japanese auction. The results suggest that bidders do not solely base their valuation on their private value estimate, but instead partly base their reservation price on the other bidders’ valuation of the good. Motivated by the experimental observations, a bidding model is presented in Chapter Five.

This model differs from Milgrom and Weber’s general model in a number of respects. Milgrom and Weber assume valuations are exogenous and affiliated. In our boundedly rational model bidders are uncertain about their own valuation and partly base their own valuation on other bidders’ private information, i.e. independent signals. Bidders update their valuation using the information revealed through the exit prices of the other bidders. The final price is reached in a dynamic process, bidders forming their valuation adaptively.

16 An exception being Kirchkamp and Moldovanu (2001), who conduct laboratory experiments for a simple model of interdependent values testing efficiency of the Japanese and second-price sealed-bid auction. Their empirical results with respect to revenue are consistent with the theoretical predictions: they find that seller revenue is equal under both formats and bidder-payoff higher in the Japanese-auction. 34 The model presented in this paper is a general model applicable to all kinds of goods, provides predictions on expected price and revenue and insight on the updating-procedure and price formation.

2. Experiment

There have been many laboratory experiments carried out testing revenue-equivalence between the Japanese and the second-price sealed-bid auction. The following result is characteristic of the results obtained in laboratory experiments (e.g. Kagel, Harstad and Levin (1987)): bids in the second-price sealed-bid auction are above Nash equilibrium predictions; bids in the Japanese auction correspond to Nash equilibrium predictions.

Risk aversion does not qualify as a possible explanation for this result, because it is a dominant strategy in a second-price sealed-bid auction to bid one’s private valuation – independent of the risk-attitude or number of rivals.

Kagel, Harstad and Levin explain overbidding in the second-price sealed-bid auction by a bidder’s lack of ability to understand that bidding above his valuation does not increase his chances of winning, except in cases where this is not desirable. They further explain that overbidding is not found in the Japanese auction, because the open auction format makes it clear that once the counter reaches a bidder’s private valuation, no gains can be made by remaining active.

Returning to the original problem of finding the format that yields highest expected seller revenue, empirical results turn out not to conform to the theoretical predictions. Theory predicts that the English auction leads to greater or equal revenue than the second-price sealed-bid auction; experiments show that the second-price sealed-bid auction leads to higher revenue than the English auction. A seller now faces the decision of either trusting the theoretical prediction or the empirical result, in which case he would choose the second-price sealed-bid auction and hope that his bidders will make the mistake of bidding above the equilibrium bid.

35 Below we present an experiment that differs from standard experiments in that it is designed to test how revenue and bids in the second-price sealed-bid and Japanese auction compare in practice, in the sale of real goods:

2.1 Experimental Set-Up

The experiment was conducted with undergraduate business and economics students at the University of Vienna and Vienna University of Economics and Business Administration in May and June 2001. Students were not paid for participating in the experiment. Half of the experiments were conducted with unpaid volunteers, and half of the experiments as an alternative to the “normal” course program. After the experiment participants were debriefed on the hypothesis tested and theoretical predictions.

The thirty experiments were divided into four sessions. Seven experiments were conducted with 5 participants, seven with 7 participants, eight with 12 participants and eight with 17 participants.

In a series of experiments a single good was sold twice, first by means of a second-price sealed-bid auction and successively by an Japanese auction without announcing the final price obtained in the second-price sealed-bid auction. The second-price sealed-bid auction was conducted first because the secret format of the second-price sealed-bid auction discloses no information to bidders, does not allow them to draw conclusions on the other bidders’ valuations and final price. At the beginning of the Japanese auction, the bidders were thus in the same informational-state as before the second-price auction.

The Japanese auction was conducted as follows: The auctioneer calls out the current price starting at zero17, i.e. zero Austrian Schillings18 (ATS), increasing the price by the increment of 1 ATS. The price was raised by the minimum increment after about one second. A bidder was considered to be an active bidder until he raised his hand to signal his exit. At any point in time, the number of active bidders and the

17 The auction started at a price of zero ATS, so that bidders were not be forced to pay for a good that they did not want. 18 1 Euro is equivalent to 13,76 Austrian Schillings. 36 exit prices of the bidders who had already quit were publicly known. The auction ended when the before-last bidder quit the auction, only one more bidder remaining active. The remaining bidder is the winner of the Japanese auction and in case he turns out to be the overall-winner of both runs (explained below) has to pay a price equal to the highest exit price, i.e. the exit price of the second highest bidder19.

Since one and the same good is auctioned off in two auction runs, the good can only be allocated to either the winner of the second-price or the winner of the Japanese auction. It may be the case that the same person wins the good in both runs and at the same final price, but in case this situation does not apply, the winner of the good is determined by throw of the die at the end of the two runs20. The probability that the second-price or alternatively the Japanese auction turns out to be the auction relevant for the transfer of the good is thus one half.

This method has the advantage of allowing a good to be sold twice, while holding all conditions equal (same group of bidders, same good, same informational structure), except the auction rules. If two units of the same good were sold, valuations would be different from the one unit case due to automatically decreased demand by the winner of the first round (amongst others).

The winner receives the good and has to pay the relevant final price21.

19 If the last and before-last bidder exit simultaneously, the final price is determined by the bid of the before-last bidder, which in this case constitutes the last exit price. 20 The probabilistic determination of the run, that is relevant for pay was also used by e.g. Kagel and Levin (1986), p.897 (in their case by tossing a coin). 21 As (winning) bidders carried unobservable amounts of money in their wallet, they were not obliged to pay the final price immediately, but had one week of time within which they could pay the final price. Bidders knew this before the auction commenced. 37 2.2 The Goods

The following goods were sold:

- Toblerone (a mixed version of dark and white chocolate22) - Turron (a Spanish sweet) - French wine - Posters and T-shirts (bought in the USA with US specific design) - Handmade pottery

The goods sold in the experiment do not fall into the category of purely private value goods, because there was uncertainty about various aspects of the quality of the good. None of the auction goods were offered for sale in Austria. The food and drinks sold are experience goods. Because they were not offered for sale in Austria, there was uncertainty about the quality, in terms of the taste of the product. Some bidders had perhaps been to Spain and had tasted the Turron and thus had better knowledge about their preference for the good.

Bidders also had uncertainty about the value of the good in terms of the purchase price. The goods were unique goods in the eyes of the bidders, because it was not possible to get a second unit in Austria, but bidders were aware of the fact, that the goods were readily available in the country of purchase. These are reasons why the goods cannot be viewed as a purely private value good.

The goods had purchase prices in the range of one to twelve Euro, most of them in the range of four to six Euro.

22 Pure dark and pure white Toblerone can be bought in Austria, but not the mixed version. 38 3. Results

The results of the experiment: Final Price Diff. Diff. Higher Participants 2nd Jap (in %) Final Price 1 1 Turron 30 25 -5 -17 2nd Price 17 2 Wine 90 111 21 23 Japanese 17 3 Praline de Café 35 30 -5 -14 2nd Price 17 4 Pottery 10 5 -5 -50 2nd Price 17 5 Book 50 42 -8 -16 2nd Price 17 6 Ameretti 45 33 -12 -27 2nd Price 17 7 Wine 30 23 -7 -23 2nd Price 17 8 Toblerone 20 18 -2 -10 2nd Price 17 2 1 Crema C. 30 25 -5 -17 2nd Price 5 2 Pottery 21 20 -1 -5 2nd Price 5 3 Turron 60 55 -5 -8 2nd Price 5 4 T-Shirt 121 120 -1 -1 2nd Price 5 5 Cap 30 25 -5 -17 2nd Price 5 6 Biscuits 40 39 -1 -3 2nd Price 5 7 Toblerone 25 20 -5 -20 2nd Price 5 3 1 Duck 33 32 -1 -3 2nd Price 12 2 Wine 75 95 20 27 Japanese 12 3 SF Badge 20 19 -1 -5 2nd Price 12 4 Turron 25 25 0 0 Equal 12 5 Ireland Badge 25 10 -15 -60 2nd Price 12 6 Toblerone 25 21 -4 -16 2nd Price 12

7 Ameretti 37 36 -1 -3 2nd Price 12 8 Chocolate 20 24 4 20 Japanese 12 4 1 Turron 34 25 -9 -26 2nd Price 7

2 Wine 48 39 -9 -19 2nd Price 7 3 Key-Chain 28 12 -16 -57 2nd Price 7 4 T-Shirt 50 34 -16 -32 2nd Price 7 5 Toblerone 16 26 10 63 Japanese 7 6 Book 30 30 0 0 Equal 7 7 Poster 25 7 -18 -72 2nd Price 7 Table 3

39 On average the final price of the Japanese auction was 13% below the final price of the second-price sealed-bid auction. The bids of all bidders can be found in the appendix.

3.1 No Revenue-Equivalence

Thirty experiments were conducted in order to test revenue-equivalence between the second- price sealed-bid and the Japanese auction. In twenty-four of the thirty experiments the final price of the second-price auction was higher than that of the Japanese auction; in four experiments the final price of the Japanese auction was higher and in two experiments the final prices of the two auctions were equal. On average the final price in the Japanese was 14% below that of the second-price sealed-bid auction.

3.2 Lower Bid-Variance in Japanese Auction

The bids in the Japanese auction were far less dispersed than in the second-price sealed-bid auction. In two-thirds of all experiments bid-variance was lower in the Japanese than in the second-price sealed-bid auction23. To test whether there was a significant difference in the bid variance, F-Tests were conducted. In 63% of the experiments, the Japanese auction had a significantly lower bid-variance than the Japanese auction (according to the F-Tests).

3.3 Average Bid Not Significantly Different

Comparing the mean bid with that of the second-price auction (for every good sold) the t- tests show no significant difference (for any of the thirty goods sold). On average the mean bid in the Japanese auction was 0.6% above that of the second-price sealed-bid auction. Thus, the mean bid of the Japanese auction was little influenced, especially considering that the highest bid was not taken into consideration in the statistic, because the Japanese auction does not reveal the highest bid and thus in order to compare the two formats the highest bid in the second-price sealed-bid auction was also left out.

23 See Appendix. 40 3.4 Reasons for Lower Bid-Variance in Japanese Auction

Comparing the change in bid-level of every bidder in the two runs shows that originally low- valuing bidders revised their bids upward, while originally high-valuing bidders revised their bid downwards in the Japanese auction. Bidders who made a below average bid in the second-price sealed-bid auction, revised their bid upwards by 62% on average (median: 30,3%) in the succeeding Japanese auction. Bidders who made an above average bid in the second-price sealed-bid auction revised their bid downward by 30% on average (median: 19%) in the succeeding Japanese auction. As stated in Chapter 3.3 the mean bid for each good was fairly equal in the two auction runs. The change in variance was caused by a change in the upper and lower bound of the interval.

3.5. Learning Effects

In previous literature learning effects were observed in experiments, so that bids in the Japanese auction adjusted to dominant strategy predictions after a few rounds. In the experiments above, the difference in final prices between the second-price sealed-bid and the Japanese auction did not change in the course of the auction. This is not surprising because in standard laboratory experiments, bidders are paid the difference between their valuation and the final price, thereby receiving feedback on their bidding behaviour. Bidders in this experiment do not receive feedback on whether they overbid, in fact one cannot tell whether a bidder overbid (by mistake) or revised his valuation intentionally.

4. Interpretation

Experimental results show that bids are far more clustered together in the Japanese than in the second-price sealed-bid auction. The secret format of the second-price sealed-bid auction implies that bidders receive no other information than their private signal. The open format of the Japanese auction in contrast reveals information about the valuations of the other bidders, by publicising all exit prices. The lower final price in the Japanese auction and the clustering of bids could indicate that bidders try to take other bidders’ valuations into account when

41 forming their own valuation of the good, this however only being possible under the open auction format.

The discussion in Chapter Two and the empirical findings presented above all imply that bidders have some form of interdependent valuations. Auction theory (almost) exclusively focuses on the Milgrom-Weber model when treating interdependent valuations. My empirical results (as well as previous laboratory experiments), however, do not correspond to the theoretical predictions of the Milgrom-Weber’s model: the Japanese auction leads to lower revenue than the second-price sealed-bid auction in practice, theory predicting the opposite.

Regarding bid dispersion, my experiment shows that the open Japanese auction leads to an ex- post affiliation of bids: bidders with a high valuation in the sealed-bid auction lowering their bid in the open auction and those with a low valuation in the sealed-bid auction raising their bid in the open auction. Milgrom-Weber in contrast assume that private signals are ex-ante affiliated leading to an upward clustering of bids in the open English auction.

The surprising experimental results and the fact that they do not conform to the Milgrom- Weber model calls forth the need for a different model of interdependent valuations. In the next section a general model of interdependent valuations is presented. Bidders are uncertain about their valuation and learn from the exit prices of the other bidders, updating their valuation every time new information (in form of exit prices) is revealed. Bidders have interdependent values, but independently distributed signals, this perhaps being a less restrictive assumption than Milgrom-Weber’s assumption of correlated signals.

The bidding strategy modelled is boundedly rational – it is not calculated whether it represents a Nash-equilibrium. Real bidders are not perfectly rational and do not have the ability to calculate their expected valuation conditional on the valuations of their rivals. The updating procedure presented here has the advantage of being empirically motivated and is close to being rational in that bidders satisfy their target-function by a suitable estimation method.

A further advantage of the model presented below is that the updating-procedure is not only implied but also modelled in particular. The procedure and result is thus better 42 comprehensible to the reader. Learning and updating in the Japanese auction is not limited to the highest two bidders, but instead all active bidders engage in the updating-procedure. The degree of uncertainty about one’s own valuation specified by lambda can be adapted and thus applied to a wide variety of goods.

5. The Model

A single seller wishes to sell a single indivisible object to one of n buyers participating in a Japanese auction.

The Japanese auction: Every bidder knows how many bidders are participating in the auction. There is a counter counting upwards starting with zero. A bidder is an active participant in the auction until he exits. A bidder exits the auction once his reservation price24 is reached. Once a bidder quits the auction, he cannot return. When a bidder quits the auction, all remaining bidders are informed about the price at which the particular bidder quit the auction. At every point in time the active bidders know how many bidders are still active and know the exit prices of all bidders who have already quit. The auction ends when the before- last bidder quits the auction, which is when there is only one more active bidder remaining. This last recorded exit price is the auction’s final price.

At the outset of the auction, bidder i receives a signal si about his valuation of the good. The private signal is not the sole factor determining bidder i’s reservation price. It is also dependent on the other bidders’ valuation of the good. Bidders do not enter the auction with perfect knowledge about their own valuation, but learn from the valuations of the other bidders. This can be due to prestige reasons; bidders do not want to possess a good if no one else thinks it is valuable, on the other hand, a good becomes more valuable to a bidder when the other bidders value the good highly.

24 The reservation price is the maximum willingness to pay. It is the price at which a bidder is indifferent between purchasing the good and not purchasing it. 43 A second reason why bidders decide to incorporate the private valuation of each of the other bidders into their own reservation price is because bidders believe that they can extract information about the quality of the good from the valuation of the other bidders. Imagine for example a classic common value good such as an oil field that has not been drilled yet. Every bidder will use all data material and research reports accessible to him in order to estimate the field’s value. A bidder knows that a multitude of research reports exist, but he himself does not possess knowledge of all of them. Knowing that his own information is limited, a bidder does not let his reservation price equal his private value estimate, but instead only denotes a certain weight to his private value-estimate. His total valuation (the reservation price) is composed of the weighted sum of his private value-estimate and a measure for the other bidders’ private value estimates. The model is thus applicable both for goods for which bidders have reputational concerns, as well as for classic common value goods.

5.1 The First Round

n... number of bidders at the beginning of the auction k… number of bidders who have already quit the auction λ... measure of how important the common value is to a bidder, 0 ≤ λ ≤ 1, every bidder has the same λ si... private signal of bidder i, the si are uniformly distributed ∼ [0,1] th ek... k observed exit price pi … reservation price (valuation) of bidder i C... common value

At the outset of the auction every bidder draws a private signal from a uniform distribution U∼[0,1]. Every bidder knows his private signal, but not the private signals of the other bidders. Every bidder knows that the signals si are uniformly distributed on the interval [0,b], but does not know the upper bound.

A bidder’s reservation price in round k is the weighted sum of the private signal si and the common value of this round. pi (k +1) = λ *Ck + (1− λ) * si Every bidder knows how the reservation price is formed and knows in which way the valuation of the other bidders 44 changes from round to round. The common value is weighted with λ , λ taking on values between zero and one. λ denotes how important the valuation of the other bidders is to bidder i, that is how relevant bidder i believes the information included in the valuation of the others to be. Every bidder has the same λ .

Bidders update their valuation in every round, the common value denoting the estimate of the mean private signal of all other bidders. Because bidders cannot observe the private signals of the other bidders, they estimate the mean private-signal from the exit prices observed (the private signals of the bidders having already quit the auction can be inferred from the exit prices observed).

Bidders estimate the average private signal by the Maximum-Likelihood method, using the number of remaining active bidders and the exit prices observed so far for the estimation. 1 n Bidders want to estimate the mean private signal of all other bidders, Ci = ∑ s j . n −1 j=1 j ≠i

Bidders form their valuation adaptively by following a complicated learning rule; complicated because bidders have to maximise. The method is explained in the section below.

In the first round no exit price has yet been publicised. Every bidder knows that signals are uniformly distributed on the interval [0,b] and he knows his private signal, which was one sample draw from the distribution. In order to estimate the interval mean, a bidder needs to estimate the interval’s upper bound. He can do this using the maximum likelihood method, in which case the best estimate of the upper bound is the bidder’s private signal si. It follows bˆ + a s + 0 s that the best estimate of bidder i for the common value is Cˆ = = i = i . i 2 2 2

5.1.1 The First Exit The first bidder who exits the auction is the bidder with the lowest private signal. The 1 expected lowest signal drawn from the signals uniformly distributed on [0,1] is: n +1

45 When X1, X2, …Xn is a sample of n independent random variables, each having the same probability distribution function F(x) with density f(x) = F’(x) and the realizations of these random variables are ranked in increasing order25: x ≤ x ≤ ... ≤ x ≤ ... ≤ x , the kth order v1 v2 vk vn th statistic is the function X(k) that assigns to each realization of the series (X1,…Xn) the k smallest value xvk. Altogether, there are n order statistics X(1), X(2) , …, X(n). Each order statistic is a random variable. If X is uniformly distributed on the domain [0,1], k E []X = ( k ) n + 1

5.1.2 Common Value Estimation and the Updating Procedure At the outset of the auction, a bidder’s best estimate of C is half his private signal. Once the first bidder exits the auction, bidders use this information to estimate the most likely mean of the uniformly distributed private signals by maximising the following likelihood function:

n−1 n Prob (lowest private signal = s1) = f (s1 )(1− F(s1 ))   1 The maximum likelihood method is used to estimate the unknown parameters of a population of which an observable sample was drawn. The maximum likelihood method is used in this model because we are confronted with a unique auction good and a unique set of bidders, presenting small data from which to make inferences (see Chapter 5.3 for further justifications).

The likelihood function above symbolises the probability that the first bidder has a private signal equal to s1, times the probability that n-1 bidders have a private-signal greater than s1, times a combinatorial constant. Realisations of private-signals are ranked, s1 denoting the first private signal, s2 the second, s1< s2<…

The combinatorial constant reflects the fact that there are a number of possible combinations when choosing one bidder out of a group of n bidders, having a private-signal below or equal to s1. 1 The density function of a uniform distribution [a, b]: f (x) = b − a x − a The probability function of a uniform distribution [a, b]: F(x) = b − a

25Section taken from Wolfstetter (1999), p.344. 46 Assuming that all bidders use the maximum likelihood method to calculate their valuation in the first round, bidders can infer s1 from e1 .

In the first round the likelihood function (given the first private signal is s1 and (n-1) active bidders remain) is:

n−1 st 1  s1 − a  n max L:= Prob (1 private signal = s1, n-1 bidders still active) = 1−    b     1 b1 − a  b1 − a  1

The b that maximises the above expression is found to be b1 = s1 *n , in the first round, where a is equal to zero.

The expected first exit, E[e1 ] = λE[C(1) ] + (1− λ)E[s1 ]

s1  = λE  + (1− λ)E[s1 ]  2  1 1 = λ + (1− λ) 2(n +1) n +1

n−1 st 1  1  n max L:= Prob (1 private-signal = s1, n-1 bidders still active) = 1−    b     1 b1  b1 (n +1)  1 1 n And, b = n = 1 n +1 n +1

b1 constitutes the upper bound of the distribution of private signals estimated in round one. The lower bound of the private-signal distribution (a) is zero by definition.

Bidders use b1 to calculate the common value of the next round. Bidder i, who still is active, defines the common value as the mean private signal of all other bidders. It is calculated by taking the average of all inferred private signals of the bidders who have quit the auction already, k, and the interval mean of the signal distribution of the remaining active bidders times the number of active bidders excluding himself, n-k-1.

1  b1 + s1  C2 = s1 + ()n − k −1  n −1  2 

The second exit price is: e2 = λC2 + (1− λ)s2

47 5.2 The General Procedure

A bidder carries out the following three steps in every round, estimating bk (the upper bound), calculating Ck (the common value) and his reservation price:

1   b + s   k k  Ck =  s1 + ... + sk + (n − k −1)  n −1  2 

pi (k +1) = λCk + (1− λ)si

The bidder with the lowest valuation in this round will be the next bidder to exit the auction. All remaining active bidders infer the private signal of the exit price observed in this round e − λC by: s = k k . k 1− λ

Given the updating-procedure described above, bidders treat the likelihood function as if it were a constant. Ck being a constant, pi(k) is an affine transformation of the uniformly distributed si. The pi(k) therefore are also uniformly distributed.

The current exit price is the lowest reservation price of all active bidders in this round. This new exit price is publicised and again bidders calculate their new reservation price by maximising the likelihood function:

n−k n max L:= f (s1 ) f (s2 )... f (sk )(1− F(sk ))   b k  whereby, k...Number of bidders who have already quit the auction n...Number of bidders who were participating at the beginning of the auction

Strictly speaking, the probability that a bidder exits in the price-interval [p, p+∆] is,

p + ∆ F ( p + ∆) − F ( p) = ∫ f ( x)dx ≈ f ( p)∆ p

This approximation is correct only for small values of ∆.

