AUCTIONS By: Jessica Wisler
“The foundation of trade is mutual gain, people make exchanges because they expect them to improve their well-being, although sometimes one of the counter parties is later disappointed (Koch, P.99).”
An auction entails a potential buyer competing for the right to own a good, service or anything of value . The auctioneer is either seeking bids to sell a service/item to a purchaser for its highest price or is seeking bids to purchase a service/item from a supplier for its lowest price. Either way an auctioneer will benefit from having many bidders as competition leads to better terms for the auctioneer. Companies can act as either the bidder or the auctioneer for goods or services they want to purchase or sell. Thus it is important for managers to understand auction models, bidding strategies and revenue expectancies to make optimal selling and purchasing decisions for their company (Baye, p. 456).
TYPES
Types of auctions differ by the timing of the bid (whether it is sequential or simultaneous) and the amount the bidder is required to pay. There are four main types of auctions: English (ascending bid) auctions; First-price, sealed bid auctions; Second-price, sealed bid auctions; and Dutch (descending bid) auctions.
The English (ascending bid) auction is the most common type of auction. In an English auction a single item is being sold to a highest bidder. The auction begins with an opening bid then the auctioneer will ask if anyone is willing to pay a higher price. The auctioneer will take higher prices (bids) in sequentially until no one is willing to pay a higher price. The purchasing price is the price at which the last competitor drops out (Baye, P. 457). The English auction is the only auction type that the bidder has knowledge of bids made by others. An example of an English auction can be watched on BBC America’s Cash in the Attic. The television show works with families who want to raise money for a specific project. The show's experts help them go through their possessions, looking for potential items of value. Anything that is found then goes to auction (BBC America-Cash in the Attic).
In a first-price, sealed bid auction the highest bidder wins the item just as in an English auction but all bids are simultaneously written down and handed to the auctioneer. The auctioneer awards the item to the person with the highest bid and no one knows one another’s bids (Baye, P. 457). The bidder pays what s/he bid for the item. Fish auctions use first-price, sealed bid auctions (McConnell, 2000).
Second-price, sealed bid auctions also consist of bidders simultaneously submitting bids, without the knowledge of the other bidders, to the auctioneer and the highest bidder wins. The difference from the first-price sealed bid auction is that the winning bidder only has to pay the second largest-bid. eBay’s proxy bidding system is mimics a second-priced auction. The system permits a bidder to submit their maximum price “reservation price.” This amount is kept secret by the system which automatically updates the bid using the smallest increment possible above the previous bid until the previous bid is higher then the reservation price. The winner pays the price of the second highest bid plus the bidding increment (Baye, P. 458).
A Dutch (descending bid) auction is where the seller sets a very high price for an item (higher than it is believed anyone will pay) and the auctioneer starts at this price then sequentially lowers the price until a bidder is willing to pay the last price announced. In a Dutch auction bidders do not know the bids of the other players and the bidder pays what s/he bid for the item (Baye, 458). This type of auction is convenient when it is important to auction goods quickly, since a sale never requires more than one bid. An example is the Dutch Flower Auction which is where the auction type received its’ name. First-price, sealed bid auctions and Dutch auctions are identical in terms of optimal bidding behavior and profits earned by the auctioneer (Baye, 457).
VALUATIONS
Merriam-Webster defines Valuation as “the act or process of valuing; specifically: appraisal of property” as well as “the estimated or determined market value of a thing” (Merriam-Webster Online). What information is available to bidders for their valuation of an item in an auction is known as the information structure.
When all bidders know for certain the worth, valuation, of an item the information structure is called perfect information (see table 1 for example). Perfect information is rare in that there are very few items that have a true consensus of their worth both in the intrinsic value of the item and the additional value one may put on the item due to personal taste.
More common is an estimation of worth by bidders to determine their valuation of the item. When each bidder’s valuation of the item being auctioned off is not known by themselves and/or other bidders, asymmetric information within an auction occurs. When personal taste exists as part of the valuation this is known as private value. When personal taste is not dependent on the valuations of other bidders this is known as independent private value (Baye, P.459).
A correlated (affiliated) value estimate is where a bidder does not know their own or others valuation of an item. They must estimate the value for the item through research. This estimate of worth is also correlated with other bidder’s valuations. If one bidder has a high value estimate, then others bidders are more likely to have high value estimates.
When a correlated value estimate exists with no personal/individual taste involved then a special case arises called a common-value auction. Again, all bidders will have different estimates based on their research and tests (Baye, P.460). Table 1, below, provides the information structures discussed above and examples of items that lend themselves to these information structures.
Table 1: INFORMATION STRUCTURES Information Structures Defined Example Exact worth of item is Perfect Information current $10 bill known by all bidders Personal taste is part of the Private Value* a collectible (antique furniture) bidder's valuation of an item Valuation of art at $200 Bidder's valuation is because it matches the dependent on personal Independent Private bidder's home décor vs. Art taste known only to the Value* Reseller’s valuation at $75 bidder and not other based on the quality and bidder's valuations resale value of the art piece. Real Estate (must research the Bidder does not know their Correlated (affiliated) local market & estimates of own or others' valuation of Value* Estimate worth vary based on research an item done) Special case of correlated value estimates; no Oil Deposits (finite amount in personal taste is added to ground & estimates of how Common Value* the valuation; true worth much oil vary depending on exists but not known to research done) bidders * Asymmetric information exists within the auction.
AUCTION THEORY
Auctions, in general, may be viewed as games with incomplete information (Harsanyi, 1967). Thus one can apply game theory to assess auction bidding strategies and revenue. Within game theory is the Nash Equilibrium. A Nash equilibrium, defined by Baye, is, “ A condition describing a set of strategies in which no player can improve her payoff by unilaterally changing her own strategy given the other players’ strategies (P.357).” All auctions have a Nash equilibrium, a bid that perfectly balances the risk of losing to a higher bidder where no profit is made against the possibility of greater profits where the lower the bid, the greater the profit (Holt, 2004). The following describes the appropriate bidding strategy to obtain the highest expected profit for risk neutral bidders which are bidders that are indifferent between a risky prospect and a sure thing as well as revenue expectancies for both risk neutral and risk-averse bidders.
BIDDING STRATEGIES for NEUTRAL BIDDERS: An English auction bidder with Independent private values should continue bidding until the price exceeds their valuation of the item. If the player were to drop out with a bid lower than their valuations, they lose the chance of winning at the value they placed on the item. If they continue bidding higher than their valuations, they pay higher than they already valued the item.
A second-price, sealed bid auction bidder with independent private values has an incentive to bid exactly their own valuation of the item since they pay the second-highest bid and not their own. If the player were to bid lower than their valuations, they reduce the chance of winning. If they were to bid higher than their valuations, they increase their chance of winning but only in so much that they pay higher than they already valued the item. So the dominant strategy is to bid their valuations.
A first-priced, sealed or Dutch auction bidder does not know the valuations of their fellow bidders. Since the highest bid wins the bidder wants to lower their valuation down to avoid having a substantially higher bid then the rest of the bidders. This is known as Bid Shading. The profit earned by doing this offsets the reduced chance in winning. The more bidders there are in the auction the more competition their will be and the closer the bid needs to be to the bidder’s valuation. The following formula uses the bidder’s own valuation (v), the total number of bidders (n), and the assumption that bids have an evenly distributed range between the lowest (L) and the highest to compute the player’s optimal bid (b). v L b v n A correlated values auction bidder has the most complex information structure in that they do not know their valuation or the other bidders’ valuations of the item. In this case the lack of information on the valuation of the item lends towards a higher tendency to over bid and in the case of English Auctions and correlated values the bidder must adjust their valuations as others bid to put forth an optimal bid.
The common values auction exacerbates the tendency to over bid in that the winner is the one who has the highest estimate of the true worth of the item (i.e., oil) while all other estimates are lower. Logic follows that the true value is problem an average of all the estimates and not the highest estimate. This is known as the winner’s curse. The winner’s curse is most pronounced in sealed bid auctions because no information can be gathered on the estimates of other bidders.
Table 2: BIDDING STRATEGY Auction type Information Structure Bidding Strategy continue bidding until the price English Independent Private Values exceeds your valuation of the item Second-price Independent Private Values bid your valuation of the item
First- v L Independent Private Values b v price/Dutch n adjust estimate of valuation on other bidders' estimates; English Affiliated Value Estimates continue bidding until the price exceeds your valuation of the item revise downward your private Sealed Bids Affiliated Value Estimates estimate
REVENUE: One of the major findings of Auction Theory is the Revenue Equivalence Theorem, which states that the auctioneer’s expected revenues are the same for all four auction types. All independent private value auctions’ bidders already know their independent private valuations and learn nothing more about the worth of the item from the auction. Thus the revenues are equal. English and second-price auctions each result in the bidder paying the second highest valuation and the first-price and Dutch auctions encourage bid shading by all in which the net effect is an overall equal reduction in valuation. Thus the highest bid after Bid Shading is the equivalent of the second highest valuation. This is illustrated below in Table 3.