48 The ∆s are constant and do not influence the Maximum-Likelihood Estimation. Every time a bidder exits the auction, all remaining active bidders calculate the common value a new with the updated information, to form their new reservation price. This iteration is carried out until there is only one more active bidder left. Once n-k is equal to one, the auction ends.

5.3 Estimation Procedure

The estimation procedure used above is the maximum likelihood method.

Ideally an estimator should be unbiased and consistent. An estimator is unbiased when it does not consistently under- or overestimate the true value. In this case, the maximum-likelihood n estimator slightly underestimates the true value. The estimate of b, bˆ = s . k k k n k n E[bˆ ] = E[s ], whereby E[s ] = , so that E[bˆ ] = k k k k n +1 k n +1

An estimator is consistent when it converges more closely to the true value as the sample size increases. The maximum likelihood estimator fulfils the desirable property of being consistent: as the sample size (here: the number of bidders) increases, the estimator converges n n to its true value: bˆ = s and E[bˆ ] = k k k k n +1 ˆ If n → ∞ , E[bk ] = b =1

5.4 The Expected Final Price

The expected final price is equal to the expected exit price of the (n-1)th bidder and is determined by first calculating the expected common value after k bidders, that is n-2 bidders have quit the auction:

49   n − 2 n    +  1 1 2 n − 2   E[]C =  + + ... + + (n − 2) n + 1 n + 1   n−2 n − 1  n + 1 n + 1 n + 1  2           n−2 i ∑ 2n − 2 = i=1 + (n + 1)(n − 1) 2(n + 1)(n − 1) n(n + 1) n + n − 1 2n − 2 = − + 2(n + 1)(n − 1) (n + 1)(n − 1) 2(n + 1)(n − 1) n 2 + n − 4n + 2 + 2n − 2 = 2(n + 1)(n − 1) n 2 − n = 2(n + 1)(n − 1) n(n − 1) = 2(n − 1)(n + 1) n = 2(n + 1)

th  n  n −1 The expected exit price of the (n-1) bidder: E[en−1 ] = λ  + (1− λ)  2(n +1)  n +1

5.5 Results of the Model

The expected final prices calculated for the ten-bidder model:

Expected Final Prices

0,9 0,8 0,7 0,6 0,5 0,4 0,3 Final Price 0,2 0,1 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 λ

Figure 1: λ=0 represents the purely private value case, λ=1 represents the purely common value case

The final price of the Japanese auction (which is also the seller-revenue) is determined by the last recorded exit price, which corresponds to the exit price of the second highest bidder:

50  n  n −1 E[en−1 ] = λ  + (1− λ) . As can be seen from the diagram above, the auction’s  2(n +1)  n +1 expected final price is largest when λ = 0 . In this case the expected final price is equal to n . The expected final price decreases, as λ gets larger. This is because the common 2(n +1) n n n −1 value, C, is a constant (as are the estimates of C) equal to and < for 2(n +1) 2(n +1) n +1 n ≥ 2. The final price determined by the combination of the second highest private signal and the estimated common value, pi (n −1) = λCn−2 + (1− λ)sn−1 , results in smaller final prices as λ gets larger. When a common value element is taken into account in the reservation price, the final price is always lower than in the private value case.

In order to compare the results of the model with the final prices observed in the second-price sealed-bid and Japanese auction to the experimental results (Chapter 3), we need to calculate bidding behaviour in the second-price sealed-bid auction. The information-structure of the second-price sealed-bid auction corresponds to the first round of the Japanese auction, when no exit price has yet been publicised. A bidder only knows that signals are uniformly distributed on [0,b] and knows his private signal. In order to estimate the common value, he tries to infer the interval mean, by using the maximum likelihood method to estimate the upper bound of the signals. As signals are uniformly distributed, a bidder takes his private signal to be the best estimate of the upper bound of the signal distribution. Bidder i’s best s estimate of the interval mean, knowing that the lower bound is zero, is thus i . By using the 2 maximum likelihood method for estimating the interval mean, bidders avoid the winner’s curse, because the maximum likelihood method tends to underestimate the common value when the sample is small (one in this case).

We conclude that the second-price sealed-bid auction results in an expected final price greater than that of the Japanese auction for λ > 0 and a final price equal to that of the Japanese auction for λ = 0. This result is in accordance with the experimental results. The second-price sealed-bid auction does not offer the possibility to learn about the valuations of the others, bidders can only use their private signal for estimating the common value. In the Japanese auction bidders can learn about the valuation of the others. Being better informed

51 about the other bidders valuations, bidders are able to form a reservation price that reflects their preferences more accurately.

Another interesting feature of the Japanese auction model is the fact that bidders with low private signals revise their bids upwards and bidders with high private signals revise their bids downwards (for λ > 0). This result also corresponds to the experimental observations. The chart below shows the standard deviation of the expected exit prices in the ten-bidder model:

Bid Dispe rsion

0,3 0,25 0,2 0,15 0,1 0,05 Standard Deviation 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 λ

Figure 2

The standard deviation of the exit prices is largest for λ = 0. The diagram above shows that bids are more narrowly dispersed when the common value element is of greater importance. The results of the model correspond very well with the results from the experimental sale of real consumption goods described above in Chapter Three. (The mean λ for the goods sold in the experimental auction was 0.28; the median λ was 0.27).

The model thus provides an explanation for both the lower final price in the Japanese in comparison to that of the second-price sealed-bid auction and for the observation that bids were more narrowly distributed, closer “stuck together” in the Japanese than in the second- price sealed-bid auction.

λ , the factor of importance of the other bidders’ valuations, can be varied, being able to account for all cases ranging from purely private (λ=0) to purely common valuations (λ=1). 52 One advantage of this model is its wide-reaching application to all kinds of goods. Furthermore, the adverse selection bias encountered in the classic common value model does not appear in this model. The maximum-likelihood method allows bidders to estimate the correct common value directly without having to disclose information on the estimation error, upper- and lower bound (as in the classic common value model). The approach presented here provides readers and bidders with a clear and understandable bidding model that explains how bidders use information publicised in the bidding course to update their valuation due to prestige concerns or in order to update their information about the true value of the good.

6. Conclusion

Revenue equivalence between the second-price sealed-bid and Japanese auction is tested in the experimental sale of real consumption goods. A series of experiments shows that the final price of the second-price sealed-bid auction lies significantly above that of the Japanese auction. Furthermore, bids were much more narrowly dispersed in the Japanese than in the second-price sealed-bid auction.

The empirical observations motivated a general bidding model applicable to the purely private value, the purely common value and all intermediate cases. Bidders face uncertainty about their own valuation and include the private value estimate of all other bidders in their own valuation of the good. It turns out that the Japanese auction offers bidders the opportunity to learn about the valuation of other bidders from the publicly observable exit prices. Bidders update their reservation price every time someone quits the auction, the final price thus being determined iteratively.

The model reaches the same two striking results attained in the experimental sale of real goods: First, that the expected final price of the Japanese auction is lower than that of the second-price sealed-bid auction and second, that bids are more “stuck together”, more narrowly dispersed, in the Japanese than in the second-price sealed-bid auction. The model can thus show and explain the real observations.

53

Finally, the model could be extended to allow some bidders to have high and others low λ values. In this case low λ bidders will revise their bids more strongly than the high λ bidders.

54 7. Appendix

7.1.Bids in session one (17 bidders):

1 2 3 4 5 6 7 8

Turron Wine Praliné Pottery Book Ameretti Wine Toblerone

2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 1 0 0 0 0 0 0 1 0 0 0 2 1 4 0 1 1 0 0 2 0 0 0 10 13 0 1 0 0 0 7 0 5 1 5 1 0 0 3 1 2 0 25 30 0 2 0 0 0 8 0 5 1 6 0 4 0 4 3 3 0 28 45 1 3 0 0 0 8 1 6 0 9 1 5 0 5 3 5 0 40 85 3 3 1 0 0 15 0 9 0 10 0 5 0 6 5 5 0 50 51 0 5 1 1 0 15 1 10 1 10 1 7 0 7 6 7 0 50 101 10 8 0 1 0 16 2 12 0 11 0 9 0 8 6 10 1 50 80 6 9 2 4 -7 19 1 14 0 11 0 9 0 9 10 10 0 50 102 10 11 2 4 0 20 2 15 1 15 1 10 1 10 10 9 -1 60 55 1 14 -9 5 3 21 1 25 0 17 0 10 2 11 11 11 0 70 95 -2 15 -5 5 0 27 2 25 0 20 0 15 1 12 15 10 2 70 100 -2 15 -1 5 1 28 0 25 0 20 0 15 0 13 15 14 0 80 80 0 16 -4 6 2 31 0 30 0 22 0 15 0 14 19 15 1 85 103 -1 16 -1 10 5 1 35 0 30 0 30 1 15 0 15 30 25 0 90 103 -0 20 -1 10 5 1 36 0 40 1 30 1 20 0 16 35 25 0 101 111 -0 35 30 0 11 1 50 42 0 45 33 1 30 18 1 20 23 0 17 30 win 81 win 48 win 11 win 55 win 50 win 35 win 27 win

Table 4: Individual bids were not recorded in six out of the Japanese auctions.

7.2 Bids in session two (5 bidders):

1 2 3 4 5 6 7 Crema Cat. Pottery Turron T-Shirt Cap Biscuits Toblerone

2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 1 20 21 0,1 5 21 0,8 20 26 0,3 1 1 0,0 1 10 0,4 20 20 0,0 2 11 0,5 2 20 15 -0,4 15 21 0,5 25 19 -0,3 10 1 -0,2 15 15 0,0 22 20 -0,2 12 10 -0,3 3 30 25 -2,5 20 21 0,2 25 26 0,1 50 56 0,4 25 25 0,0 25 22 -0,4 15 15 0,0 4 30 20 -5,0 20 20 0,0 60 55 0,3 121 120 0,0 30 16 2,5 40 39 0,1 25 20 0,8 5 60 win 70 win 90 win 150 win 51 win 56 win 40 win

Table 5 55 7.3 Bids in session three (13 bidders):

1 2 3 4 5 6 7 8 Duck Wine SF Badge Turron Ireland Badge Toblerone Ameretti Chocolate

2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 1 0 0 0,0 0 0 0,0 0 1 0,1 5 7 0,2 1 2 0,1 0 3 0,2 0 0 0,0 0 1 0,1 2 5 19 0,9 25 25 0,0 1 1 0,0 10 10 0,0 3 3 0,0 5 17 1,1 5 5 0,0 2 2 0,0 3 5 5 0,0 26 36 0,7 3 1 -0,5 10 10 0,0 3 3 0,0 11 13 0,4 17 17 0,0 3 1 -0,2 4 12 17 0,6 30 37 0,6 3 7 1,0 11 17 1,1 4 5 0,2 12 9 -0,7 18 6 -4,1 10 10 0,0 5 13 13 0,0 30 41 1,0 4 2 -0,7 13 13 0,0 5 5 0,0 12 14 0,5 19 12 -3,7 10 10 0,0 6 22 26 -2,7 35 50 2,5 4 4 0,0 15 7 -6,5 5 6 0,2 15 16 0,9 20 25 5,5 11 13 6,5 7 24 22 0,6 45 45 0,0 5 5 0,0 15 17 1,6 5 5 0,0 20 11 2,3 23 25 -1,0 12 12 0,0 8 28 26 0,3 45 60 -3,8 7 6 6,0 15 15 0,0 10 8 2,4 20 18 0,5 24 33 -2,9 12 15 -4,3 9 30 25 0,5 50 50 0,0 7 7 0,0 16 16 0,0 12 9 1,1 20 17 0,8 28 30 -0,3 12 11 1,4 10 30 20 1,1 57 71 -0,9 10 10 0,0 21 21 0,0 12 9 1,1 21 21 0,0 30 36 -0,7 13 14 -0,6 11 30 32 -0,2 74 74 0,0 18 19 -0,1 22 22 0,0 25 10 0,9 21 20 0,2 30 25 0,6 20 15 0,6 12 35 16 1,3 75 95 -0,6 20 3 1,3 25 24 0,1 25 9 1,0 25 9 1,8 37 36 0,1 20 18 0,2 13 33 win 85 win 25 win 33 win 35 win 28 win 43 win 22 win

Table 6

7.4 Bids in session four (7 bidders):

1 2 3 4 5 6 7

Turron Wine Key Chain T-Shirt Toblerone Book Poster

2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 2nd Jap l 1 9 7 -0,2 10 30 0,8 5 5 0,0 12 17 0,3 7 11 1,0 5 7 0,2 2 4 0,2 2 12 12 0,0 20 20 0,0 5 9 0,6 25 28 0,5 9 9 0,0 10 10 0,0 10 9 -0,5 3 15 10 -0,9 20 20 0,0 5 11 0,9 30 29 -0,7 9 13 2,0 13 28 4,3 12 13 5,0 4 15 21 1,1 30 25 -1,0 10 10 0,0 40 34 0,7 12 16 -4,0 17 16 2,0 12 13 5,0 5 25 25 0,0 36 36 0,0 15 11 1,1 50 33 0,9 13 13 0,0 24 28 -0,5 25 7 1,4 6 35 12 1,6 80 39 0,9 28 12 1,0 59 32 1,0 16 26 -2,0 30 30 0,0 25 9 1,3 7 34 win 48 win 38 win 30 win 30 win 38 win 44 win

Table 7

56 7.5 F-tests and T-tests:

critical critical

Bidders F-tests p-value f-value sign t-statistic p-value t-value l 1 1 1 Turron 17 1,8 0,1 2,4 n 0,4 0,4 1,7 0,2 2 2 Wine 17 0,7 0,2 0,4 y -1,6 0,1 1,7 1,6 3 3 Praline de Cafe 17 no data no data no data no data no data no data no data 4 4 Pottery 17 no data no data no data no data no data no data no data 5 5 Book 17 no data no data no data no data no data no data no data 6 6 Ameretti 17 no data no data no data no data no data no data no data 7 7 Wine 17 no data no data no data no data no data no data no data 8 8 Toblerone 17 no data no data no data no data no data no data no data 1 2 1 Crema C. 5 2,0 0,3 9,3 n 1,3 0,1 2,0 -2,0 2 2 Pottery 5 200,0 0,0 9,3 y -1,6 0,1 2,4 0,4 3 3 Turron Almond 5 200,0 0,0 9,3 y 0,1 0,5 1,9 0,1 4 4 T-Shirt 5 0,9 0,5 0,1 y 0,0 0,5 1,9 0,1 5 5 Cap 5 4,2 0,1 9,3 n 0,2 0,4 2,1 0,7 6 6 Biscuits 5 1,0 0,5 0,1 y 0,4 1,9 0,8 -0,1 7 7 Toblerone 5 4,3 0,1 9,3 n -0,1 0,5 2,1 0,3 1 3 1 Turron 7 2,0 0,2 5,1 n 0,8 0,2 1,8 0,3 2 2 Wine 7 9,5 0,0 5,1 y 0,4 0,3 1,9 0,1 3 3 Key-Chain 7 13,2 0,0 5,1 y 0,4 0,3 1,9 0,6 4 4 T-Shirt 7 7,6 0,0 5,1 y 1,0 0,2 1,9 0,4 5 5 Toblerone 7 0,3 0,1 0,2 y -1,4 0,1 1,9 -0,5 6 6 Book 7 0,8 0,4 0,2 y -0,6 0,3 1,8 1,0 7 7 Poster 7 6,7 0,0 5,1 y 1,3 0,1 1,9 2,1 1 4 1 Duck 13 1,7 0,2 2,8 n 0,2 0,4 1,7 0,2 2 2 Wine 13 0,8 0,3 0,4 y -0,8 0,2 1,7 0,0 3 3 SF Badge 13 1,5 0,3 2,8 n 0,6 0,3 1,7 0,6 4 4 Turron 13 1,0 0,5 0,4 y 0,0 0,5 1,7 -0,3 5 5 Ireland Badge 13 8,8 0,0 2,8 y 1,2 0,1 1,8 0,6 6 6 Toblerone 13 2,0 0,1 2,8 n 0,4 0,3 1,7 0,7 7 7 Ameretti 13 0,7 0,3 0,4 y 0,0 0,5 1,7 -0,5 8 8 Baci 13 1,2 0,4 2,8 n 0,1 0,5 1,7 0,3

Table 8: In the first session there is no data for 3-8, because in these experiments erroneously only the final prices, but not the individual bids in the Japanese auctions, were recorded.

57

PART THREE: Experimental Test of Revenue Equivalence

Overview In this chapter further experimental tests of revenue equivalence are conducted. Revenue equivalence of the second-price sealed-bid and the Japanese auction is tested when the price attained in the sealed-bid auction is publicised before conducting the Japanese auction. Revenue equivalence of the first-price sealed-bid, second-price sealed-bid and the Dutch auction is tested. And revenue-equivalence between the second-price sealed-bid and the English-outcry auction is tested.

58

1. Motivation

As explained above in Part One, theoretical predictions and experimental laboratory results differ significantly with respect to revenue predictions for the standard auction formats. Whereas theory predicts that both independent and affiliated private values26 and interdependent valuations with independently distributed private signals lead to revenue equivalence, laboratory experiments show that sealed-bid auctions lead to significantly higher revenue than their strategically equivalent counterpart27. It seems that important elements of auctions are ignored in the theoretical literature.

Due to the Internet, auctions have become a widely used selling mechanism. Sellers want to achieve the highest possible price and can choose auction rules accordingly. Due to the non- conforming theoretical and laboratory results, experiments are conducted to test revenue equivalence in the sale of real goods.

Theoretical revenue predictions comparing all four standard auction formats28 to one another differ with respect to the assumptions about bidder valuations. The goods sold in the experimental auctions were goods with uncertain value and uncertain quality (see Part One Chapter 3.3).

2. Experimental Set-Up

The experiments were conducted (as explained in Part Two) with undergraduate business and economics students at the University of Vienna and Vienna University of Economics and Business Administration in May and June 2001. Students were not paid for participation in the experiment. Half of the experiments were conducted with unpaid volunteers, and half of the experiments were conducted as an alternative to the “normal” course program. After the experiment, participants were debriefed on the hypothesis tested and theoretical predictions.

26 Valuations are private and satisfy the criterion of strict positive affiliation (Milgrom and Weber, 1982). 27 Two auction formats are strategically equivalent, when the expected seller revenue is equal and an identical bidder would choose the same strategy in both auction forms. The first-price sealed-bid auction is strategically equivalent to the Dutch auction and the second-price sealed-bid auction is strategically equivalent to the Japanese auction under the (independent) private value assumption. 28 First-price sealed-bid, second-price sealed-bid, Dutch, and Japanese auction . 59 3. Revenue Equivalence Between the Second-Price and the Japanese Auction

In a series of thirty experiments a single good was sold twice, first by means of a second-price sealed-bid auction and successively by an Japanese auction without announcing the final price obtained in the second-price sealed-bid auction. The second-price sealed-bid auction was conducted first because the secret format of the second-price sealed-bid auction discloses no information to bidders, does not allow them to draw conclusions on the other bidders’ valuations and the final price. At the beginning of the Japanese auction, the bidders were thus in the same informational state as before the second-price auction.

3.1 Breakdown of Revenue Equivalence

Thirty experiments were conducted in order to test revenue-equivalence between the second- price sealed-bid and the Japanese auction. In twenty-five of the thirty experiments the final price of the second-price auction was higher than that of the Japanese auction, in three experiments the final price of the second-price sealed-bid auction was higher and in two experiments the final prices of the two auctions were equal. On average the final price in the Japanese was 13% below that of the second-price sealed-bid auction.

3.2 Testing the Effect of Revealing Public Information

In the following experiment the results of Part One Chapter Two regarding revenue- equivalence of the second-price sealed-bid versus the Japanese auction are tested when revealing the final price attained in the second-price sealed-bid auction before carrying out the Japanese auction.

Hypothesis 1: Revealing Public Information Influences Bids

Does it make a difference whether the final price of the second-price sealed-bid auction is revealed before carrying out the Japanese auction? Fourteen experiments were carried out with a group of twelve participants, seven revealing the final price attained in the second- price sealed-bid auction and seven without revealing this information. 60 Final Price 2nd Price Revealed or Not 2nd Jap Diff Diff in % 1 Ireland Revealed 33 31 -2 -6,1 2 Toblerone Revealed 28 27 -1 -3,6 3 Ameretti Revealed 20 21 1 5,0 4 Chocolate Revealed 35 37 2 5,7 5 T-Shirt Revealed 50 51 1 2,0 6 Biscuits Revealed 35 36 1 2,9 7 Pottery Revealed 25 24 -1 -4,0 1 Teddy Not Revealed 25 10 -15 -60,0 2 Wine Not Revealed 73 90 17 23,3 3 SF Badge Not Revealed 18 18 0 0,0 4 Turron Not Revealed 26 22 -4 -15,4 5 Australia Not Revealed 34 33 -1 -2,9 6 Crema Cat. Not Revealed 29 28 -1 -3,4 7 Poster Not Revealed 55 52 -3 -5,5 Table 9

3.2.1 Results When the final price of the second-price sealed-bid auction was revealed before carrying out the Japanese auction, the final price of the Japanese auction was roughly equal to that of the second-price sealed-bid auction. The final price of the Japanese auction was on average 0.3% above that of the second-price sealed-bid auction.

In the experiments where the final price of the second-price sealed-bid auction was not revealed, the final price of the Japanese auction was on average 9 % below that of the second-price sealed-bid auction.

We can conclude that revealing the second-highest bid of the second-price sealed-bid auction leads to a much higher final price in the Japanese auction than not doing so. In fact, revealing the final price of the second-price sealed-bid auction leads to approximate revenue- equivalence between the Japanese and the second-price sealed-bid auction.

This result coincides with Milgrom and Weber (1982), revealing public information increases seller revenue. 61 Data: Testing Effect of Revealing Information

1 2 3 4 5 6 7 Ireland Toblerone Ameretti Chocolate T-Shirt Biscuits Pottery 2nd Jap 2nd Jap 2nd Jap 2nd Jap 2nd Jap 2nd Jap 2nd Jap 1 0 0 5 7 0 1 0 0 0 0 0 5 0 0 2 5 19 10 10 1 1 5 5 0 5 1 7 0 0 3 5 5 10 10 3 1 17 17 0 7 10 10 0 1 4 12 17 11 17 3 7 18 6 5 10 14 14 1 1 5 13 13 13 13 4 2 19 12 5 22 15 17 2 2 6 22 26 15 7 4 4 20 25 10 25 15 16 7 7 7 24 22 15 17 5 5 23 25 15 30 16 16 8 7 8 30 25 15 15 7 1 24 win 20 32 17 15 9 11 9 30 20 21 21 7 7 28 33 25 28 18 19 15 14 10 30 31 22 22 10 10 30 30 30 40 21 25 22 19 11 33 win 25 25 18 21 30 32 50 42 29 26 23 20 12 33 16 28 27 20 win 35 37 50 win 35 36 25 24 13 35 27 33 win 25 3 43 31 55 51 37 win 27 win Table 10: Results when the final price of the second-price auction was revealed

1 2 3 4 5 6 7 Teddy Wine SF Badge Turron Australia Crema Cat Poster 2nd Jap 2nd Jap 2nd Jap 2nd Jap 2nd Jap 2nd Jap 2nd Jap 1 1 2 0 15 2 3 0 3 0 0 0 0 8 12 2 3 3 19 19 3 3 5 17 1 1 0 0 10 13 3 3 3 20 20 3 4 11 13 2 3 5 5 10 10 4 4 1 34 35 5 5 12 9 3 1 11 12 13 15 5 5 5 38 38 7 5 12 14 3 9 15 13 14 15 6 5 1 40 35 8 10 20 11 4 8 15 12 15 16 7 5 5 48 37 9 12 20 18 5 16 19 17 18 19 8 10 5 50 52 10 15 20 17 7 12 22 17 24 25 9 12 5 50 53 15 15 21 21 14 19 23 24 25 25 10 12 6 55 65 15 17 21 20 17 24 24 24 35 32 11 25 10 70 75 15 18 25 9 34 28 28 28 45 43 12 25 win 73 90 18 18 26 win 38 33 29 27 55 52 13 35 3 100 win 26 win 28 22 22 win 36 win 62 win Table 11: Experiments where the final price of the second-price sealed-bid auction was not revealed

62 4. English Outcry versus Second-Price Sealed-Bid Auction

Most experimental tests of revenue equivalence between the second-price sealed-bid auction and the English auction model the English auction as an ascending-clock (i.e. Japanese) auction. In the experiment described below the second-price sealed-bid auction was compared to the English outcry auction, carried out as follows: bids could be made, whereby a subsequent bid always had to be at least one currency-unit29 higher than the current bid. When no more bids are made the auctioneer counts three hammer-hits. If no bid is made within these three hammer-hits, the auction ends.

Hypothesis 2: The English outcry auction is revenue equivalent to the second-price sealed- bid auction English Bidders 2nd Price Outcry Difference Difference (in %) Wine 25 100 100 0 0 Toblerone 25 37 41 4 11 Pasta Nero 25 45 56 11 24 Wine 25 105 180 75 71 Wine 19 95 70 -25 -26 Turron 19 45 80 35 78 Toblerone 19 20 21 1 5 Pasta Nero 19 25 31 6 24 Table 12

4.1 Results

Out of the eight auctions conducted, the second-price sealed-bid auction led to a higher price in six experiments, the English-outcry auction led to a higher price in one experiment and the two auction formats were tied once. On average the English-outcry auction led to a 23.4 % higher final price than the second-price sealed-bid auction.

29 1 Austrian Schilling (i.e. about € 0.73) higher than the previous bid 63 It can be concluded that the English auction does not produce the same revenue, when conducted as an English-outcry and when conducted as a Japanese auction. Whereas the Japanese auction yields lower seller revenue than the second-price sealed-bid auction, the English outcry auction yields higher seller revenue than the second-price sealed-bid auction.

Bid dispersion cannot be analysed in this experiment, because the format of the English outcry auction does not release information on the exit prices of any of the non-winning bidders.

5. Revenue Equivalence: First-Price Sealed-Bid and Dutch Auction

Experimental tests of revenue equivalence generally compare a subset of the four standard auction formats to one another. Most often, the two pairs of strategically equivalent auctions (the English and second-price sealed-bid; or the Dutch and first-price sealed-bid auction) are compared to one another in the private values setting. In this section the Dutch and first-price sealed-bid auction are compared to one another.

Theory predicts that the Dutch and the first-price sealed-bid auction are revenue equivalent in case of independent (or affiliated) private valuations.

Laboratory experiments indicate that there is no revenue equivalence between the Dutch and first-price sealed-bid auction. Instead, for example Coppinger et al (1980) and Cox et al (1982) find that prices are significantly higher in the first-price sealed-bid than in the Dutch auction.

64 5.1 Results

1st Price Dutch Difference Difference (in %) Pottery 45 42 3 7 Poster 153 120 33 22 Toblerone 25 21 4 16 Turron 37 35 2 5 Wine 73 68 5 7 Ameretti 32 29 3 9 Crema Cat 31 33 -2 -6

Table 13

Results show no revenue equivalence between the Dutch and first-price sealed-bid auction. The Dutch auction leads to higher prices than the first-price sealed-bid auction. The final price in the Dutch auction was on average 8% lower than that in the first-price sealed-bid auction. My experimental results conform to the experimental laboratory results. Cox et al (1982) offer two explanations for this phenomenon. Their first explanation is based on the existence of a positive utility of suspense during the price-countdown in the Dutch auction. The positive utility of suspense is additive with respect to the expected utility of income from the auction.

Their second explanation “the probability miscalculation model” involves bidders engaging in an updating procedure in the Dutch auction. Seeing that their rivals have not called the Dutch auction to a halt yet, they lower the estimate of their rival’s valuations mistakenly.

Cox et al (1983) test the two hypotheses and find no evidence of the “suspense model”. Their results do show evidence in favour of the “probability miscalculation model”, however further tests are necessary for validation.

No results can be given concerning the individual bids because the Dutch auction only reveals one bid, the bid of the winning bidder.

65 6. Comparison: Second-Price Sealed-Bid, First-Price Sealed-Bid and Japanese Auction

In Chapter 3.1 we found that the secret second-price sealed-bid auction leads to higher seller- revenue than the open Japanese auction. In Chapter 3.3 we found that the secret first-price sealed-bid auction leads to higher seller-revenue than the open Dutch auction. Our experimental results conformed to the results of laboratory experiments testing revenue- equivalence in the independent and affiliated private value setting. Neither of the two conforms to the theoretical predictions.

In order to complete the experimental investigation of revenue equivalence, a comparison between the first-price sealed-bid, second-price sealed-bid and the Japanese ascending-clock auction is undertaken in the following section.

Fifteen experiments were carried out, testing revenue-equivalence of the first-price sealed- bid, second-price sealed-bid and Japanese auction. Eight experiments were conducted in the session with seventeen bidders and seven experiments were conducted in the session with five bidders. The auctions were carried out in the following order: first-price sealed-bid, then second-price sealed-bid and last the Japanese auction. The purpose and advantage of this order is to have the same informational structure at the outset of each of the three auctions. This is possible because the first-price sealed-bid and second-price sealed-bid auction can be carried out without revealing any information. Bids are submitted secretly and neither bids nor final prices are publicised. The Japanese auction reveals information due to its open format and thus is carried out after the other two auctions.

6.1 Results

17 bidders 5 bidders 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 Turron Wine Praliné Pottery Book Ameretti Wine Tobler- Crema Pottery Turron T-Shirt Cap Biscuits Tobler- one Cat. one 1st 27 85 42 10 50 35 50 29 50 50 75 121 50 120 20 2nd 30 90 35 10 50 45 30 20 30 21 60 121 30 40 25 Jap 25 111 30 5 42 33 23 18 31 21 55 120 25 39 20 Table 14

66 In eight out of the fifteen experiments, the first-price sealed-bid auction led to the highest final price, in three experiments the first-price sealed-bid auction was tied with another auction for having the highest final price and in four experiments the first-price sealed-bid auction was not the auction yielding the highest final price.

On average the first-price sealed-bid auction led to 16% higher final prices than the second- price sealed-bid auction. The first-price sealed-bid auction led to 27% higher final prices than the Japanese auction on average.

6.2 Interpretation

Clearly we do not find revenue-equivalence between the three auction formats. The final price of the first-price sealed-bid auction was higher on average than that of the second-price sealed-bid and Japanese auction. In case of independent and affiliated private valuations this empirical result would contradict the theoretical prediction.

Theoretical prediction for revenue ranking in case of affiliation under risk-neutrality: According to Milgrom and Weber (1982), affiliation leads to the following ranking of expected final prices under risk-neutrality:

Dutch = first-price sealed-bid auction § second-price sealed-bid auction § Japanese auction

The experimental results do not correspond to theoretical predictions for the case of affiliated valuations, because the second-price sealed-bid auction produced higher revenue than the Japanese auction. The experimental results also do not correspond to theoretical predictions for the purely common value model, because theory would predict lower prices in the first- price sealed-bid than the second-price sealed bid or Japanese auction.

One possible explanation for why the first-price sealed-bid auction led to higher seller- revenue than the second-price sealed-bid and the Japanese auction is risk-aversion. Risk aversion does not affect the bidding strategy in the second-price sealed-bid and Japanese auction, but leads to higher seller-revenue in the first-price auctions.

67 In case of affiliated valuations and risk-averse bidders, Milgrom and Weber reach the following result with respect to revenue-ranking: Dutch = first-price sealed-bid < second- price sealed-bid § Japanese auction.

In laboratory experiments the first-price auction yields consistently higher revenue than the second-price sealed-bid auction. See for example: Coppinger et al (1980), Cox et al (1982), Kagel and Levin (1983). Our experimental results conform to the laboratory results.

Field studies also show slightly higher prices for the sealed-bid auction than the Japanese auction. Walter Mead (1967) analysed data from U.S. timber auctions and found that sealed- bid auctions led to about 10% higher revenue than Japanese auctions. Hansen (1985b, 1986) criticised these results claiming that data selection was biased. After correcting for the bias, he concluded that sealed-bid auctions did lead to higher prices but that the difference was statistically insignificant and the revenue-equivalence hypothesis could not be rejected.

Our experiments conform to the empirical results obtained in field and laboratory studies, but not to the theoretical predictions.

7. Six Results of the Experimental Investigation of Revenue Equivalence

Second-Price Sealed-Bid and the Japanese Auction:

1.) The second-price sealed-bid auction leads to a higher final price than the Japanese auction.

2.) The bid dispersion is smaller in the Japanese auction than in the second-price sealed-bid auction.

3.) Revealing public information (revealing the final price of the second-price sealed-bid auction) weakens the effect above. Revealing public information is to the advantage of the seller.

68 Second-Price Sealed-Bid and English outcry Auction:

4.) The English outcry auction yields higher seller revenue than the second-price sealed-bid auction. The English outcry auction leads to higher revenue than the Japanese auction.

First-Price Sealed-Bid and the Dutch Auction:

5.) The first-price sealed-bid auction leads to higher revenue than the Dutch auction.

First-Price Sealed-Bid, Second-Price Sealed-Bid and Japanese Auction: 6.) The first-price sealed-bid auction leads to higher revenue than the second-price sealed-bid auction and the Japanese ascending-clock auction.

8. Conclusion

Revenue equivalence is tested for the four standard auction formats in the sale of real consumption goods. The sealed-bid auctions produce higher revenue than their strategically equivalent open auction counterparts; the first-price sealed-bid leads to higher revenue than the Dutch auction, the second-price sealed-bid auction leads to higher revenue than the Japanese auction. The theoretically expected strategic equivalence between the two auction pairs is robust with respect to risk-aversion and thus presents a puzzle. Furthermore, the first- price sealed-bid auction yields higher revenue than both the second-price sealed-bid and the Japanese auction. The results found in the sale of real goods are confirmed by numerous laboratory experiments, however stand in contrast to theoretical literature.

69

PART FOUR: Internet Auctions and their Framework

1. Introducing Internet Auctions

The break-through of the Internet has led to a huge boom of auctions. The best-known Internet auction houses in the Consumer-to-Consumer segment are currently Ebay, Amazon and Yahoo. These three auction houses will be the ones dealt with in the following chapters.

We aim to investigate the rules, success and problems of the current Internet Auctions, when success is defined in terms of maximisation of seller-revenue. Economists do not generally evaluate the entire framework an auction operates under such as psychological influences, legal and structural constraints – even though these are also revenue determinants. The aim of the economist is to find the mechanism (the bundle of rules) under which the expected seller revenue is maximised.

The success of an auction can be determined by the rules chosen or by the auction environment as a whole. In case the current auctions turn out not to deliver the seller revenue hoped for, it is necessary to determine the source. In this Chapter we want to look at the big picture, at the general framework Internet Auctions are embedded in.

1.1 Three Business Models: Ebay, Amazon, and Yahoo

In order to describe the framework of Internet Auctions let us begin with the three auction houses: Ebay, Amazon, and Yahoo.

Ebay, with headquarters in San Jose, California, started out in September 1995 and had its initial public offering in September 1998. Ebay is the best–known auction house today and was one of the first, but not the first consumer-to-consumer auction-house: Onsale had come earlier starting its business in May 1995. Yahoo followed October 1998, Amazon in March 1999. 70

Ebay controls more than 80% of the online-auction market, with Amazon and Yahoo lagging far behind30. Unlike Amazon and Yahoo, Ebay is not a retailer and can thus avoid a number of complexities and costs31. Ebay collects fees (about seven to eight percent of the sales price) for being an intermediary and for providing the auction platform. The autos category accounts for 30% of Ebay’s gross sales32.

Yahoo is a portal, has 3260 employees33 and 185 million visitors worldwide34. Yahoo offers a lot of services, users spending on average one and a half hours per day35 on the website. This has given Yahoo the possibility of tracing the customers’ steps through the web pages and learning about their preferences. Yahoo uses targeted ads which sell for thirty to sixty times the price of untargeted ads, but is dependent on dot.com advertising with sixty-percent of its advertising revenue coming from dot.com companies36.

Much of Yahoo’s growth comes from overseas. Nevertheless Yahoo closed five of its European auction services (UK& Ireland, Germany, France, Italy and Spain) in June 2002. It is still very successful in Japan, where Ebay shut down its respective auction service in March 200237.

Amazon is not only an auction-house but acquires, stores and delivers brand name products. It has seven huge distribution centres in the USA, one each in Britain, France, Germany, and Japan. Amazon built a warehouse in every country it entered and is hoping for an

30 “Ebay’s Bid to Conquer All” by Adam Cohen, Time (New York), Feb 5th 2001, p.48-51. 31 “Plugged in Yahoo Blues: So much for the new economy” by Mark Veverka, Barron’s (Chicopee), March 12th 2001. 32 In the year 2000 Ebay started the Ebay Motors category in form of a partnership with the used car dealer Auto Trader. “Margaret Whitman”, Business Week, Jan 8th 2001, p.68. 33 “Is there life in E-Commerce?”, The Economist, Vol.358 Issue 8207, Feb 3rd 2001, p.19-20 34 Figures for the year 2000. “Yahoo revises estimates, loses CEO as online ads drop” InfoWorld (Framingham), March 12th 2001, p.23 35 “Internet Pioneers: We have lift-off”, The Economist, Feb 3rd 2001, p.69-72. 36 “Internet Pioneers: We have lift-off”, The Economist, Feb 3rd 2001, p.69-72. 37 “Yahoo shutters European Auction Sites” by Troy Wolverton on Cnet News.com, June 28th, 2002 (http://news.com.com/2100-1017-940580.html). 71 improvement in the efficiency of Europe’s transportation systems38. Due to its fast-moving centralised inventory and relatively fixed handling costs, Amazon has a competitive advantage in business areas such as consumer electronics.

1.1.1 Revenue

Registered Gross Users Merchandise (in millions) Sales per day (in $) Ebay 22,5 12 Million Yahoo 236 500 000 Amazon 29 200 000 Table 15: Figures taken from Goldsborough and Veverka39:

Auctions closing per day Revenues per month (in $) 190 000 000 Ebay 340 000 (18 000 000) 19 000 000 Yahoo 88 000 (7 900 000) 2 000 000 Amazon 10 000 (620 000) Table 16: Size Estimates Summer 1999, estimated standard errors in parenthesis40

Monthly Volume ($) Number of Sites 10,000 or less 83 10,001 to 100,000 27 100,001 to 1,000,000 21 1,000,000 or more 7 Table 17: Size Estimates November 199841

As can be seen from the tables above, Ebay’s monthly revenue is ten times as large as that of Yahoo, which likewise is ten times as large as that of Amazon. Causes are discussed below.

38 “Yahoo revises estimates, loses CEO as online ads drop”, March 12th 2001. 39 “Internet Auctions Examined” by Reid Goldsborough , Link-up (Medford) Nov/Dec 2000, p.24 and “Plugged in Yahoo Blues: So much for the new economy” by Mark Veverka, Barron’s (Chicopee), March 12th 2001. 40 Taken from: Lucking-Reiley (2000), p.248. The size estimates were computed by choosing a day in June or July to visit each site, observing the number of auctions on that day and taking a sample of closed auctions to estimate the average revenue per auction closing. 41 Lucking-Reiley (2000), p.230 72 1.2 Network Effects

This chapter shows which network effects are present in Internet Auctions and how they work.

Internet auctions are characterised by network externalities, i.e. external demand side scale economies. Network externalities are conditions that give each user benefits as the set of users expands. External demand side economies of scale imply that when a new user subscribes to the service, the other users benefit: the benefit thus being external to the new user42.

The platform with the highest number of users (potential bidders) attracts the highest number of sellers. The bigger the auction platform, the higher the utility for each buyer, because they benefit from a reduction in search costs, a richer variety, and a better comparison due to more items per category.

A higher number of bidders directly affects the expected return of the seller positively. As the number of bidders increases, the valuation of the second highest bidder approaches that of the highest bidder (in the independent private values model).

Logging onto an auction generates costs for the buyer. Once a buyer is registered as an auction user, he does not need to enter his personal information and credit card information again, when he next wishes to buy an item via an auction. More importantly, a larger variety of goods produces higher utility for the bidder. Shoppers shop where they expect to find something that they will want to buy.

Logging onto a new website also produces costs for the seller, having to learn the specifics of the auction-house and having to enter information about himself and his good. He can reduce these costs - except for the specific information about the good, description and picture of the item - by using the same auction-house for all his sales. The fact that a buyer or seller faces costs when conducting his transactions through a new and different auction-house shows the existence of switching costs and leads to lock-in.

42 Rohlfs (2001), p.14. 73 It is assumed that network externalities and switching costs help the largest player, Ebay in growing larger, pushing Amazon and Yahoo into the background. Internet auctions also show evidence of the first-mover advantage at work. Ebay being the first-mover in Europe was probably partly responsible for Yahoo shutting down five of its European auction services in June 2002. In contrast, Yahoo was the first-mover in Japan, where Ebay decided to shut down its services in March 2002.

1.2.1 Loyalty The registration effort required for participation in the auction is an exit barrier; in order not to incur these costs again, bidders have an incentive to stick with the first auction house they deal with. The feedback rating system is another feature that promotes loyalty. On Ebay the successful bidder and the seller receives plus one, zero or minus one points, after the deal is closed, the payment made and the good shipped - from their respective transaction partner. The rating of a bidder or seller is displayed next to his name on the website. Sellers and bidders who have a rating above zero have an incentive to keep on conducting transaction with that auction house, because the feedback rating serves as information to other participants about the trustworthiness.

The feedback-rating system acts as a lock-in for bidders and provides an incentive for bidders to remain loyal to their auction house and to conduct all auction purchases through the same auction house. The switching costs benefit the first-mover, who will further benefit from network-effects and positive feedback (i.e. the process with which an increase in customer- base leads to a further increase in customer-base and so forth).

1.3 The Selling Mechanism

1.3.1 Auctions and Posted Prices There are a number of ways a good can be sold, using posted prices, bargaining or auctions. When selling a single-unit item the seller ideally wants to achieve a price equal to the highest bidder’s reservation price. If the seller were perfectly informed he would simply charge a price equal to the highest bidder’s reservation price. Auction theory assumes that there is asymmetrical information, that the seller does not know the bidders’ valuations. The seller searches for an auction mechanism that extracts the maximum amount of consumer surplus from the buyer. The rules of the English auction give bidders the chance to post bids. A buyer 74 will find it useful to bid (up to his reservation price) because this is the only way he can possibly win. Valuations will thus be revealed naturally. This is in contrast to a posted-price, where no revelation mechanism is used. Given asymmetrical information about the bidders valuations, it is highly unlikely that the seller will be able to set a posted price that precisely corresponds to the highest valuation.

The four standard auction formats discussed in the theoretical literature are presented in Part One. However, none of these auction mechanisms claim to be able to extract the reservation price from the highest valuing bidder. Instead, as shown by William Vickrey’s Revenue Equivalence Principle, the expected revenue is equal to the second highest bidder valuation in all four standard auction formats (under specific assumptions).

The main advantage of auctions in comparison to posted prices (when selling multi-units) is that auctions offer the possibility to price-discriminate. Wang (1993) shows that the seller prefers auctions to posted-price selling when bidder valuations are more strongly dispersed.