Due to the asymmetric information of correlated values revenue equivalency does not hold and bidders shrink their bids based only on their private value estimates to avoid the Winner’s Curse. In English auctions bidders gain the post information of other bidder’s value estimates and can adjust their values acccordingly. This gives them more confidence in their estimates and they shrink their bids less. In First-price and Dutch auctions bidders learn nothing of each others estimates and thus shrink their bids accordingly (greater than the English auction). In the second-price auction bidders know they will only have to pay the second highest bid thus they do not shade their bid as much as in the English auction. The results are illustrated in the affiliated value estimate row in table 3.
Table 3: EXPECTED REVENUES (Risk-Neutral bidders) Information Structure Expected Revenues
Independent Private Values English = Second-price = First-Price = Dutch
Affiliated Value Estimates English > Second-price > First-Price = Dutch (Baye, P. 465) Risk-averse bidders are those that prefer a sure amount of profit to a risky prospect with a greater expected value. Surprisingly risk aversion players bid more aggressively in first-price auctions with independent private values because they are less willing to accept the risk of being outbid by shading down their bids so they shrink their bids by less. Lastly, the affiliated value estimates for these bidders’ results is more aggressive bidding for English auctions as well. The English auction provides bidder information which lessens the Winner’s curse thus making the risk-averse bidder more confident in not Bid Shading. Thus the English auction always results in greater revenue than second-price and maybe even first- price. The results are below in table 4. Table 4: EXPECTED REVENUES (Risk-Averse bidders) Information Auction Structure type Expected Revenues Independent Private Values English English = Second-price = First-Price = Dutch Independent Second- Private Values price English = Second-price = First-Price = Dutch Independent First- Private Values price First-Price = Dutch > Second-price = English
Affiliated Value ALL English > Second-price < First-Price = Dutch Estimates >
MARKET-BASED MANAGEMENT APPLIED
Koch Industries follows a Market-Based Management (MBM) approach. Within this approach are five dimensions with the first dimension described as the vision. The vision is “Determining where and how the organization can create the greatest long term value (Koch, P.26).” Throughout Koch’s book, “Science of Success”, Koch addresses the importance of value driving profit. Subjective value is discussed in the sense that value is subjective and not directly measurable. The only way to properly measure value is through the actions of the market (the purchasers). Understanding what drives value and the need for value creation aids Koch Industries in maintaining their competitive advantage.
Furthermore, because Koch is a leader in natural resource-based products Koch must properly assess the correct bidding strategy for their natural resources. They must understand that if they are attempting to procure a natural resource from the government they will be dealing in a common value (correlated) auction and will need to engage in Bid Shading to avoid the Winner’s curse and to get the natural resources at a price for which they can still create true value and profits. As Koch puts it, “An effective business vision begins and ends with value creation (P. 55).”
QUESTIONS Question 1: When the Government auctions off oil rights bidders are using an information structure of… a) perfect information b) independent private value c) correlated value estimates d) both a and b
Question 2: You’re participating in an auction where all the 10 bidders have independent private values of 5, 7, 9, 11, 12, 12, 17, 19, 21 and 23. Your own valuation is 12. Determine your own optimal bidding strategy in a first price, sealed bid auction. a) $11.30 b) $12 c) $12.78 d) $12.16
Question 3: Koch,” seeking the highest valued alternative for every resource,” wants to auction off one of his asphalt plants. The bidders are risk neutral and have affiliated value estimates. What auction type will maximize his revenue from the sale? a) All four auction types will lead to equal revenue b) First-Price c) English d) Both b and c
Question 4: A bid that perfectly balances the risk of losing to a higher bidder where no profit is made against the possibility of greater profits (where the lower the bid, the greater the profit) is… a) not possible b) an audit’s Nash Equilibrium c) an example of perfect information d) the result of subjective value
Question 5: Auctions can be viewed in terms of games with incomplete information. a) True b) False
ANSWERS Answer 1: c; Answer 2: a; Answer 3: c; Answer 4: a; Answer 5: b
REFERENCE: Baye, Michael. R. (2009). Managerial Economics and Business Strategy, 6th Edition. St. Louis: McGraw-Hill Irwin. “Cash in the Attic.” BBC America . 2009. Worldwide Americas Inc. 26 Apr. 2009