1.4 The Goods

1.4.1 Suitable for Auctions The theoretical literature recommends auctions under the following circumstances:

- The seller is a monopolist - Demand is unknown to the seller, high uncertainty about demand - Unique goods, goods in limited supply - Perishable goods

1.4.2 Goods Sold - Currently fashionable items (signed Harry Potter books, Pokemons) - Collectibles (60% of all Internet Auctions sell collectibles, e.g. coins, stamps.43) Empirically one finds a large amount of collectibles sold through Internet Auctions. - Antiques and art - Second hand goods - Small, easy to ship (most deliveries take place through parcel delivery)

43 David Lucking-Reiley (2000), p. 231. 75 - Cheap. Collectibles traded on Ebay have median prices well below $100 with almost no items above $100044. - Used cars - Perishable goods, such as plane tickets, hotel rooms, last-minute holiday-packages

Category Sites, that Sites that are list this specialised in category this category Collectibles 90 56 Antiquities 40 10 Star Memorabilia 16 7 Stamps 11 5 Coins 17 2 Toys 17 0 Playing Cards 14 0 Electronics and Computers 48 9 Jewellery 17 1 Computer Software 16 0 2nd hand Items 15 7 Sports Items 13 4 Travel Services 7 5 Real Estate 4 2 Wine 3 2 Table 18: Taken from Lucking-Reiley (2000), p.233.

Suitable Goods Sold in Internet-Auctions - Perishable Goods - Travel: Airline Tickets, Bed and Breakfast, Hotel, Packages - Tickets: Concerts, Musicals, Sporting Events - Collectibles: Stamps, Coins

Goods Sold But Not Recommended By Theory - Consumer Durables: Computers, Photo Equipment, Clothes - Real Estate: Commercial, Residential, Land

44 Lucking-Reiley (2000), p.232.

76 1.5 The Auction Formats Used

According to a survey of 142 auction sites by Lucking-Reiley (2000, p.237), the following auction formats were used:

121 Japanese 15 first-price sealed-bid 5 second-price sealed-bid 3 Dutch 4 continuous-trading double auctions45 6 used more than one auction format46

The auction format used most often is clearly the Japanese Auction. Part One presents the four standard auction formats and an introduction to Auction Theory. Given the figures above, we would assume that the Japanese auction has a quality that makes it most attractive for auction houses.

1.5.1 The Choice of Auction Format by the Auction House An auction house is a firm that maximises its profit. Two of its sources of revenue are the insertion and commission fee that sellers have to pay. The commission fee is dependent on the final price reached, the seller therefore striving to maximize his sales (measured in monetary units). A sale will only be successful when an item is matched with a buyer, this being more probable the larger the customer base.

Buyers prefer an auction format that maximises their expected revenue and sellers prefer an auction format that maximises their expected seller revenue. As the seller revenue is equal to the price paid by the buyer, there is a trade-off between the buyer and seller revenue.

The seller’s choice of auction format is only based on his expected revenue, but bidders do not base their decision of participating in an auction exclusively on their expected revenue. Instead they also care about the availability of interesting goods, which in turn depends on the auction format the sellers prefer. The choice of auction format is characterised by a strong

45 Double auctions allow continuous updating of seller offers and buyer bids 46 The sum is more than 142, because some sites offer more than one auction format 77 interdependency of preferences. Empirical results about seller preferences can be found in Part Five.

2. Internet-Specific Characteristics

2.1 Internet Specific Advantages

There are a number of advantages in using the Internet as a platform to conduct auctions on.

Accessibility, Reach The Internet provides access to a huge number of people.

Cheaper Technology Auctions become cheaper relative to other pricing mechanism due to the lower-cost Internet technology. Therefore a higher number of items can profitably be sold. The only true costs of Internet auctions are auction fees and transportation costs, dependent on transportation distance and weight of item.

Capacity A traditional auctioneer like Sotheby’s can only perform a certain number of auctions per day because of the limited capacity of its rooms and staff. Online auctions are able to deal with huge capacity and are able to benefit from economies of scale47.

Lower Fees Fees are much lower for Internet Auctions than for traditional auction houses. Ebay’s fees amount to about five to seven percent of the final bid; Sotheby’s charged a buyer premium of 15% over the final bid price and a standard seller’s commission fee of 20% of the bid price48.

47 “Internet Pioneers: We have lift-off”, The Economist, Feb 3rd 2001, p.69-72. 48 Hildesley, C.H. (1997), „The Complete Guide to Buying and Selling at Auctions“, W.W.Norton, New York quoted in Lucking-Reiley (2000), p235. 78 Lower Costs The bidders face lower costs due to lower fees, no travel costs, no time loss of travelling to and attending the auction. The costs of logging on to the Internet, registering for the auction, bidding and keeping track of the auction are very low in comparison to actually attending a traditional auction or sending an agent.

2.2 Internet Specific Problems

Anonymity of the Internet The anonymity of the Internet creates various sources of uncertainty for the buyer and the seller.

Lack of Information The number of successful transactions, that is transactions where a good is sold to a buyer at a price acceptable to the seller, is dependent on the size of the market, the number of sellers and buyers conducting transactions on the website. The fact that only a small number of goods find buyers49 can be partly caused by an informational problem. Search engines and product notification emails for subscribed categories are useful in calling auctions to the attention of buyers and matching sellers with buyers.

Uncertainty About the Nature of the Good Buying an item through the Internet means that one does not get the chance to see the item before purchasing it. The buyer has to base his purchase decision on the description of the object. This problem is fundamental to the Internet, but photos and accurate descriptions by the seller can prevent unwanted purchases.

Uncertainty About the Enforceability of the Contract One reason why some potentially interested bidders decide not participate in Internet auctions is the uncertainty with respect to the observance of the contract, due to a lack of legal security. There is lack of legal security ensuring the enforcement of contracts, leaving both the seller and buyer no other option but to trust the other party. The seller is uncertain whether he will ever receive the money; the buyer is uncertain whether he will ever receive the good.

49 See Part Five Chapter 3.5 79 Auction houses have however taken measures to increase information about the trustworthiness of the sellers and buyers, through the implementation of a rating system, where sellers and buyers are awarded points by their transaction partners. Uncertainty about the arrival of the good and payment can be mitigated by using escrow services, agents that inform the seller upon receipt of payment by the buyer, in order for sellers to be able to then safely send the good to the buyer. Intermediaries of this kind already exist, although they are costly, they also reduce a great deal of uncertainty.

Fraud Two types of fraudulent behaviour are particular of Internet auctions, shilling and shielding.

Shilling: The seller enters an (artificially) high bid, when only one or few bidders are left, in order to drive up the price

Bid Shielding: A bidder who is truly interested in the item, enters a low bid and asks a friend (collaborator) to enter a very high bid. This high bid has the aim of discouraging bidders who have reservation prices between the low first bid and the shielding high bid. Just before the auction ends the high bidder retracts his bid.

Measures to prevent fraudulent behaviour include a feedback and rating systems for both sellers and buyers; escrow services where the buyer sends his payment to the escrow agent, who then informs the seller that he can now send the item to the buyer; and co-operations with prosecutors to encourage defrauded buyers and sellers to sue.

Transportation Costs Transportation costs are responsible for favoring light (weight-wise), small items and short- distance transactions as auction-goods. Ebay and Amazon have both started regional auction- sites, such as ebay.de or amazon.de directed in the German market. Regional auctions are not only advantageous with respect to transportation resulting in cost-savings and less risk of breakage; they also provide the possibility of inspecting the good prior to purchase.

80 2.3 Outlook

Some of the problems discussed above could be solved or at least weakened. The problems related to the enforceability of the contract can be partly solved by the use of intermediaries, who supervise the transaction by waiting for the receipt of the money until they advise the seller to send the good to the buyer. Uncertainty will also be reduced once the legal framework for e-commerce is clearly set out.

The current structural framework definitely accounts for a lack of bids and transactions, but the auction rules might also not be perfect to stimulate an exciting auction. Nevertheless the Internet can be seen as an amazing opportunity for determining the price and value of a good, when nearly the entire world is available as a potential bidder. The Internet provides the opportunity for reaching a huge number of people, who could bid quickly, comfortably (from their own computer), and without global limits.

3. The Internet Auction Rules

3.1 Bid Submission and Procedure There are two ways in which bidders can submit bids on Internet auctions, by a straight bid or a proxy bid.

Straight Bid A bid can be submitted as a straight bid. When a straight bid constitutes the winning bid, the winning bidder has to pay a price equal to his bid. When a straight bid is outbid, Yahoo, Amazon and Ebay provide “outbid notification” by email.

Proxy Bid A bid can be submitted as a proxy bid. The bidder enters a bid denoted as his “maximum willingness to pay”. This automated proxy-bidding mechanism bids automatically, placing a bid one minimum-increment above the current high bid on behalf of the bidder, until the bidder’s “maximum willingness to pay” is reached.

81 3.2 Bidder and Seller Registration

Yahoo: In order to be able to sell an item or submit a bid, the seller / bidder must enter his name, email address, birth date, gender, zip code, occupation, industry, and personal interests.

Ebay: In order to be able to sell an item or submit a bid, the seller / bidder must enter his name, Ebay user ID or email address, billing address, credit card number and expiration date. Bidders have to let Ebay verify their credit card before they are allowed to place bids of more than $15.

Amazon: A bidder and seller must enter his name, address, phone number, email address, and valid credit card information. He also has to register with Amazon.com Payments, who require a credit card issued by a U.S. bank.

3.3 Auction-Length

The length of Internet-auctions varies between two and fourteen days. A length of seven days is most common50. The seller can generally choose the auction length within set limits.

Yahoo: Sellers choose a length from two to fourteen days. Ebay: Sellers choose a length of three, five, seven, or ten days Amazon: Sellers can choose a length of one, three, five, seven, or fourteen days.

Ending Rule Yahoo: The auction ends at a specified end date, except if the option “automatic extension” is chosen. In this case, if bids are placed less than five minutes before the (tentative) auction end, the auction continues for five more minutes.

Ebay: The auction ends at a time specified by the seller.

50 Lucking-Reiley (2000). 82 Amazon: The auction ends at a specified end date, with the additional requirement, that there must be no bids within the last ten minutes of the auction. If bids are placed less than ten minutes before the auction end, the auction is extended until the last ten minutes are bid-free.

3.5 Auction Fees51

Yahoo: Listing Fee: between $0.2 and $1.5 Final Value Fee: between 1% to 4% of the final sale price Reserve Price Fee: The reserve fee lies between $0.4 and $0.75, which is refunded if the auction closes successfully.

Ebay: Insertion Fee: between $0.3 and $3.3 Final Value Fee: between 1.25% to 5% of the final sale price Reserve Price Auction Fee: between $0.5 and $1, which is fully refunded if the item sells.

Amazon: Listing Fee: $0.1 per listing Closing Fee (required only if the auction is a success): between 5% of final price and $25.63 plus 1.25% for any amount above $1000

3.6 Additional Features

Reserve Price The seller has to choose a starting price for his auction. The starting price is the lowest possible price at which bids are accepted.

Yahoo, Ebay, Amazon: Additionally the seller can choose to use a reserve price, which is then the relevant minimum price at which the seller is obliged to sell the item.

Sellers can choose to use a secret reserve price. In this case the reserve price is not revealed. The website indicates that there is a secret reserve price as long as the reserve price has not

51 Data from November 2001 83 been met. Amazon and Ebay do not reveal bidder identities and bid amounts as long as the reserve price has not been met.

Buy Price Yahoo: The seller has the possibility of setting a buy price. When a buyer bids the buy price, the auction ends immediately and the buyer receives the good at this price.

Early Close Yahoo, Ebay: Sellers can choose the Early Close option, which enables them to close the auction at any time during the auction and sell the item to the current winning bid. Amazon: The same option is offered as a “Take-It Price”.

First Bidder Discount Amazon gives sellers the option of a first bidder discount. The winning-bidder gets a discount of ten percent on the final price if he was also the first bidder.

Cancelling Bids Yahoo: Bids can only be cancelled at the seller’s discretion.

Bidding Increments Yahoo: $0.1 to $10 Ebay and Amazon: $0.05 to $100

Payment Method Yahoo: Credit Card, Money Order, Check Yahoo PayDirect! Sending and Receiving money by email, when both parties have a Yahoo PayDirect! Account. Escrow Service: A third party acts as an agent, holding the buyers' money until there is proof that the item was shipped and received.

Ebay: Credit Card

84 Online Payments with Billpoint

Amazon: Credit Card, Money Order, Check, C.O.D. Online Payments with Amazon.com Payments

Ratings and Feedback Buyers and Sellers rate each other.

Ebay, Yahoo: +1: is added for each positive comment or praise. 0: is given for neutral comments. -1: is given for each negative comment or praise.

Amazon: Five stars is the highest possible rating.

4. Some Implications of the Auction Rules

One major difference in the auction rules of Ebay, Amazon, and Yahoo is the ending rule. Ebay uses the hard-closing ending, Amazon the automatically extended ending and Yahoo offers the seller the choice.

Uncertainty about the Number of Bidders Bidders in Internet auctions are uncertain about the total number of participating bidders. There is no requirement to post a bid early or to pre-register for an auction, therefore bidders can join the auction until the very last minutes of the auction duration. The auction sites publicise the number of bidders who have posted bids so far, but new bidders can join anytime until the last moments of the auction.

When all bidders have independent private valuations, not knowing the number of bidders does not influence bidding behaviour in the Japanese and second-price sealed-bid auction, but does influence bidding behaviour in the Dutch and first-price sealed-bid auction (see Part One Chapter 1.5).

85

In the case of interdependent valuations, the number of participating bidders affects the bid and final price. If all bidders have the same assumption about the number of bidders then the final price will be equal to the case when the number of bidders is publicly known.

Effect on Profitability Ebay’s monthly revenue is far higher than that of Amazon52 and Yahoo. This could be due to a first-mover advantage and network effects. However, Ebay using „more profitable“ rules might be an important cause too. The main difference between Amazon and Ebay is the ending rule used. Yahoo in contrast offers sellers the possibility to choose their auction end. Whether the ending rule affects profitability and which auction end the seller prefers will be investigated in Part Five.

Effect on the Timing of Bids On average Amazon auctions have fewer last-minute bids than Ebay auctions53. The existence of late bidding and the effect of rules on the timing of the bid are discussed extensively in Part Five.

Auction Fees Fees increase the auction house’s revenue (ceteris paribus) and have the advantage of inducing commitment on part of the seller. When a seller can post goods on a website at no cost, he has an incentive to choose a high reservation price54: if he does not find a seller at the high price, he can lower his reservation price and try selling the good again just a few days later. However, when the seller has to incur fees for every good he offers on the website, he has an incentive to post a reservation price that he believes has reasonable chances of being met. This allows the auction house to save on costs and raises its percentage of successful auctions.

52 See Part Four Chapter 1.1.1. 53 Roth and Ockenfels (2000). 54 The economic term “reservation price” corresponds to the term “minimum-price” used by the auction-houses. 86 Out of the three auction houses studied, Yahoo was the only one where sellers could offer goods without having to pay a listing fee. However, in February 2001, Yahoo also decided to introduce auction fees55.

55 Exact date: February 9, 2001. Taken from “Yahoo shutters European Auction Sites” by Troy Wolverton on Cnet News.com 28. June 2002 (http://news.com.com/2100-1017-940580.html). 87

PART FIVE: Late Bidding Investigation

Overview Internet auctions are analysed with respect to two different ending rules (hard close and automatic extension) and three different product categories (cars, computers and paintings). We find that Internet auctions are characterised by late bidding with a strong price-increase in the last hundredth of the auction. This effect is stronger for art than for car or computer auctions. Furthermore, the winner enters the auction at a very late point in time: on average in the last hundredth of the auction. This is true for art, car, and computer auctions. The late entry of the winning bidder is caused by the fear that lower-valuing bidders with interdependent valuations will revise their bid upwards due to common value or prestige effects.

88 1. Introduction

Internet auctions are a relatively new phenomenon. In the past years many new consumers have been attracted to Internet auctions for various reasons, for example because Internet- access has become the norm and because trust in the security of payment via the Internet has grown.

Observing Internet-auctions, an interesting new phenomenon is found: late bidding. In order to investigate whether late bidding is a rational bidding strategy I present two models of interdependent valuations. The first model is a general model of interdependent valuations; the second model a model with reputational effects. The bidding strategy and expected final prices are calculated for the symmetric and asymmetric (Expert-Amateur) case in both models. The effects of interdependencies on bidding-behaviour and price are compared to those of the automatically extended auction.

In order to empirically test the theoretical predictions, data is used from hundreds of Yahoo auctions. We want to find out whether bidders wait to submit bids until the very last moment and how this affects the price path over the complete auction duration; whether there is a late bidding effect in the sense that the price increases over-proportionately at the end of the auction. Roth and Ockenfels (2000) were the first, to my knowledge, to publish an empirical study on bidding on the Internet. They investigate auctions with regard to the number of bids submitted in the last twelve hours and find that many bids are submitted in the last few hours56. In this work price-formation is studied during the complete auction duration.

The theoretical prediction that late bidding is dependent on the ending-rule is tested empirically57. The theoretical models presented in Chapter Two predict that sellers prefer the automatically extended auction to the hard close auction. Yahoo auction data is used to verify the prediction because Yahoo lets the seller choose between the hard close and automatically extended ending. Late bidding is studied for three categories of goods: computers, art and cars, different goods implying different valuations and bidding behaviour.

56 The average auction length of seven days translates into 168 hours. Roth and Ockenfels only analyse the last 12 hours, thereby ignoring 156 hours (on average). 57 Roth and Ockenfels (2000) find a higher number of late-bids in Ebay than in Amazon auctions. Ebay has a hard close end and Amazon an automatically extended auction end. 89 2. Theoretical Investigation

Auction theory analyses four standard auction-formats with respect to their revenue implications. The Ebay, Amazon, and Yahoo auctions all fit the definition of an English auction, i.e. an open ascending bid auction. In order to differentiate between the different English auction formats on the Internet, the standard model for the English auction has to be modified for the specific rules. The main difference in the rules of Ebay, Amazon and Yahoo is the ending rule. The Ebay auction has a fixed ending. The Amazon auction has an ending rule specifying that when bids are submitted in the last ten minutes before the tentative end, the auction be extended until the last ten minutes are free of bids. Yahoo lets the seller choose the ending rule, offering a hard close or a tentative end with 5-minute automatic extension.

One big difference between the English ascending-bid auction and the current Internet auctions is that there is uncertainty about the number of bidders. As discussed in Part One Chapter 2.3, uncertainty about the number of bidders is of no relevance in second-price auctions with independent private valuations. Internet auctions, like most other auctions, are characterised by some form of interdependent valuations. The Milgrom-Weber model represents a general model of interdependent valuations, using affiliated interdependent valuations. In the model presented in Part Three bidders have interdependent valuations with independently distributed signals.

Below I present four different forms of interdependent valuations: the symmetric model of interdependent valuations used in Part Two, the model from Part Two but with asymmetric valuations (an Expert-Amateur Model) and a second Expert-Amateur Model where the amateur has a prestige value. Finally I present an Internet auction model for the general Milgrom-Weber framework. The asymmetric models of interdependent valuations reflect the fact that bidders in Internet auctions often have very different informational structures – participants in Internet auctions for antiques include professional dealers as well as “innocent” house-wives.

Two ending rules are compared to one another: hard close and automatic extension. An auction format representative for the hard close auction is presented. The price and seller revenue of the hard close auction is compared to that of the automatically extended auction.

90 2.1 Theoretical Investigation of Late bidding

An increase in the number of bids submitted toward the end of Internet auctions has been noticed and conjectured by bidders, Internet auction houses, as well as academics (e.g. Roth and Ockenfels).

Some economists have already started to work on finding rational explanations for late bidding. Roth and Ockenfels (2000) present a model in which technical problems create a positive probability that the auction house does not receive a late bid. This can induce late bidding as a collusive attempt to keep the price low. Rasmussen (2001) presents an Internet auction model with asymmetrically informed bidders. After a certain point in time, the uninformed bidder has the possibility to discover his private but unknown valuation at a certain cost. In turn, late bidding can be a rational strategy.

2.1.1 The Moral Hazard Incentive One intuitive explanation that might account for late bidding is the moral-hazard incentive of the auction house. Auction houses earn profit by the commission they charge buyers and/or sellers based on the final selling price. The auction house would like to earn as high commission payments as possible: a greater number of successful sales increase the commission as well as higher selling prices.

A bidder can bid by making a single bid (if the winning bid is a single bid, the winner has to pay a price equal to his own bid) or by making his maximum-willingness-to-pay known to the proxy-bidding agent (who will bid automatically by raising the current high price by the minimum-increment until his bidder appears as the high-bidder – within the limit of the maximum-willingness to pay). It is not rational for a bidder to use single bids58 (see Chapter 3.3.2 below). The proxy-bidding mechanism asks bidders to enter the maximum-willingness- to-pay into the auction’s website. The auction house now has the possibility to make a seller’s dream come true, posting a fake bid just below the highest reservation price and thereby raising the price to just a minimum-increment below the high-bidders reservation price. This would enable the auctioneer to extract the total surplus from the high-bidder, thereby leading

58 Single bids can be rational if rivals are intimidated by jump bids (jump bids are bids that are higher than the current high-bid plus a minimum-increment. Easley and Tenorio (1999) study jump bidding on the Internet, Avery (2002) models strategic jump bidding in English auctions. 91 to the first-best outcome. Legally this is not allowed, but technically it is possible. Of course the auction house has a smaller incentive to engage in such fraudulent activities than would the seller, because the auction house only receives a certain fraction of the final price as commission. Nonetheless, the moral hazard incentive is present. If bidders are aware of this and believe it to be a serious threat (due to the anonymity of the internet), late bidding would be a logical consequence. Even though I believe the moral hazard explanation to be plausible and realistic, in the following sections and models we assume that the moral hazard incentive is of no relevance and search for other explanations.

2.1.2 Interdependent Values When all bidders have private values and believe their rivals to have private values too, late bidding is not reconcilable with standard auction theory. There is no reason for a bidder to hold back his valuation until the very last minutes when none of his rivals is influenced by his valuation and he is also not influenced by the valuations of his rivals.

In the following section we therefore concentrate on models of interdependent valuations. At least one bidder has a valuation that depends on private information of another bidder.

2.1.3 General Bidding Model In the following section I will show bidding behaviour for various models of interdependent valuations. In section 2.1.3, I use two variants of the model from Part Two; the symmetric case, where all bidders have the same λ value and the expert-amateur model, where there is one expert with a λ equal to zero competing against amateurs with a λ greater than zero. In section 2.1.4 late bidding is tested for a prestige-value model, for the symmetrical and the expert-amateur (i.e. asymmetrical) case. In section 2.1.6 late bidding is tested for the Milgrom-Weber general symmetric model of interdependent valuations.

Revenue in the hard close auction is compared to that of the automatically extended auction. The revenue-comparison is conducted for the case when the representative bidder (for whom the bidding strategy is calculated) is the winning high bidder.

92 The automatically extended auction is modelled as a Japanese auction (as done by Bajari and Hortascu, 2000)59. The Japanese auction is modelled like in Part Two, where the valuation 1 n (reservation price) of bidder i is defined by: pi = λCi + (1− λ)si , where Ci = ∑ s j . Private n j=1 j ≠i signals si are drawn from the uniform distribution U∼[0,1]. It is further assumed that bidding is not costly and that there is no fraudulent misconduct on part of the auction house.

2.1.3.1 Model of the Hard Close Auction

One further reason why it is impossible to explain late bidding with standard auction theory is because the theoretical model used for modelling an English auction - the auction format predominantly used by Internet auctions is the Japanese (ascending clock) auction. However, the Japanese auction60 offers no possibility for late bidding because bidders have to log-on to the auction at the beginning of the auction, have to publicise their exit price and cannot re- enter the auction once they have logged-off. The Japanese auction does not represent the rules of the hard-closing Internet auction well, because bidders in hard-closing Internet auctions have the possibility to place bids until the very last moments of the auction. In the following analysis I use a model for the hard-closing auction format that represents the Internet auction more accurately.

The model representing the hard close auction consists of a Japanese auction followed by a second-price sealed-bid auction61. Bidders are obliged to participate in the Japanese auction, but can bid zero. Bids in the Japanese auction are binding. The final price of the Japanese auction is revealed before the beginning of the second-price sealed-bid auction. The second- price sealed-bid auction represents the “sniping”-phase of the auction; i.e. the very last minutes of the auction, when there is no more time to react to bids made.

Late bidding Proposition: The high bidder bids zero in the first round (in the Japanese auction).

59 The automatically extended auction is modelled as a Japanese auction. In reality bidders in automatically extended auctions have the possibility to wait until the very last moments of the auction to post their bids, but due to the extension rule there can be no secret last minute bids. Rivals have the possibility to react to bids. 60 Described and modelled in Part Two. 61 Bajari and Hortascu (2000) use this set-up to model an Ebay auction. 93

When planning his bidding-strategy, a bidder is interested in the case where he is the winner. That is a bidder plans his strategy for the case when he has the highest private signal. In case a bidder is not the winner, his payoff is assumed to be zero.

The decision is looked at from the point of view of a bidder who believes that his rival - the price-determining bidder, i.e. the bidder with the second-highest valuation - has an interdependent valuation. As explained above, when a bidder believes or knows that the price- determining bidder has an independent valuation he has no incentive to bid late.

The proposition is proved by showing that it is a dominant strategy for this bidder to bid zero in period one (the Japanese auction) and to wait until period two (the sniping phase) to bid his valuation. This is true for the case when he himself has an interdependent valuation (the symmetric case) and when he has certainty about his valuation (he is an expert) but his rival has an interdependent valuation (his rival is an amateur).

When the representative bidder has a private valuation and the price-determining rival also has a private valuation – even though the representative high-bidder falsely assumes his rival to have an interdependent valuation – sniping will be of no advantage. The only time a private valuation high-bidder is worse off by sniping than by early bidding is when his private signal is tied with that of his rival (who also has a private valuation). In this case the bidder who submits his bid earlier wins, but this event has a probability equal to zero.

2.1.3.2 Symmetric Model: All bidders have the same λ n... number of bidders at the beginning of the auction k… number of bidders who have already quit the auction λ... measure of how important the common value is to a bidder, 0 ≤ λ ≤ 1, every bidder has the same λ si... private signal of bidder i, the si are uniformly distributed ∼ [0,1] th ek... k observed exit price pi … reservation price (valuation) of bidder i C... common value

94 The auction is carried out in two stages: first a Japanese auction and then a second-price sealed-bid auction. The Japanese auction ends when the penultimate bidder quits the auction, the price at which he does this is the final price. Bids in the Japanese auction are binding.

Bidder i’s valuation: pi = λC + (1− λ)si . The common value is further defined as the mean 1 n private signal of all other bidders: Ci = ∑ si . As explained in Part 2 Chapter 5, bidder i n j= 1 j ≠i only knows his own private signal si , but does not know the private signals of all the other bidders. Bidders estimate the common value in each round.

It is rational for a bidder to make a final bid equal to his reservation price62. However, it might not be rational for a bidder to reveal his valuation to his rival bidders, knowing that they take his valuation into account in the common value. By bidding zero in the Japanese auction and waiting to bid his valuation in the second-price auction, he can keep his valuation secret from his rivals.

Bidders must decide when to place their bid. They are allowed to bid in both stages of the auction in the Japanese auction (called truthful) or in the second-price auction (called sniping). A bidder bases his bidding strategy on the case when he receives the highest signal. A bidder receives payoff zero when he does not win the auction. When a bidder wins, he receives a payoff equal to their final-bid minus the second-highest bid.

Below expected payoffs are calculated when bids are posted truthfully (posted in the Japanese auction) and when bidders snipe (post their bids in the second-price auction). The other bidders are assumed to bid truthfully, when either A or B bids truthfully.

62 See Part One Chapter 2.1.3 for explanations. 95 B Truthful Snipe 1 1− λ  1 1− λ  1  2 − 3λ  1  2 − λ  Truthful   ,     ,   n  n +1 n  n +1 n  2(n +1)  n  2(n +1)  A 1  2 − λ  1  2 − 3λ  1  2 − λ  1  2 − λ  Snipe   ,     ,   n  2(n +1)  n  2(n +1)  n  2(n +1)  n  2(n +1) 

Table 19: Expected Payoffs in case of symmetrical valuations

The expected payoff of a bidder is determined by the probability of winning the auction multiplied by the expected payoff in case of winning the auction.

Bidder A’s expected payoff is higher from sniping than from truthful bidding. The same is true for B. It is therefore a dominant strategy for all bidders to snipe. The equilibrium is (snipe, snipe), which gives the winner the highest possible payoff and correspondingly leads to the lowest seller revenue.

The probability of winning the auction is equal to the probability of being the high-signal holder in the symmetrical case. The high-signal holder always wins the auction. Bidding truthfully or sniping influences the payoff he receives as a winner, but not the chance of winning. This is because a bidder’s valuation is the weighted average of his signal and the common value. The private signal of a high-signal holder is (by definition) higher than his 1 common value. The probability of being the high-signal holder is , which is equal to the n probability of winning. The payoffs when a bidder wins are given in the calculations below. 1 They are then multiplied by the probability of being the winner, which is , and this will n correspond to the numbers found in Table 19 above.

a.) Calculations when all bidders are truthful All bidders bid their honest valuation in the Japanese auction. Bids are made as described above in Part 2 Chapter 5. There is no bidding in the subsequent second-price sealed-bid auction.

96

Winner Payoff: The winner’s payoff is composed of his valuation minus the second-highest bid. Bidder i has a valuation of the form pi = λ *C + (1− λ) * si , therefore the winner’s payoff is calculated as follows:

= λ *C + (1− λ)sn − λC − (1− λ)sn−1

= (1− λ)sn − (1− λ)sn−1

Expected Payoff:  n n −1 E[P]= (1− λ) −   n +1 n +1  1  = (1− λ)   n +1

b.) Calculations when A snipes and B bids truthfully: When A does not participate in the Japanese auction, all (n-1) other bidders believe that there are only (n-1) bidders participating and therefore calculate the common value incorrectly, they underestimate the true common value. The common value is estimated by estimating the upper bound of the distribution of the signals s. This is calculated by using the signal realisations revealed through the exit prices and the number of still active bidders. See Part 2 Chapter 5 for more details on the common value estimation procedure.

When the highest signal (the n-th signal) is missing, the (n-1) mistaken bidders calculate the

Cn−3 , as follows: There are n-1 bidders participating in the Japanese auction. After the (n-3)rd bidder quits the auction, there are still two bidders remaining. They calculate the common value using the (n- 3) lower signals and then estimating the value of the distribution of the two missing signals. k…number of bidders who have quit the auction so far k = n-3

97 1  bˆ + a Cn−3 (k) = s1 + s2 + ... + sn−3 + (n − 2 − k)  n − 2  2   ˆ  1 E[b] + E[sn−1 ] = s1 + s2 + ... + sn−3 +  n − 2  2  1  1 2 n − 3 n − 3 + n −1 E[Cn−3 (k)] =  + + ... + +  n − 2 n +1 n +1 n +1 2(n +1)  1 n(n +1) n + n −1+ n − 2 n − 3 + n −1 =  − +  n − 2 2(n +1) n +1 2(n +1)  1 n(n +1) 6n − 6 2n − 4  =  − +  n − 2 2(n +1) 2(n +1) 2(n +1) 1 n(n +1) − 4n + 2 =   n − 2  2(n +1) 

1  n 2 − 3n + 2  =   n − 2  2(n +1)  (n − 2)(n −1) = 2(n − 2)(n +1) n −1 = 2(n +1)

A does not join the Japanese auction, but observes its outcome and can therefore observe the (n-2) lowest signals, from which he can estimate the distribution of the remaining two signals. He can calculate the common value using the procedure described in Part 2 Chapter 5.6.

1  bˆ + a Cn−2 = s1 + s2 + ... + sn−2 + (n − k)  n −1  2  1  1 2 n − 2 n − 2 n  E[Cn−2 ] =  + + ... + + +  n −1 n +1 n +1 n +1 2(n +1) 2(n +1) 1 n(n +1) n + n −1 2n − 2  =  − +  n −1 2(n +1) n +1 2(n +1)

1  n 2 + n 4n − 2 2n − 2  =  − +  n −1 2(n +1) 2(n +1) 2(n +1)

1  n 2 − n  =   n −1 2(n +1)

98 1 n(n −1) =   n −1 2(n +1) n = 2(n +1)

When A wins, his payoff is determined by:

Payoff = λCn−2 + (1− λ)sn − λCn−3 − (1− λ)sn−1

A’s expected payoff, when he is the winner:

E[P] = λE[Cn−2 ] + (1− λ)E[sn ] − λE[Cn−3 ] − (1− λ)E[sn−1 ] n n n −1 n −1 = λ + (1− λ) − λ − (1− λ) 2(n +1) n +1 2(n +1) n +1 1 1 = λ + (1− λ) 2(n +1) n +1 1 1 = − λ + 2(n +1) n +1 1 1 = − λ n +1 2(n +1)

When B wins, his payoff is determined by:

Payoff = λCn−3 + (1− λ)sn − λCn−2 − (1− λ)sn−1

B’s expected payoff, when he is the winner:

E[P] = λE[Cn−3 ] + (1− λ)E[sn ] − λE[Cn−2 ] − (1− λ)E[sn−1 ] n −1 n n n −1 = λ + (1− λ) − λ − (1− λ) 2(n +1) n +1 2(n +1) n +1 −1 1 = λ + (1− λ) 2(n +1) n +1 3 1 = − λ + 2(n +1) n +1 1 3 = − λ n +1 2(n +1)

99 c.) Calculations when A is truthful and B snipes: Like b.), but payoffs of A and B are reversed. d.) Calculations when all bidders snipe: When no bidders participate in the Japanese auction, the final price is zero. In the subsequent second-price sealed-bid auction naïve bidders could believe that no other bidders are participating and could take therefore take the common value to be zero, but here bidders are forward looking – knowing that sniping is possible – and use the maximum-likelihood method to estimate the common value. The winner’s payoff is thus calculated as follows: ˆ = λCn−2 + (1− λ)sn − λCn−1 − (1− λ)sn−1 n whereby C = (see above) n−2 2(n +1)

The expected winner’s payoff: λ E[P] = (E[s ] − E[s ])(1− ) n n−1 2 n n n −1 n −1 = λ + (1− λ) − λ − (1− λ) 2(n +1) n +1 2(n +1) n +1 1 1 = λ + (1− λ) 2(n +1) n +1

s A’s final bid is: λ A + (1− λ)s 2 A s B’s final bid is: λ B + (1− λ)s 2 B s s s s A wins when λ A + (1− λ)s > λ B + (1− λ)s , i.e. s − λ A > s − λ B . 2 A 2 B A 2 B 2 s s B wins when s − λ A < s − λ B . A 2 B 2 The probability of winning is ½ for each bidder.

2.1.3.3 Expert-Amateur

Bidder i’s valuation is determined by pi = λC + (1− λ)si . There is one bidder with a λ = 0 . He has an independent private valuation and is known as the expert. All other bidders have a 100 λ > 0 , they are amateurs. A bidder’s λ is known by all bidders. This case could for example depict an Internet auction, where there is one person who has an entirely private valuation. When planning his bidding strategy, he forms a belief on the kind of bidders he will encounter in the auction. He assumes for example that the other bidders are merely Internet surfers who develop an ad hoc interest in the good. They have a private estimate of the item’s value, but include the mean valuation of the others in their own valuation. An expert expecting such rivals has to consider carefully at what point in time he should reveal his true valuation.

Amateur Truthful Snipe  1 n −1   1 n   1 n − 2   1 n  p  + λ  , (1− p ) − λ  p  + λ  , (1− p ) − λ  ts   ts   tt   tt    n +1 2(n +1)   n +1 2(n +1)   n +1 2(n +1)   n +1 2(n +1)  Truthful  1 n −1   1 n   1 n −1   1 n  p  + λ  , (1− p ) − λ  p  + λ , (1− p ) − λ  ss   ss   st   st    n +1 2(n +1)   n +1 2(n +1)   n +1 2(n +1)   n +1 2(n +1)  Expert Snipe Table 20: Payoffs in the expert-amateur case. Payoffs shown are expected payoffs.

pss = pst = pts > ptt n p = Prob (s > λ + (1− λ)s ) tt E 2(n +1) M n −1 p = Prob (s > λ + (1− λ)s ) st E 2(n +1) M

As can be seen from the table above, the expert’s payoff is higher when he chooses to snipe than when he bids truthfully, given that the amateur bids truthfully. The payoff of the expert is equally high whether he chooses to snipe or to bid truthfully, given that the amateur snipes. The expert thus has a weakly dominant strategy, to snipe. It is a weakly dominant strategy for the amateur to bid truthfully, because his payoff is slightly higher when all bidders bid truthfully. The equilibrium reached will therefore be (snipe, truthful), which yields the same payoff as the case (snipe, snipe).

101 The amateur’s probability of winning is dependent on n and λ . This is because the amateur includes the other bidder’s private signals in his valuation and by doing so, lowers his valuation in comparison to his private signal. The probability of being the high-signal holder 1 is , but the probability of winning is now higher for the expert than for the amateur n (because the amateur’s λ > 0 is always higher than that of the expert, which is zero). The probability of winning is at least as high for a bidder when he snipes, as when he bids truthfully. a.) Calculations when all bidders are truthful: In this case all bidders participate in the Japanese auction and there is no more bidding in the subsequent second-price sealed-bid auction. The payoffs are as follows,

Expert’s payoff, when the expert wins: sn − λCn−2 − (1− λ)sn−1

Amateur’s payoff when the amateur wins: λCn−2 + (1− λ)sn − sn−1

n C = n−2 2(n +1)

Expert’s payoff when expert wins:

PE = sn − λC(n−2) − (1− λ)sn−1 n n n −1 = − λ − (1− λ) n +1 2(n +1) n +1 1 n −1 n = + λ − λ n +1 n +1 2(n +1) 1 2(n −1) − n = + λ n +1 2(n +1) 1 n − 2 = + λ n +1 2(n +1)

Amateur’s payoff when amateur wins:

PM = λC(n−2) + (1− λ)sn − sn−1 1 n n = + λ − λ n +1 2(n +1) n +1

102 1 n − 2n = + λ n +1 2(n +1) 1 n = − λ n +1 2(n +1)

The final bid of the expert is sE . The expected final bid of the amateur is n λ + (1− λ)s . 2(n +1) M n The expert wins if s > λ + (1− λ)s . E 2(n +1) M n The amateur wins if s < λ + (1− λ)s . E 2(n +1) M

sE is distributed U ∼[0,1]. n  n n  λ + (1− λ)sM is distributed, U ∼ λ ,λ + (1− λ) . 2(n +1)  2(n +1) 2(n +1) 

The probability of winning is dependent on n and on λ . The expert’s probability of winning is larger when λ is larger and n is smaller. The reverse is true for the amateur.

b.) The expert snipes, the others bid truthfully: When only one bidder participates in the Japanese auction, the Japanese auction ends at a price equal to zero, because the rule says that the auction ends when the penultimate bidder quits the auction, which is zero in this case. In the subsequent second-price sealed-bid auction all bidders post a bid equal to their reservation price, pi = λC + (1− λ)si . As no bids were posted in the Japanese auction, bidders could assume that the common value thus is zero, however as forward-looking bidders they assume that it is still possible that other bidders are participating and estimate the common value as described in 2.1.3.2 c.).

n −1 The final bid of the expert is s . The final bid of the amateur is λ (1− λ)s . E 2(n +1) M

When the expert wins, he receives the following payoff:

PE = sn − λCn−3 − (1− λ)sn−1

= E[sn ] − λE[Cn−3 ] − (1− λ)E[sn−1 ] 103 n n −1 n −1 = − λ − (1− λ) n +1 2(n +1) n +1 1 n −1 n −1 = + λ − λ n +1 n +1 2(n −1) 1 n −1 = + λ n +1 2(n +1)

When the amateur wins, he receives the following payoff: n P = λC + (1− λ)s − s , whereby E[C ] = M n−2 n n−1 n−2 2(n +1)

= sn − sn−1 − λsn + λCn−2

The amateur’s gain from winning is λCn−2 + (1− λ)sM and not λCn−3 + (1− λ)sM , because ex post all signals are revealed and he can calculate the common value with full information.

In case the amateur wins, he expects the following payoff:

E[PM ] = E[sn ] − E[sn−1 ] − λE[sn ] + λE[Cn−2 ] n n −1 n n = − − λ + λ n +1 n +1 n +1 2(n +1) 1 2n n = − λ + λ n +1 2(n +1) 2(n +1) 1 n = − λ n +1 2(n +1)

n −1 The final bid of the expert is s . The final-bid of the amateur is λ + (1− λ)s . E 2(n +1) M n −1 The expert wins, if s > λ + (1− λ)s . E 2(n +1) M n −1 The amateur wins, if s < λ + (1− λ)s . E 2(n +1) M

sE is distributed U ∼[0,1].

104 n −1  n −1 n −1  λ + (1− λ)sM is distributed, U ∼ λ ,λ + (1− λ) . 2(n +1)  2(n +1) 2(n +1)  c.) The expert bids truthfully, the amateurs snipe: In this case the Japanese auction takes place with (n-1)-bidders. From the Japanese auction, they calculate the final common value when the (n-3)rd bidder quits the auction. Calculation of the common value is presented above in Chapter 2.1.3.2.

s The final bid of the expert is s . The final bid of the amateur is λ M (1− λ)s . E 2 M

When the expert wins, his payoff is calculated as follows: ˆ PE = sn − λCn−1 − (1− λ)sn−1 s = s − λ n−1 − (1− λ)s n 2 n−1 λ = s − s (1− ) n n−1 2

The expert’s expected payoff in case of winning: λ E[P ] = E[s ] − E[s ](1− ) E n n−1 2 n n −1 λ = − (1− ) n +1 n +1 2 1 λ(n −1) = + n +1 2(n +1) 2 + λ(n −1) = 2(n +1)

When the amateur wins, his expected payoff is calculated as follows:

PM = λCn−2 + (1− λ)sn − sn−1 n C = n−2 2(n +1)

The amateur’s payoff in case of winning: 105 E[PM ] = λE[Cn−2 ] + (1− λ)E[sn ] − E[sn−1 ] n n n −1 = λ + (1− λ) − 2(n +1) n +1 n +1 1 n n = − λ + λ n +1 n +1 2(n +1) 1 n − 2n = + λ n +1 2(n +1) 1 n = − λ n +1 2(n +1)

s The final bid of the expert is s . The final-bid of the amateur is λ M + (1− λ)s . E 2 M s The expert wins, if s > λ M + (1− λ)s . E 2 M s s The amateur wins, if s < λ M + (1− λ)s , i.e. when s < s − λ M . E 2 M E M 2

sE is distributed U ∼[0,1]. s λ s < s − λ M is distributed U ∼ [0,1− ] . E M 2 2 λ λ If s > 1− , then the expert always wins. This event occurs with probability . E 2 2 λ If s < 1− , then the expert wins half the time. This event occurs with probability E 2 1  λ  1−  . 2  2  λ 1 λ 1 λ The probability that the expert wins is thus, + − = + . The probability that the 2 2 4 2 4 1 λ amateur wins is − . 2 4 d.) All bidders snipe: In this case no bids are posted in the Japanese auction, which ends with a final price of zero. Bidders could assume from the outcome of the Japanese auction that there are no other bidders participating, however knowing of the possibility that sniping is possible, they take

106 this into account and estimate the common value using the maximum likelihood method (see above under 2.1.3.2.c.).

The expert’s payoff when he is the winner: ˆ PE = sn − λCn−1 − (1− λ)sn−1 λ = s − s (1− ) n n−1 2

The expert’s expected payoff when winning: λ E[P ] = E[s ] − E[s ](1− ) E n n−1 2 2 + λ(n −1) = 2(n +1)

The amateur’s payoff, when he is the winner:

PM = λCn−2 + (1− λ)sn − sn−1

The expected amateur’s payoff when he wins: E[C ] E[P ] = λ n−2 + (1− λ)E[s ] − E[s ] M 2 n n−1 n n n −1 = λ + (1− λ) − 2(n +1) n +1 n +1 n n 1 = λ − λ + 2(n +1) n +1 n +1 1 n = − λ n +1 2(n +1)

s The final bid of the expert is s . The final-bid of the amateur is λ M + (1− λ)s . E 2 M s The expert wins, if s > λ M + (1− λ)s . E 2 M s s The amateur wins, if s < λ M + (1− λ)s , i.e. if s < s − λ M . E 2 M E M 2 107 sE is distributed U ∼[0,1]. s λ s < s − λ M is distributed, U ∼ [0,1− ] . E M 2 2 λ λ If s > 1− , then the expert always wins. This event occurs with probability . E 2 2 λ If s < 1− , then the expert wins half the time. This event occurs with probability E 2 1  λ  1−  . 2  2  1 λ The probability that the expert wins is thus + . The probability that the amateur wins is 2 4 1 λ − . 2 4

2.1.3.4 Resulting Bidding Behaviour

Late bidding Result: In the model above I show that a bidder will receive higher payoff by bidding zero in period one (during the Japanese auction) and waiting until period two (the sniping period) to bid his true valuation, than by bidding his true valuation in period one.

This is true in the expert-amateur setting; i.e. when a bidder has an independent private valuation and expects his rivals to have some uncertainty with regard to their valuation (λ > 0) . In the symmetric setting, i.e. when all bidders have a valuation composed of a common and a private value element with the same λ , it is better for a bidder to snipe, if his rivals are not sniping; in case the rivals are sniping, the payoff is equal whether a bidder snipes or not. Because all bidders devise their bidding strategy for the case of being the high signal holder, it is expected that all bidders will engage in sniping. The expected seller revenue is equal to: E[s ] E[R ] = λ n−1 + (1− λ)E[s ] HardClose(sniping ) 2 n−1 n −1 n −1 = λ + (1− λ) 2(n +1) n +1 n −1 n −1 n −1 = + λ − λ n +1 2(n +1) n +1

108 n −1 n −1− 2n + 2 n −1 n −1 = + λ = − λ n +1 2(n +1) n +1 2(n +1)

2.1.3.5 Revenue Comparison: Hard Close and Automatically Extended Auction In the automatically extended auction, the revenue would be equal to the case when all bidders bid truthfully:

E[RAutoExt ] = λE[C] + (1− λ)E[sn−1 ]

 1 n − 2  n −1 = λ +  + (1− λ)  2 2n(n +1)  n +1

The revenue in the automatically extended auction is equal to the revenue in the hard close auction when all bidders bid truthfully. It is shown that at least bidders in the hard close auction will engage in sniping, which lowers seller revenue. In turn the hard close auction leads to lower seller revenue than the automatically extended auction. The Ebay auction would thus be expected to yield lower seller revenue than the Amazon auction.

2.1.4 Prestige Value Model One type of interdependent valuation that can be found is that of bidders having a valuation with additive utility. Bidders of this type receive utility from their own private valuation and utility from the valuation a participating expert bidder attaches to the good.

Similar interdependent valuations are used in Krishna (2002, p.126), Izmalkov (2001), and Perry & Reny (2001). An interdependent valuation of this kind might also arise when it is painful for a bidder to lose, that is, when his payoff from losing an auction is negative. It is equivalent to say that a bidder of this kind attaches extra value to winning and this value is thus dependent on the other bidder’s valuation.

A valuation of this kind may be realistic for very rich buyers when bidding for unique goods such as Impressionist art. When a Van Gogh painting is offered at an auction, bidders will most probably have an idea of their maximum willingness to pay, but are likely to be flexible within a certain range – as long their budget constraint is not surpassed. Van Gogh paintings are rarely offered on the market, so that a true fan (someone who values the possession of the

109 painting very highly) with a high budget will adapt his valuation to the “market”, i.e. his rivals’ bids.

A valuation of this kind might also be realistic for goods where the budget constraint is not a strong influence, for example in the case of cheap but unique paraphernalia offered on the Internet.

2.1.4.1 Symmetrical Case Two bidders: Bidder A and bidder B. Two periods. Bidders can bid in period one and/or in period two. Bids made in period one are publicised before period two. The bidder who posts the highest bid wins. The final price is determined by the high-bid of the non-winning bidder.

Each bidder draws a private signal s from U ∼[0,1] before the auction begins. The bidders do not know the signal drawn by the other bidder, they only know the signals are uniformly distributed on [0,b] . The valuations of the two bidders are as follows:

VA = s A +αsB

VB = sB +αs A

s ...private signal V ...valuation

Vit …valuation of bidder in period t b ...bid 1 0 < α < 2

B Early Snipe 1 1 3 5 Early (s − s )(1−α) , (s − s )(1−α) (s − s )(1−α) , (s − s )(1−α) 2 A B 2 B A 8 A B 8 B A A 5 3 1 1 Snipe (s +αs − s ) , (s +αs − s ) (s +αs − s ) , (s +αs − s ) 8 A B B 8 B A A 2 A B B 2 B A A Table 21: Payoff Table for symmetrical bidders

110

The expected payoff is determined by the probability of being the high bidder multiplied by the payoff that this bidder receives when he is the winner.

A has a higher expected payoff from sniping than from truthful bidding, given that B bids early. This is because by bidding in period two, A avoids the prestige-effect of B that drives the price up. A has a dominant strategy to snipe. The same is true for B, respectively. The equilibrium will therefore be (snipe, snipe). This makes it impossible for a bidder to infer anything about the other bidder’s valuation from his bid timing, because in any case a bidder will bid late. Calculations are given below.

The probability of winning is equal to the probability of being the high-signal holder in the cases (snipe, snipe) and (truthful, truthful). This is because both bidders have the same informational structure, when they both choose to bid at the same time. In these two cases the probability of winning is ½ for each bidder and thus expected payoffs are equal to the payoffs given in the respective boxes above multiplied by ½.

When one bidder decides to snipe and the other bids truthfully, the probability of winning is higher for the bidder who snipes than for the truthful bidder. The sniper wins when his signal is greater than his truthful rival’s signal multiplied by (1−α) . The sniper’s probability of winning is greater than that of the truthful rival, becauseα > 0 . This will increase a bidder’s incentive to engage in sniping, thereby strengthening the result given above that the equilibrium outcome will be (snipe, snipe).

a.) Both bidders bid early:

Valuations in the first period: VA1 = s A

VB1 = sB and both bid accordingly.

Second Period:

Now, A forms the belief that B’s valuation VB = sB

B forms the belief that A’s valuation VA = s A

111 A updates his valuation to VA2 = s A +αsB

B updates his valuation to VB2 = sB +αs A and both bid accordingly.

A’s payoff, when he wins = (s A − sB )(1−α)

B’s payoff when he wins = (sB − s A )(1−α) Each bidder’s probability of winning is equal to ½. b.) A snipes, B bids early First Period:

VB1 = sB and B bids accordingly

VA1 = s A , but A does not post a bid

Second Period: bA2 = VA2 = s A +αbB B does not post a bid in the second period.

A’s payoff, when he wins: s A +αsB − sB

A wins if s A > αsB − sB

B’s payoff, when he wins: sB +αs A − s A −αsB = (sB − s A )(1−α)

B wins if s A < αsB − sB

A’s probability of winning is higher than B’s probability of winning.

A wins if s A > sB −αsB , i.e. if s A > (1−α)sB .

s A :U ∼[0,1]

(1−α)sB :U ∼[0,(1−α)] , because sB :U ∼[0,1]

If s A > (1−α) , A always wins. Prob[s A > (1−α)]=1− (1−α)= α . 1−α If s < (1−α) , A wins half of the time. Prob[s < (1−α)]= . A A 2 1−α 1+α Prob[s > (1−α)s ]=α + = A B 2 2

112 1+α 1+α The probability that A wins is and the probability that B wins is 1− . 2 2 Expected probability that A will win: 1+ E[α] 1+ 0.25 1.25 5 E[Prob[s A > (1−α)sB ]] = E = = = = 0.625  2  2 2 8 Expected probability that B will win:  1+ E[α] 1+ 0.25 1.25 5 3 E[Prob[s A < (1−α)sB ]] = E 1− = 1− = 1− = 1− = = 0.375  2  2 2 8 8 c.) A bids early, B snipes

First Period: bA1 = s A B does not post a bid.

Second Period:

B updates his valuation to VB2 = sB +αs A = sB +αbA . A does not post another bid.

A’s payoff when he wins: (s A − sB )(1−α) . A wins if s A > sB +αs A , i.e. if s A −αs A > sB .

B’s payoff when he wins: (sB − sB )(1−α) . B wins if sB +αs A > s A , i.e. if sB > s A −αs A . 1+α 5 B’s probability of winning is , his expected probability of winning is . 2 8 1+α 3 A’s probability of winning is 1− , his expected probability of winning is . 2 8 For calculations see b.) above. d.) Both bidders snipe 1st Period: no bids nd 2 Period: bA2 = s A and bB2 = sB

A’s Payoff, when he wins, i.e. if s A > sB : s A +αsB − sB

B’s Payoff, when he wins, i.e. if s A < sB : sB +αs A − s A A wins with probability ½, B wins with probability ½.

113 2.1.4.2 Expert-Amateur Case In the section below, bidding behaviour in the prestige value model is looked at for the case where one bidder has certainty about his valuation, he is known as the expert; and the other bidder is uncertain about his valuation, he is an amateur. Both bidders have a valuation of the type presented above: Vi = si +αs j , but the expert has an α = 0 , while the amateur has an α > 0 . This case is realistic for Internet auctions, where bidders are often very different and can be thought to have asymmetrical valuations. One bidder, sure of his valuation, competes with a bidder who is uncertain about his valuation and for whom it is important how highly the expert values the good.

Two bidders: an expert E and an amateur M Two periods. Bidders can bid in period one and/or in period two. Bids made in period one are publicised before period two. The valuations of the two bidders are as follows:

VM = sM +αsE

VE = sE b ...bid s ...private signal V ... valuation of bidder i in period t 1 0 ≤ α < 2

In order to find out whether it is more profitable for the expert to bid truthfully or to engage in sniping, his payoffs are calculated and presented in the table below. The corresponding calculations can be found from a.) to d.).

Amateur Truthful Sniping 3 5 3 5 Truthful (s − s −αs ) , (s +αs − s ) (s − s −αs ) , (s +αs − s ) 8 E M E 8 M E E 8 E M E 8 M E E Expert 1 1 1 1 Sniping (s − s ) , (s +αs − s ) (s − s ) , (s +αs − s ) 2 E M 2 M E E 2 E M 2 M E E Table 22: Expected payoff table: Prestige value model for the expert-amateur case.

114 The expert benefits from sniping. His expected payoff is higher. By bidding in period two, the expert can recreate a second-price sealed-bid auction and avoids the prestige-effect of the amateur that drives the price up. It is a dominant strategy for the expert to engage in sniping. The same is true for the amateur. This makes it impossible for a bidder to make an inference on the rival’s valuation, because in any case the rival will snipe.

The probability of winning is higher when a bidder engages in sniping than when he bids truthfully. Calculations can be found below from a.) to d.).

Calculations: a.) Calculations when both bidders bid early

First Period: bE1 = VE1 = sE

bM1 = VE1 = sM

Second Period:

Amateur updates valuation to VM 2 = sM +αsE and bids accordingly.

Final Price:

If the expert wins the final price is P = sM +αsE .

If the amateur wins the final price is P = sE .

Expert’s payoff when he wins: sE − sM −αsE .

Amateur’s payoff when he wins: sM +αsE − sE = sM − (1−α)sE .

If sM +αsE > sE , i.e. sM > sE −αsE , then the amateur wins.

If sE > sM +αsE , i.e. sM < sE −αsE , then the expert wins.

1+α 3 The expert’s probability of winning is 1− , his expected probability of winning is . 2 8 1+α 5 The amateur’s probability of winning is , his expected probability of winning is . 2 8 For calculations see 2.1.4.1 b.) above.

115 b.) Calculations when the amateur bids early and the expert bids late First Period: bM1 = VM = sM The expert does not post a bid.

Second Period: bE 2 = VE = sE

Final price if expert wins: sM

Final price if amateur wins: sE

Expert’s payoff if he wins: sE − sM . Expert wins if sE > sM .

Amateur’s payoff if he wins: sM +αsE − sE . Amateur wins if sE < sM .

Both bidders have a probability of winning of ½. c.) Calculations when the expert bids early and the amateur snipes First Period: bE1 = VE = sE Amateur does not post a bid.

Second Period:

Amateur updates his valuation to bM 2 = VM = sM +αbE . Expert does not post a bid in the second period.

Final Price: sM +αbE

Expert’s Payoff: sE − sM −αsE , E wins if sM < sE −αsE .

Amateur’s Payoff: sM +αsE − sE , wins if sE (1−α) > sM .

M wins if sM > sE (1−α) . E wins if sM < sE (1−α) . 1+α 3 The expert’s probability of winning is 1− , his expected probability of winning is . 2 8 1+α 5 The amateur’s probability of winning is , his expected probability of winning is . 2 8 For calculations see 2.1.4.1 b.) above.

116 d.) Calculations when both bidders snipe First Period: no bids Second Period: bE 2 = VE = sE and bM 2 = VM = sM

Final Price: sM

Expert’s Payoff when he wins: sE − sM . He wins if sE > sM .

Amateur’s payoff when he wins: sM +αsE − sE . He wins if sM > sE . Each bidder’s probability of winning is ½.

2.1.4.3 Result of Prestige Value Auctions Irrespective of whether bidders have symmetrical or asymmetrical valuations, all bidders will engage in sniping and thus the equilibrium final price in the prestige-value auction will always be equal to s2ndHighest . The equilibrium seller’s payoff is thus equal to that of a second- price sealed-bid auction.

2.1.4.4 Payoffs in the Automatically Extended Auction a.) Symmetrical Valuations With α > 0: The final price and thus the seller revenue can be infinitely high in an Internet auction ending by automatic extension. In an Internet auction of the Amazon type, there are not only two periods in which to post bids, but instead the auction continues as long as bids are posted.

When bidders have a valuation of the type Vi = si +αs j , bidders will want to revise their valuation upwards every period. This process can continue infinitely.

Imagine for example the following scenario in the Japanese auction: In the beginning of the auction a bidder i plans to stay in the auction for at least until the counter reaches his private signal. But when the current price is equal to si − minimum increment, bidder i can infer that the high bidder’s valuation must be greater than or equal to si (because the current price is calculated as the second highest bid plus a minimum increment). Bidder i thus updates his valuation to Vi = si +αs j , whereby he can deduce that s j ≥ si , therefore updates his valuation toVi = si +αsi . The high bidder also updates his valuation. The auction continues infinitely,

117 thereby raising the seller revenue to extreme levels. A self-reinforcement effect of this kind creates a clear seller preference for auctions with automatic extension. b.) Asymmetrical valuations

In this case bidders have valuations of the kind Vi = si +αs j , but not all bidders have the same α value, because at least one bidder has an α = 0 . Here there are two bidders, the amateur with α > 0 and the expert E with α = 0 . In the beginning of the auction, both bidders plan to stay active at least until the counter reaches their private signal. When the current price is equal to sM − min. increment, the amateur knows that the expert’s signal must be greater than or equal to his own, sE ≥ sM . The amateur then updates his valuation to: VM = sM +αsE . The auction ends when the first bidder exits the auction. This is the case when the current price is equal to sE or when the minimum increment is smaller than VM . The auction ends when the first of the two ending conditions is reached. Interdependent valuations of the kind presented above create a strong incentive for experts to engage in sniping, because the amateur - when informed about the expert’s valuation - can revise his valuation to values higher than that of the expert.

2.1.5 Payoff Comparison: Hard Close and Automatically Extended Auction

In the model 2.1.3, where bidders have valuations of the type pi = λC + (1− λ)si , the equilibrium outcome is that all bidders engage in sniping. The seller revenue from the hard close auction is higher than that from the automatically extended auction. This is true for both the symmetrical and the asymmetrical case.

In the prestige value model the seller revenue from the equilibrium outcome in the hard close auction is lower than that from the automatically extended auction. This is true irrespective of whether bidders have symmetrical or asymmetrical valuations (shown above).

2.1.6 Milgrom-Weber Model

2.1.6.1 Bidding in the hard close auction The hard close and the automatically extended auction are both sub-variants of the English auction. If we wish to compare the two formats in the general symmetrical model of interdependent valuations, as proposed by Milgrom-Weber, we can use their model of the

118 Japanese auction63 to model the automatically extended auction (see above for the reasoning). The hard close auction is characterised by the fact, that the last and thus highest bids can be submitted secretly, unobservable to the rest of the bidders. The hard close auction can be modelled as the Japanese auction with one modification: the bidder with the highest private signal has the possibility to participate secretly in the Japanese auction. In this case the Japanese auction is of the usual kind, except for the fact that all bidders (other than the high- bidder) erroneously believe that there are only (n-1)-bidders participating in the auction. When calculating their valuation based upon the exit prices observed, they are not able to take the highest signal into account, as it is unknown to them. All bidders except the high-bidder therefore believe to have a lower valuation than they actually have and will exit too soon. The high-signal bidder will win the auction, but at a final price lower than in the case when his participation is observable.

Modifying the Japanese auction, so that the high-signal bidder can participate secretly, leads to lower seller revenue, because all other bidders calculate their valuation under the false belief that there are only (n-1) bidders participating, who have the lower (n-1) signals drawn from the distribution.

If the high-signal owner has the possibility to participate secretly, he will choose to do so, because it lowers the final price, thereby increasing his payoff. It is the interdependency of signals that creates an incentive for the high-bidder to hold back his signal. The hard-closing auction of the Ebay type allows bidders to hold back their signal. When a bidder decides whether to participate openly or secretly, he will base his decision on the assumption that he is the high-signal owner. In all other cases he does not have the possibility to attain a positive payoff anyway. That is why the decision is looked at from the perspective of the high-signal owner.

Because all bidders base their bidding-decision on the assumption that they are the high-signal owner, that would result in all bidders participating secretly. In this case the outcome would resemble that of the second-price sealed-bid auction in the Milgrom-Weber model. The proof for why the expected final price is lower when the highest signal is not revealed is similar to the proof presented in Milgrom-Weber (1982) for why the Japanese auction leads to higher

63 For an explanation of the Milgrom-Weber Model see Part One Chapter 3.3.2. 119 seller revenue than the second-price auction (and to the proof of why it is more profitable for the seller to reveal public information).

A bidder’s valuation is a function of all bidders’ quality signals X 1 , X 2 ,..., X n . Vi := u(X i ) .

The function u is increasing in all its arguments and symmetric in {.X j } j≠i

Bidder 1 observes the quality signal X 1 .

Y1 ,Y2 ,...,YN −1 are defined to be the signals in descending order of X 2 , X 3 ,..., X N respectively.

Therefore bidder 1 has a valuation V1 = u(X 1 ,Y1...,YN −1 ).

Affiliation of the signals (X 1 ,Y) implies that the conditional expected values of V1 ,

w(x1 , y1 , y2 ) := E[V1 X 1 = x1 , Y1 = y1 ,Y2 = y2 ] and v(y1 , y2 ) := E[V1 Y1 = y1 , Y2 = y2 ] are strictly monotonically increasing in all their arguments. v(y1 , y2 ) is the conditional valuation of bidder 1 after having observed the signals Y1 = y1 and Y2 = y2 . w(x1 , y1 , y2 ) is the conditional valuation of bidder 1 after having observed the signal realizations X 1 = x1 ,

Y1 = y1 , Y2 = y2 .

Expected price in the normal Japanese auction compared to the secret Japanese auction:

E[PJap ]= E[w(Y1 ,Y1 , X 1 ){X 1 > Y1}]

≥ E[v(Y2 ,Y2 ){Y1 > Y2 }]

= E[PSecret ].

When one bidder can keep his valuation secret and this is the bidder with the highest signal, all other bidders form a mistakenly lower expected value of the good. The second-highest bidder determines the price and he will bid too low in the secret auction (hard close auction). In the automatically extended auction, where no bidder can keep his signal secret, the second- highest bidder will be able to take account of the highest signal when forming his valuation. It follows from the assumption that u is increasing in all its arguments, that the expected price is lower in the hard closing auction than in the automatically extended auction.

120 2.1.7 General Prediction for Interdependent Valuations In the general model, in the prestige value model and in the Milgrom-Weber model bidders in the hard close auction bid zero in the first period (the Japanese auction) and bid their true valuation in the sniping period. A bidder holds back his valuation until the sniping period when he knows (or believes) that his rivals do not have independent private valuations, but are instead uncertain about their valuation. The advantage of late bidding is that the expected price is lowered and the expected payoff increased, without changing the probability of winning the auction.

In the general bidding model, the prestige-value model, and the Milgrom-Weber Model, the expected auction revenue of the hard close auction is higher than that in the automatically extended auction.

2.1.8 Late bidding with Respect to the Ending-Rule Late bidding (sniping) is expected in the hard close auction when bidders expect the second- highest bidder to have a valuation of λ greater than zero (shown above in Part Five Chapters 2.1.3, 2.1.4 and 2.1.6).

No late bidding is expected in the automatically extended auction.

2.1.9 Late Bidding According to Good Type No late bidding is expected in automatically extended auctions. Predictions for late bidding in hard close auctions for computers, cars and paintings: a.) Computers: Bidders are expected to have a λ equal to zero and believe others to have a λ equal to zero, too. Valuations are expected to lie within a very narrow distribution. No late bidding is expected. b.) Cars: Some bidders are expected to have interdependent valuations, due to uncertainty about their valuation. Late Bidding is expected. c.) Art: Many bidders are expected to have interdependent valuations due to fashion and prestige reasons. Late Bidding is expected.

121 2.2 Seller’s Choice of Ending-Rule

Clearly, sellers prefer a hard close to an automatically extended ending for selling computers. In case of cars, there are more successful auctions ending by automatic extension than hard close and the same is true for art auctions.

The seller’s preference for auctions ending by automatic extension can be explained with the results from Section 2.1 on late bidding. In this section it is shown that an auction ending by hard close yields lower seller revenue than an automatically extended auction. Based on this result, sellers are expected to prefer automatically extended auctions.

Sellers prefer the hard close ending in case of computers, because computers are readily available at a known market price. Computer auctions do not conform to the model presented in Section 2.1, because participating bidders have no uncertainty about the true value. The reason why sellers prefer the hard close ending for computers is because buyers aiming for the lowest possible price will prefer shorter and time-constrained auctions that accumulate as few rival bidders as possible.

122 3. Empirical Investigation

As introduced in Part Five Chapter Two, economists have begun to study Internet auctions. Bajari and Hortacsu (2000) use Ebay coin auctions to estimate the winner’s curse and the expected profit necessary to motivate entry. Katkar and Lucking-Reiley (2001) study Ebay Pokemon auctions to find a seller’s motivation for using reserve prices.

Roth and Ockenfels (2000) were the first to publish empirical research on the late bidding phenomenon. They study the last twelve hours of Ebay and Amazon auctions and find that many bids are submitted toward the end of these twelve hours. Furthermore, they find time- invariance when plotting the cumulative number of bids submitted against time for the last twelve hours, six hours, three hours, last hour, and last ten minutes.

In the following section I empirically investigate my theoretical late bidding predictions (presented in Part Five Chapter Two). Late bidding is expected in the hard close auction but not in the automatically extended auction. Especially in the case of asymmetrical valuations (the Expert-Amateur model), the expert is expected to enter the hard-closing auction in the very last moments of the auction. In all three models the expected seller’s revenue is higher in the automatically extended auction than in the hard close auction. Therefore sellers are expected to prefer the automatically extended auction.

Yahoo auctions are chosen for investigating the theoretical predictions, because Yahoo offers the seller the possibility to choose between the hard close and the automatically extended auction. Using Yahoo data, I can compare bidding behaviour for two different ending rules and determine which ending rule the seller chooses more often. Data is taken from three categories of goods in order to further differentiate the results according to the type of good.

As noted in Part Five Chapter 2.1.9, different types of goods imply different bidder valuations. Computer buyers are expected to have little uncertainty about their valuation; λ = 0 , so late bidding is not expected. Car buyers are expected to have some uncertainty about their valuation – asymmetrical valuations (Expert-Amateur case) are expected resulting in late bidding by at least some bidders (the experts). Buyers of Art sold on Yahoo auctions are expected to have some uncertainty about their valuation due to reputational effects,

123 therefore the behaviour is expected according to the prestige value model – possibly with asymmetrical valuations. Late bidding is expected.

A sample of three hundred Yahoo auctions – completed between November 2000 and January 2001 – downloaded from the Yahoo website, were included in the data-analysis. Only auctions with at least two bidders were included. Hundred auctions were taken from each of three categories: computers, cars and art. Computer auctions were taken from the sub- categories: laptops and personal computers; cars from the sub-category general, and art from the sub-categories paintings and drawings.

The following central hypotheses were tested empirically: Hypothesis 1: Internet auctions are characterised by late bidding, where late bidding means that there is a strong over-proportional price increase at the end of the auction. Hypothesis 2: The over-proportional price increase toward the auction end is stronger for auctions with a hard close than for those with an automatically extended ending. Hypothesis 3: There is more late bidding when there is uncertainty about the value of the goods, therefore more late bidding in art than in computer-auctions. Hypothesis 4: The winning bidder enters the auction shortly before the auction end. Hypothesis 5: The winning bid is posted as a proxy bid. Hypothesis 6: Sellers prefer automatically extended auctions.

3.1 Late Bidding

3.1.1 Existence of Late bidding Hypothesis 1: Internet auctions are characterised by late bidding, where late bidding means that there is a strong over-proportional price increase at the auction end.

3.1.1.1 Complete Auction Duration Hypothesis 1 is tested by plotting the bidding path, the current price against time. Hundred auctions were surveyed for each of the three product groups. The seller is allowed to choose the auction duration; therefore auctions are of different durations. The starting and final price was also different for almost every auction surveyed. The different time lengths and different minimum and end prices were made comparable by setting the final price equal to one and the minimum price chosen by the seller equal to zero. On the x-axis the starting time was

124 normalised to zero and the end time set equal to one. The auction time duration was then split into hundred intervals from zero to one, i.e. intervals from 0, 0.01, 0.02, 0.03…to 1. The y- axis in the graphs below represent the increase in the normalised price from one period to the next, whereby the minimum price in period 0.0 was taken as 0 and the final price in period 1.0 was taken as one.

Observation 1: Internet auctions are characterised by late bidding; late bidding meaning that there is a strong over-proportional price increase at the auction end. This is true for all three categories of goods. The bidding paths for computers, art and cars are shown below. The price increase is strongest in the last hundredth of the auction duration for all three categories of goods.

Cars, Art, and Computers

0,25

0,2 Cars

0,15 Art Computer crease n 0,1 ce I i r 0,05 P

0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time Figure 3

Computers

0,25 0,2 0,15 crease n

e I 0,1 c i r

P 0,05 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time

Figure 4

125

Cars

0,25 0,2

crease 0,15 0,1

Price In 0,05 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Time Figure 5

Art

0,25

0,2 0,15 ease

r 0,1 c In 0,05 0 Price 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time Figure 6

3.1.1.2 Last Twelve Hours Auction durations vary widely from only one day to twelve days, it is thus interesting to find out how high the price is twelve hours before the auction end and to magnify the time period right before the auction end.

In the graphs below, the final price is normalised to one and the minimum price chosen by the seller set to zero. This method makes auctions with different starting and final prices comparable. The bidding curves shown in the graphs below represent the mean bidding curve. Out of the hundred auctions in each category of goods, fifty were hard close and fifty automatically extended auctions.

126

Last Twelve Hours

1 0,9 0,8 0,7 Cars

e 0,6 c i 0,5 Computers

Pr 0,4 Art 0,3 0,2 0,1 0 0:00 2:24 4:48 7:12 9:36 12:00

Time

Figure 7

Observing only the last twelve hours of the average auction path, we find that the price increases very strongly shortly before the auction ends. This is especially true for art auctions: twelve hours before the auction end, the current-price has only reached 52% of its final price on average.

Last Hour

1,00 0,90 Cars

e 0,80 c i Computers

Pr 0,70 Art 0,60 0,50 11:00 11:12 11:24 11:36 11:48 12:00 Time

Figure 8

One hour before the auction end, the current price has only reached 73% of the final price in the average art auction.

3.1.2 Late bidding: Dependency on Ending-Rule

Hypothesis 2: The over-proportional price increase toward the auction end is stronger for auctions with a hard close than for those with an automatically extended ending.

127 3.1.2.1 Complete Bidding-Path In the graphs below, 0 indicates hard-closing auctions, 1 indicates automatically extended auctions. a.) Art

Art

1 0,9 0,8 0,7

e 0,6 Art 0 c i 0,5

Pr 0,4 Art 1 0,3 0,2 0,1 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time

Figure 9

The mean bidding curve of hard closing and automatically extended art auctions are rather similar. In both cases the bidding curve has the steepest rise at the end of the auction duration. Sniping seems to be prevalent in all kinds of art auctions. b.) Cars

Cars

1 0,9 0,8 0,7 e 0,6 Cars 0 c i 0,5

Pr 0,4 Cars 1 0,3 0,2 0,1 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time

Figure 10

The mean bidding curve of car auctions with a hard close and car auctions with automatic extension differ significantly. In auctions with automatic extension the current high bid rises quickly (after about a tenth of the auction duration) to 40% of its final price. In auctions with 128 a hard close, the steepest price rise takes place close to the end of the auction. Sniping occurs with significantly higher intensity in hard closing car auctions than those ending by automatic extension. c.) Computers

Computers

1 0,9 0,8 0,7

e 0,6 Computer 0 c i 0,5

Pr 0,4 Computer 1 0,3 0,2 0,1 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Time

Figure 11

The largest increase in the current high bid occurs towards the very end of the auction. That is, there is significant late bidding on Yahoo auctions. The amount of late bidding is slightly higher for automatically extended auctions.

Observation 2: Late bidding is stronger for hard closing than automatically extended car auctions. The opposite is true for art auctions.

When observing the complete bidding path, we find that the prediction that hard close auctions lead to more late bidding than automatically extended auctions does not prove to be correct for computer and art auctions. Hard closing auctions clearly lead to late bidding (the bidding path lies below the 45° line until the very end of the auction duration), but so do automatically extended auctions! The theoretical prediction corresponds to the empirical findings regarding car auctions: there is significantly more late bidding in hard closing than automatically extended auctions. Computer auctions show a little more late bidding for automatically extended auctions.

Explanations for the empirical finding that bidders do not treat automatically extended auctions as expected, could lie in bidder irrationality (inexperience) or in the usage of a “wrong” model. Before this question is analysed further the hypothesis is tested again, but this 129 time only for the bidding path in the last twelve hours of the auction duration. As stated above, auction durations vary widely, it is therefore interesting to magnify the time period right before the end. Roth and Ockenfels (2000) studied the cumulative number of bids submitted in the last twelve hours of hundreds of Ebay and Amazon auctions. They find that significantly more late bids are submitted in Ebay than in Amazon auctions. Here in contrast we are not looking at the cumulative number of bids submitted, but at the price path plotted against time.

3.1.2.2 Last Twelve Hours

Last 12 Hours

1 0,9 Cars 0 0,8 Cars 1 0,7 Computers 0 0,6 Price Computers 1 0,5 Art 0 0,4 Art 1 0,3 0:00 3:00 6:00 9:00 12:00 Time

Figure 12

The bidding path in the last twelve hours shows the same results as the complete auction path: the theoretical prediction that there is more late bidding in hard-closing than in automatically extended auctions is true for cars, but the opposite is true in the case of art. Computer auctions show little difference in late bidding with respect to the ending rule.

3.1.2.3 Reasons for Late Bidding in Automatically Extended Auctions When bidders do not expect their rivals to come back in the last few minutes of the auction, that is when they expect their rivals to treat the automatically extended auction just like a hard close auction, then there is no need to bid early and then there is a late bidding incentive just like in a hard close auction. This could be realistic in an expert-amateur scenario where the amateurs do not foresee that the experts might post late bids that would in turn raise their own valuation. Naïve amateurs could create such a result. Another explanation could be a high cost for amateurs to return to the auction at the tentative auction end in order to check whether they were overbid. If this cost is very high and experts are aware of this, they will engage in late bidding just like in a hard close auction. Late bidding in the automatically extended 130 auction is only rationally justifiable when at least some of the bidders are either naïve or have very high costs of late bidding that deter them from doing so.

Empirical findings support the proposition that many bidders do not update their valuation in the very last minutes of automatically extended Yahoo auctions. For example, only two out of the fifty automatically extended computer auctions showed bidding in the last five minutes of the auction (only when there are bids in the last five minutes of the auction, does the extension time come into play).

3.1.3 Late bidding: According To Type of Good

Hypothesis 3: There is more late bidding when there is uncertainty about the value of the goods, therefore more late bidding in art than in computer auctions.

Bidders can be assumed to have very little uncertainty about the value of a computer, some uncertainty with respect to the value (quality) of a car and a lot of uncertainty about the common value (market value and prestige value) of art.

Observation 3: There is far more late bidding in art than in car or computer auctions.

1 0,9 0,8 0,7 Art 0,6 Computers e c i 0,5 Cars

Pr 0,4 0,3 0,2 0,1 0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 Time Figure 13

131

Automatically Extended Auctions

1 0,8 Art 1

e 0,6 c i Computer 1

Pr 0,4 Cars 1 0,2 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time

Figure 14

Hard Close Auctions

1

0,8 Art 0

e 0,6

c i Computer 0

Pr 0,4 Cars 0 0,2

0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Time Figure 15

3.1.3.1 Art: Strongest Late bidding The goods sold in the category art are paintings by unknown painters, often imitations of famous paintings. Their value cannot be found in a catalogue, so that there is some uncertainty about the “market value”. When paintings are not by someone “famous”, it might be important to a buyer whether other people also think that the artwork is beautiful. A bidder might allocate a personal valuation to a painting, but is ready to pay more if others are also interested in the object.

In the case of asymmetrical valuations, whereby amateurs have a prestige value, experts (having a completely private valuation) will be especially careful to disclose their valuation to amateurs, because not only do they risk having to pay a higher price, as in the case of the general bidding model (presented in Part Five Chapter 2.1.3) but also do they risk losing the object to the prestige value bidder. The probability of winning is dramatically lowered when 132 an expert discloses his valuation to an amateur with a prestige value (as presented in Part Five Chapter 2.1.4).

3.1.3.2 Computers: Late bidding Similar For Both Ending Rules

Observation 4: Both hard-closing and automatically extended computer auctions are characterised by late bidding.

Computer prices are well known. Computers in the survey are generally “second-hand” even though they are often described as being “brand-new”.

Computers are a readily available good for which prices are well known. Buyers thus have little uncertainty about the value of a computer. There is some uncertainty regarding the quality of the computer, but a bidder cannot assume a competing bidder has better information about a particular computer than he does himself. Assuming that bidders have little or no uncertainty with respect to their valuation of the computer and assume the same for their rivals, bidders post their bids early under both ending rules: there is no strategic incentive to delay bidding when a bidder has a private valuation and assumes that his rivals also have private valuations.

One reason why bidders might nonetheless engage in late bidding is that computers are not a unique good, but are available in unlimited quantity. Bidders know the market value and can base their own valuation on the market value. The Internet offers the possibility to find a computer at a low price, particularly if – by chance – one happens to be the only one to notice the “cheap computer”. The lack of scarcity of computers eliminates the need for bidding early: a bidder can follow a number of computer auctions simultaneously, choosing the auction with the lowest current price and the least remaining time. Delaying the bid can be seen as a strategic decision in terms of the option value of finding an even cheaper computer.

Computers are readily available; therefore a buyer will not be prone to revising his bid upwards after observing last-minute bid flurries.

133 3.1.3.3 Late bidding In Car Auctions: Strongly Dependent On Ending-Rule

The goods sold in the category cars are used vehicles, some of which are old-timers. The value of used cars can be found in catalogues and can be compared with prices charged by certified dealers. The value of a car does however depend strongly on its condition, which is unobservable by bidders on the Internet. Whereas real dealers might provide certification for the car’s quality, the cars sold on the Internet do not come with a certification. Some bidders will be better informed about the value of a used car than others.

Cars are the only type of good where automatically extended auctions are characterised by a lot less late bidding than hard close auctions. Reasons for the unexpected late bidding in automatically extended computer and art auctions are discussed in Chapter 3.1.2.3. Possible reasons are high costs of returning to an auction in its last moments and naiveté of the bidders with uncertain valuations (i.e. the amateurs). Cars conform better to the theoretical predictions, because cars differ from (used) computers and art (by mostly unknown artists) in that they are far more expensive – so that the costs of returning to the auction in the last few moments to make possible updates can be assumed to be negligible. The high price of a car makes bidders believe that competing bidders will follow the auction very closely and bids might be posted at any time. Due to the high price of cars, the minimum increment is higher in absolute terms. If the bidder with the highest private signal engages in late bidding but lower valuing bidders bid early, it is possible that a rival bidder submits a bid just below the high bidder’s valuation, so that the current bid plus the minimum increment would now surpass the high-bidder’s valuation. In the case of high minimum increments (as is the case with expensive items like cars) late bidding lowers the probability of winning, when the rivals do not engage in late bidding.

In an automatically extended auction, a bidder with foresight knows that he cannot hide his valuation from his rivals, because the “extension time” gives rivals – with interdependent valuations - time to react to them. Due to the lower probability of winning an auction in case of high minimum increments, bidders are not expected to engage in late bidding in automatically extended car auctions.

134 3.1.4 Operational Investigation of Late Bidding In the section above the dynamic price-formation in Yahoo auctions was presented; price was plotted against time. It turns out that the price increases very strongly and over-proportionally towards the very end of the auction. In order to provide an in-depth treatment of the empirical study of late bidding, the price-formation is also considered operationally.

In the following section late bidding is investigated operationally: the current price is plotted against the last twenty bids in the auction course. As before, the price is normalised from zero (the starting price) to one (the final price). The average bidding curves – using the same data as above - are shown, separated according to good type and ending rule. The curve cuts the y- axis at the fraction of the price that is reached at the twentieth bid before the auction ends.

Operational Investigation of the last twenty bids made:

Hard Close - Operational

1 0,9 0,8 0,7 0,6 Art 0 0,5 Cars 0

Price 0,4 Computers 0 0,3 0,2 0,1 0 135791113151719 Last Twenty Bids

Figure 16

Auto. Extended Auctions - Operational

1 0,9 0,8 0,7 0,6 Art 1 0,5 Cars 1 Price 0,4 Computers 1 0,3 0,2 0,1 0 135791113151719 Last Twenty Bids

Figure 17

135

1 0,9 0,8 Computers 0 0,7 Computers 1 0,6 e Cars 0

c i 0,5

Pr Cars 1 0,4 0,3 Art 0 0,2 Art 1 0,1 0 135791113151719

Last Twenty Bids

Figure 18

As observed in the dynamic bidding paths (in Chapters 3.1.1, 3.1.2 and 3.1.3), the operational bidding path also shows that the price increases most strongly, over-proportionally towards the end. Furthermore, conforming to our previous results, art auctions show stronger late bidding than do cars and computers. The operational bidding paths confirm hypothesis one and three. Hypothesis two is not confirmed for art and computers, as in the case of the dynamic bidding path.

3.2 Time-Invariance

In their work on Internet auctions, Roth and Ockenfels (2000) find an interesting result. They find that Ebay and Amazon auctions are time-invariant, that is the cumulative number of submitted bids plotted against time follows a similar pattern during the last twelve hours, last six hours, last three hours, last hour, last thirty minutes and last ten minutes before the auction end. I tested whether Yahoo auctions are also time-invariant.

The graphs below show the cumulative number of bids submitted (the number of bids submitted until a given point in time as a part of the total amount of bids submitted during the whole auction duration). The high bid of every auction in the sample was standardised to one for the relevant time frame. The time was then split into deciles. In the case of the

136 automatically extended auctions, the end was taken as the tentative end, so that automatic extensions – as long as there were no further bids during the extension - did not change the auction end. That explains why the curve for the last ten minutes is not flat in the last five minutes, even though the ending-rule specifies that the last five minutes have to be bid-free.

Observation 5: Hard-closing auctions show time-invariance with respect to the bidding path. Automatically extended auctions produce only a weak form of time-invariant bidding paths.

Computers Hard Close

1 0,9 0,8 12h 0,7 0,6 6h

ubmitted 0,5 0,4 3h 0,3 0,2 1h

Bids S 0,1 0 30min

0 1 2 3 4 5 6 7 8 9 10 10min Time (in deciles) Figure 19

Computers Auto Extension 1

d 0,9 12h

e

t 0,8

it 0,7 6h 0,6 bm 0,5 3h u 0,4 S 0,3 1h

ds 0,2 i

B 0,1 30min 0 012345678910 10min

Time (in deciles) Figure 20

Cars Hard Close

1

d 0,9 12h e

t 0,8 it 0,7 6h 0,6 bm 0,5 u 0,4 3h S 0,3 1h

ds

i 0,2

B 0,1 0 30 min 012345678910 10 min Time (in deciles) Figure 21 137

Cars Auto Extension

1

d 0,9 12h 0,8

tte i 0,7 6h

m 0,6 b 0,5 u 3h 0,4 S 0,3 1h ds

i 0,2

B 0,1 30 min 0 012345678910 10 min Time (in deciles) Figure 22

Art Hard Close 1

dt 0,9 0,8 12h tte

i 0,7 0,6 6h

bm 0,5

u 0,4 3h

S 0,3 s 0,2 1h d i 0,1 B 0 30 min 012345678910 10 min Time (in deciles) Figure 23

Art Auto Extension 1 d 0,9 12h 0,8 tte i 0,7 6h m 0,6

b 0,5 3h u 0,4 S 0,3 1h 0,2 ds i 0,1

B 30 min 0 10 min 012345678910 Time in deciles Figure 24

The investigation with respect to time-invariance shows that hard close computer and art auctions show time-invariance and so do hard close car auctions, but slightly weaker. None of the automatically extended auctions show time-invariance. Three hundred auctions were surveyed in total, thus fifty in each of the six categories - split according to good type and ending rule. It would be interesting to check whether taking a larger sample would also lead to time-invariance for automatically extended auctions or whether the discrepancy remains.

138 One interesting result with respect to bidding behaviour in the last few minutes is that there seems to be less very late bidding in hard close than in automatically extended auctions. The cumulative number of bids submitted in the last ten minutes rises earlier for hard close auctions than for automatically extended auctions.

3.3 Winner’s Bidding Behaviour

Hypothesis 4: The winning bidder enters the auction shortly before the auction end.

3.3.1 Entry Time of Winner In the theoretical models of the hard close auction presented above, it was predicted that every bidder who knows (or believes) that his rival (the bidder with the second-highest valuation) has an interdependent valuation, i.e. a λ > 0 (in the general model) or an α > 0 greater than zero (in the prestige-value model), will postpone bidding his valuation to the sniping period. If all bidders believe their rivals to have a λ (or α ) greater than zero – whether the general bidding model or the prestige value model - this will lead to the most extreme form of sniping: every bidder will post his bid in the last possible moment. This will lead to lower seller-revenue in the hard close than in the automatically extended auction.

In the following section we investigate when the winning bidder enters the auction. Yahoo auctions publicise the complete bidding course for closed auctions, i.e. auctions that have already ended. This feature makes observable when the winning bidder first posts a bid. The entry time is given as a fraction of the total time, where the auction end is normalised to one and the start to zero. The average entry time is calculated with the same data as used in the previous chapters – classified according to the good and the ending rule.

Entry Time of Winner: Entry Time of Winner Computers Hard Close 0,99 Automatic Extension 0,81 Art Hard Close 0,93 Automatic Extension 0,93 Cars Hard Close 0,97 Automatic Extension 0,92 Table 23

139

Observation 6: The winning bidder enters the auction at a very late point in time. The winner enters later in hard closing than in automatically extended auctions.

It can clearly be seen that the winner enters the auction at a very late point in time in all kinds of auctions. In computer auctions the winner enters in the last hundredth of the auction, in art auctions after 93% of the auction duration has gone by and in car auctions after 97% of the auction has gone by on average. The winner enters later in hard close than in automatically extended auctions. This result conforms to the theoretical predictions.

From this result we can deduce that the winner is a bidder who believes (or fears) that his rivals have interdependent values.

3.3.2 Winning Bid: Single Bid or Proxy Bid? As introduced in the theoretical investigation in Chapter Two, bidders have the possibility of making two types of bids: single bids and proxy bids. Single bids correspond to proxy bids when they are just the minimum increment above the current price. Updating a single bid takes far more time than letting the bidding agent bid automatically, a bidder might thereby also lose out on being the high-bidder (because when two bids are made that are equally high, the first one is the winner). Why use a single bid when a proxy bid is much more time- efficient and because of being faster has a higher probability of winning? Furthermore proxy bids allow a bidder to pay the lowest possible price in case of winning – namely a price equal to the second highest bidder’s maximum willingness to pay plus the minimum increment. The same is not true for single bids, where the winner might end up paying far more than the second-highest bid.

A bidder posting single bids has to form his bid according to his first-price auction strategy. The first-price auction strategy is dependent on a bidder’s risk-attitude. There is a trade-off between a lower probability of winning and a higher expected payoff, making the bidding strategy more complicated and making an inefficient outcome more probable. As suggested by Avery (2002), jump-bids (single bids higher than the current-price by the minimum increment) can have one advantage, under certain assumptions they can signal toughness and can scare competing bidders. Altogether there are more reasons speaking in favour of proxy bids. Therefore we arrive at the following hypothesis:

140

Hypothesis 5: The winning bid is posted as a proxy bid.

Yahoo publicises the type of bid used in the bidding course of closed auctions on its website. The following information was taken from the Yahoo website as part of the same data set of three hundred auctions as used above.

Winner's bid Proxy Bid Single Bid Art 95% 5% Cars 58% 42% Computers 99% 1%

Table 24

In accordance with our theoretical prediction it follows that the winning bid in art and computer auctions is almost always a proxy bid. Winning proxy bids are more frequent for cars, but there is also a large number of winning single bids. The use of single bids can be explained as a mistake (naivety) or as a strategic decision to intimidate rivals. Most plausibly single bids are used when sellers set a reserve price and a bidder decides to bid the minimum price at which the seller is willing to sell the good to him. The buy-price serves as insurance for the seller, so that he is not obliged to sell his car at too low a price. The high number of winning single bids for cars can be seen as an indication that the market for cars is rather thin, with often only one buyer willing to pay a price acceptable to the seller64.

3.3.3 Winning Proxy-Bids In Comparison To Second-Highest Bid As postulated in Hypothesis 4, bidders are expected to bid using the proxy bidding mechanism. However, the empirical investigation shows that winning bids are sometimes single-bids. A single bid does not guarantee that the final price is only a minimum-increment above the second-highest (single or proxy) bid. By looking at the second highest bid (measured as a fraction of the final price), we can find out whether winning single-bids strongly outbid the next highest bid.

64 Once a bid is posted that is higher than the seller’s reserve price, the seller’s reserve-price is erased from the website, so that this explanation cannot be verified with the data available on the Yahoo website for closed auctions. 141

Second highest bid as fraction of final price Winning bid is single bid Winning bid is proxy bid Art 0,77 0,95 Cars 0,69 0,98 Computers 0,86 0,98

Table 25

The final price ends up being much higher than the second-highest bid when the winner posts a single bid instead of a proxy bid.

3.4 Seller’s Choice of Ending-Rule

The theoretical predictions of Chapter 2 suggest that when the second-highest bidder has an interdependent valuation (as is postulated is often the case in Internet auctions), the final price and seller revenue will be lower in the hard closing than in the automatically extended auction. The revenue is lower in the hard-closing auction due to the strategic incentive for late bidding.

Hypothesis 6: Sellers prefer automatically extended auctions.

3.4.1 The Preferred Ending-Rule The Yahoo website publicises the type of ending rule used in every auction. The data sample leads to the following results:

Percentage of auctions ending by: Hard Close Auto Extension Art 18% 82% Cars 27% 73% Computers 91% 9%

Table 26

From the chart above we can see that sellers chose the hard close ending far more often than the automatic extension ending for art and cars. In the case of computers, sellers chose the hard close ending more often. 142

The theoretical prediction and empirical evidence that sellers prefer automatically extended auctions for art is also confirmed by Mr. Wedenig from the Austrian auction house Dorotheum, who complains that Ebay – with whom the Dorotheum cooperates concerning its Internet auctions - does not let Dorotheum extend auctions, even though this would improve profitability according to Mr.Wedenig. He believes that Ebay does not allow a change in its rules in order to have consistency throughout all product categories65.

Ms. Suttner from the London Department of Sotheby’s provides further support for the empirical findings and says: “Extensions for art auctions can lead to strong price increases”66. Sotheby’s.com uses surprise-extensions when they see that there is strong bidding activity towards the end of the auction.

The result for art and cars corresponds to the theoretical prediction, whereas the result for computers does not. As explained in the chapter above, computers do not prove to be a good with interdependent valuations, but instead a good with a well-known common value. Despite the similarity of names that does not mean that the common value model applies here. On the contrary, bidders have no (or hardly any) uncertainty about their valuation, i.e. have a λ equal to zero. In this case there is no strategic late bidding incentive as predicted for the models of interdependent valuations. As discussed above in Chapter 2.1, there might still be an incentive for bidders in computer auctions to engage in late bidding: bid delay has an option value, the option value of being able to find a cheaper computer sold in one of the many other (simultaneous or slightly later) computer auctions. This incentive does not, however, differ with respect to the two ending rules.

The arguments above would explain why a seller would be indifferent between the two ending rules for computers, but why would he prefer the hard close ending? If the main objective of a buyer in a computer auction is to bargain hunt, that is to find a low price for a good he knows his valuation for with certainty, then he will not be willing to update his valuation in the extension period. He does not need to bid up to his true reservation price, because there are so many other computers offered on the Internet. In fact the possibility that an item can get snatched away by a rival in the extension period makes an automatically

65 Interview with Mag. Wedenig, Dorotheum Internet Auctions GmbH, quoted in Wagner (2002) p.62. 66 Interview with Mag. Suttner, Sothebys.com, London Department, quoted in Wagner (2002) p.37. 143 extended auction less attractive for a buyer and he will concentrate on those auctions were there is a higher chance of a bargain. The hard close auction is preferred by bargain hunters and the seller being otherwise indifferent thus prefers the hard close ending to attract buyers.

3.5 Successful Matchings

3.5.1 Average Number of Bids The last question investigated in the empirical study of Internet auctions is: how successful are Internet auctions? Out of the number of items offered, how many lead to a successful matching, that is a price equal or above the seller’s minimum or reserve price?

Yahoo does not list auctions on its closed-auctions website, that received zero bids. In contrast the closed auction website of Ebay lists all auctions conducted including those that ended without having received a single bid. The following survey was therefore conducted using three hundred Ebay auctions, hundred auctions from each of the three categories. The survey was conducted on March 7th, 2001.

The mean, median and modal number of bids is given for each of the three categories, as well as the mean, median and modal price67 attained.

Observation 7: Many goods do not receive a single bid. Most auctions are characterised by low bidding activity.

Pocket-watches Laptops Paintings Bids Price Bids Price Bids Price (in $) (in $) (in $) Mean 2 20 8,9 574,4 1,9 75 Mode 0 --- 1 --- 0 --- Median 1 7 4 126,3 0 27 Table 27

A large proportion of Internet-auctions are unsuccessful, in that there is not even one bidder who is willing to make an acceptable bid, i.e. pay a price above the seller’s minimum-price. The fact that no bid is made can be caused by lack of demand at the seller’s unrealistically

67 Only successful auctions are included in the calculation of the average price. 144 high starting or reservation price. Or it could be caused by lack of demand for the product that is quite independent of the price. As we can see in this survey zero was the number of bids occurring most often (the mode) in the hundred auctions surveyed for the categories pocket- watches and paintings.

3.5.2 Buy-Price The “buy-price” as it is called in Yahoo terminology corresponds to the seller’s reserve price in economic terms. Internet sellers often use secret buy-prices. When a good has a secret buy- price that has not yet been met, this information is displayed on the web site, but without telling the bidders how high the buy-price is. A seller reserve price has the advantage of eliminating the risk that a seller has to sell a good (which has a specific value above zero to himself) for a value below his own valuation. A reserve price however reduces the number of participants, because it scares off some low valuation bidders.

In this section the final prices are compared to the seller reserve prices, investigating how many auctions have final prices below the seller’s reserve price and how many just match the seller’s reserve price. The Yahoo-website for closed auctions lists all auctions with reserve prices, where the final price remained below or equal to the seller’s reserve price. Auctions with reserve prices that were met cannot be identified as such, as the information that a reserve price was used is eliminated once the reserve price has been met. According to the auction rules, a seller is only required to sell his good when the final price surpasses his reserve price by at least the minimum increment.

A Yahoo data set of three hundred auctions, hundred auctions per category of goods is used.

Seller Reserve Price

Not reached Just reached Cars 17% 25% Art 7% 9% Computers 15% 11%

Table 28

145 Observation 8: Many auctions end with the price just matching the seller’s reserve price.

Out of the auctions that receive a positive number of bids, a notable amount ends without the seller’s reserve price having being reached. Comparing the different categories of goods, cars have the highest percentage of auctions where the seller’s reserve price is not reached, followed by computers and the least amount for art.

Hard close car auctions often end with a price just matching the seller’s reserve-price: about 35% of the hard close car auctions and 29% of the hard close computer auctions, but only 11% of the hard close art auctions close at a price just equal to the seller’s reserve price.

This result is surprising in the sense that a seller is not obliged to sell a good to a bidder making a bid just equal to the seller’s reserve price. The high frequency of auctions ending with the reserve price just being matched suggests that sellers might be willing to sell their good for their reserve price.

4. Results of the Empirical Analysis

4.1 The Four Main Hypotheses and the Empirical Evidence

Hypothesis 1: Internet auctions are characterised by late bidding, where late bidding means that there is a strong over-proportional price increase at the end of the auction. Empirical Evidence: Empirically confirmed.

Hypothesis 2: The over-proportional price increase toward the auction end is stronger for auctions with a hard close than for those with an automatically extended ending. Empirical Evidence: Empirically confirmed for cars, not confirmed for art and computers.

Hypothesis 3: There is more late bidding when there is uncertainty about the value of the goods, therefore more late bidding in art than in computer auctions. Empirical Evidence: Empirically confirmed.

146 Hypothesis 4: The winning bidder enters the auction shortly before the auction end. Empirical Evidence: Empirically confirmed.

Hypothesis 5: The winning bid is posted as a proxy bid. Empirical Evidence: Empirically confirmed for art and computers, not for cars.

Hypothesis 6: Sellers prefer automatically extended auctions. Empirical Evidence: Empirically confirmed for cars and art, not for computers.

4.2 Further Important Results

Æ Time-invariance is found for hard closing auctions, and in a weak form for automatically extended auctions. Æ A large proportion of Internet-auctions are unsuccessful, in that no bidder is willing to pay a price acceptable to the seller. Æ Many auctions (especially car auctions) end with a price just matching the seller’s reserve price.

5. Conclusion In this section I investigate bidding behaviour on the Internet, in particular late bidding. I find that bidders have an incentive to engage in late bidding in the hard close auction. A bidder protects himself from low valuing bidders with interdependent values who would raise their bid if learning about the high bidders value. Late bidding lowers the price and seller-revenue. When prestige concerns are present in the automatically extended auction, the price can rise explosively due to self reinforcing effects.

Yahoo auction data confirm the strong presence of late bidding both with respect to the price path and the winner’s entry time. The data show that late bidding is not limited to the hard close auction but is also present in the automatically extended auction, especially for goods available in abundant quantity. The strategic incentive to delay bidding arises because of the option value of finding an even cheaper model. Furthermore, the seller’s preference for automatically extended auctions is empirically confirmed.

147

PART SIX: Conclusion

In my thesis I investigate bidding behaviour in auctions both empirically and theoretically, focusing on Internet auctions and models of interdependent valuations.

Empirical results from an experiment with real consumption goods show that the secret second-price sealed-bid auction leads to significantly higher seller revenue than the open Japanese auction. This result coincides with previous field-studies and laboratory results, but contradicts theoretical predictions. Furthermore, bidders are found to have a tendency to “stick together with their valuations”. They are able to satisfy this tendency in the open Japanese auction but not in the secret second-price sealed-bid auction.

In a general model of interdependent values but independent signals, dynamic price-formation in the Japanese auction is modelled. The updating procedure shows how bidders form their valuations endogenously, using the information revealed through the exit prices of their rivals. As a result, the Japanese auction generates lower revenue than the second-price sealed-bid auction.

In my investigation of Internet auctions I find late bidding concerning both price-formation and the timing of the winning bid. I show that bidders with interdependent valuations have an incentive to hold back their bid until immediately before the auction end in the hard close auction. Bidders hold back their valuation in order not to incite their rivals with interdependent valuations to revise their valuations upwards. Interdependent valuations can arise due to common value or reputational effects. The consequent late bidding in the hard close auction lowers seller revenue, whereas reputational concerns can lead to exorbitant seller revenue in the automatically extended auction.

Late bidding is empirically confirmed by Yahoo auction data both with respect to the winner’s entry time and the price path. Empirical results show that late bidding is not limited to the hard close auction, but is also present in the automatically extended auction. The theoretically predicted seller’s preference for automatically extended auctions is empirically confirmed. 148 Literature

Avery, Christopher (2002), “Strategic Jump Bidding in English Auctions”, Game Theory in the Tradition of Bob Wilson, Article 34, http://www.bepress.com/wilson/art34. Bajari, Patrick & Ali Hortacsu (2000), „Winner’s Curse, Reserve Prices and Endogenous Entry: Empirical Insights from ebay Auctions“, Working Paper Stanford University. Budish, Eric & Lisa Takeyama (2001), “Buy prices in online auctions: irrationality on the internet?”, Economic Letters, p.325-333. Bulow, Jeremy & John Roberts (1989), „The Simple Economics of Optimal Auctions“, Journal of Political Economy, Vol.97(5), pp.1060-1090. Compte, Olivier & Philippe Jehiel (2000), “On the virtues of the ascending price auction: New insights in the private value setting”, Working Paper C.E.R.A.S.-E.N.P.C. Coppinger, Vicki, Vernon Smith & John Titus (1980), “Incentives and Behavior in English, Dutch and Sealed Bid Auctions”, Economic Inquiry, 18(1), pp.1-22, (quoted in: Kagel and Roth (1995)). Cox, James, Vernon Smith & James Walker (1983), “A Test that discriminates between two models of the Dutch-First Non-Isomorphism”, Journal of Economic Behaviour and Organization, 4(2-3), pp.205-19. Cox, James, Bruce Roberson & Vernon Smith (1982), “Theory and Behaviour of Single Object Auctions”, in Vernon Smith, ed., “Research in experimental economics”, Greenwich, CT, JAI Press, pp.1-43. Cramton, Peter (1998), „Ascending Auctions“, European Economic Review, 42, pp.745- 756. Deltas, George & Richard Engelbrecht-Wiggans (2001), “Auctions with an inexpert bidder”, Economic Letters 73, p.35-42. Easley, Robert & Rafael Tenorio (1999), “Bidding Strategies in Internet Yankee Auctions”, Working Paper University of Notre Dame. Engelbrecht-Wiggans, Richard (1980), „Auctions and Bidding Models: A Survey“, Management Science, 26(2), pp.119-142. Hansen, Robert (1985), „Empirical Testing of Auction Theory“, American Economic Review, 75(2), pp.156-159. Hansen, Robert (1986), „Sealed-Bid Versus Open Auctions: The Evidence“, Economic Inquiry 24(1), pp.125-142.

149 Izmalkov, Sergei (2001), “English Auction with Reentry”, mimeo, Penn State University, August. Jehle, Geoffrey & Philip Reny, “Advanced Microeconomic Theory”, Addison Wesley, 2nd Edition, 2001. Johnson, Ronald (1979), „Oral Auctions versus Sealed Bids: An Empirical Investigation“, Natural Resources Journal, 19(2), pp.315-35. Kagel, John and Alvin Roth (Editors), “The Handbook of Experimental Economics”, Princeton University Press, New Jersey, 1995. Kagel, John, Ronald Harstad & Dan Levin (1987), „Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study“, Econometrica, 55(6), pp.1275-304. Kagel, John & Dan Levin (1986), „The Winner’s Curse and Public Information in Common Value Auctions“, American Economic Review, 76, pp.894-920. Kagel, John & Dan Levin (1993), “Independent Private Value Auctions: Bidder Behaviour in First-, Second-, and Third Price Auctions with Varying Numbers of Bidders”, Economic Journal, 103 (419), pp.868-79. Katkar, Rama & David Lucking Reiley (2001), “Public versus Secret Reserve Prices in Ebay Auctions: Results from a Pokemon Experiment”, NBER Working Paper 8183. Kirchkamp, Oliver & Benny Moldovanu (2001), “An experimental analysis of auctions with interdependent valuations”, Working Paper, University of Mannheim. Klemperer, Paul (1999), “Auction Theory: A Guide to the Literature”, Journal of Economic Surveys, 13(3), p.227-286. Krishna, V. (2002), “Auction Theory”, Academic Press, London. Leibenstein, Harvey (1950), “Bandwagon, Snob and Veblen Effects in the Theory of Consumers’ Demand“, Quarterly Journal of Economics 64(2), pp.183-207. Liebowitz, S.J. & Stephen Margolis (1994), “Network Externality: An Uncommon Tragedy”, Journal of Economic Perspectives, Vol.8 No.2, pp.133-150. Lucking-Reiley, David (1999), “Using Field Experiments to Test Equivalence Between Auction Formats: Magic on the Internet”, American Economic Review, Vol.89(5), pp. 1063-1080. Lucking-Reiley, David (2000), „Auctions on the Internet: What’s being auctioned and how?“, The Journal of Industrial Economics, 48(3), pp.227-252. Maskin, Eric & John Riley (1985), „Auction Theory with Private Values“, American Economic Review, 75(2), pp.150-155.

150 Maskin, Eric & John Riley (2000), „Asymmetrical Auctions“, Review of Economic Studies 67, pp.439-454. Mc Afee, R.Preston & John Mc Millan (1987), „Auctions and Bidding“, Journal of Economic Literature, 25, pp. 699-738. Mc Afee, R.Preston & John Mc Millan (1996), „Analyzing the Airwaves Auctions“, Journal of Economic Perspectives, 10(1), pp.159-175. Mc Millan, John (1994), „Selling Spectrum Rights“, Journal of Economic Perspectives, 8(3), pp.145-162. Mead, Walter, „Competition and Oligopsony in the Douglas fir lumber industry“, Berkeley, CA, Unversity of California Press, 1966, (quoted in: Lucking-Reiley (1999)). Menger, Carl, “Grundsätze der Volkswirtschaftslehre”, Hölder-Pichler-Tempsky, Wien, 1923. Milgrom, Paul (1979), „A Convergence Theorem for Competitive Bidding with Differential Information“, Econometrica, 47(3), pp.679-688. Milgrom, Paul (1981), „Good News and Bad News: Representation Theorems and Applications“, Bell Journal of Economics, Autumn, 12(2), pp.380-391. Milgrom, Paul, „The Economics of Competitive Bidding: A Selective Survey“, in Social Goals and Social Organization, Eds.: Leonid Hurwicz, David Schmeidler and Hugo Sonnenschein, Cambridge University Press, 1985. Milgrom, Paul (2000), „Putting Auction Theory to Work: The Simultaneous Ascending Auction“, Journal of Political Economy, 108(2), pp.245-272. Milgrom, Paul & Robert Weber (1982a), „A Theory of Auctions and Competitive Bidding“, Econometrica, 50(5), pp. 1089-1122. Milgrom, Paul & Robert Weber (1982b), „The Value of Information in a Sealed Bid Auction“, Journal of Mathematical Economics, 10(1), pp. 105-114. Perry, M. & Reny P. (2001), “An efficient multi-unit ascending auction”, Hebrew University, mimeo. Rasmusen, Eric, (2001), “Strategic Implications of Uncertainty Over One’s Own Private Value in Auctions”, Working Paper Indiana University. Riley, John & Samuelson William (1981), „Optimal Auctions“, American Economic Review, 71(3), pp.381-392. Rohlfs, Jeffrey, “Bandwagon Effects in High-Technology Industries”, The MIT Press, Cambride, MA, 2001.

151 Roth, Alvin & Axel Ockenfels (2000), „Last Minute Bidding and the Rules for Ending Second-Price Auctions“, NBER Working Paper No.7729. Rothkopf, Michael, Thomas Teisberg & Edward Kahn (1990), „Why Are Vickrey Auctions Rare?“, Journal of Political Economy, 98(1), pp.94-109. Tenorio, Rafael (1993), “Revenue Equivalence and Bidding Behavior in a Multi-Unit Auction Market: An Empirical Analysis”, Review of Economics and Statistics, 75(2), pp.302-14, quoted in (Lucking-Reiley (1999)). Ünver, M. Utku (2001), Internet Auctions with Artificial Adaptive Agents”, Working Paper Koc University. Vakrat, Yaniv & Abraham Seidmann (2000), “Implications of the Arrival Process on the Design of Online Auctions”, Proceedings of the 33rd Hawaii International Conference on System Sciences. Vickrey, William (1961), „Counterspeculation, Auctions, and Competitive Sealed Tenders“, The Journal of Finance, Vol.48 No.3, pp.8-37. Wagner, Bernhard (2002), “Besonderheiten von eAuctions im Kunstsektor”, Diplomarbeit Universität Wien. Wang, Ruqu (1993), “Auctions versus Posted Prices”, American Economic Review, Vol.83 No.4, pp.838-851. Wilcox, Ronald T. (2000), “Experts and Amateurs: The Role of Experience in Internet Auctions”, Marketing Letters, Vol.11 (4), pp.363-374. Wilson, Robert (1977), „A Bidding Model of Perfect Competition“, Review of Economic Studies, 44(3), pp. 511-518. Wolfstetter, Elmar, „Topics in Microeconomics“, Cambridge University Press, 1999.

152