Investigating the Alternating Periods Monopoly Arthur L

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COLLEGE OF SOCIAL SCIENCES

INVESTIGATING THE ALTERNATING PERIODS MONOPOLY

By:

ARTHUR L ZILLANTE

A dissertation submitted to the Department of Economics in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Fall Semester, 2004 The members of the Committee approve the dissertation of Arthur L. Zillante defended on August 17, 2004.

______R. Mark Isaac Professor Directing Dissertation

______Joe Cronin Outside Committee Member

______Tom Zuehlke Committee Member

______Tim Salmon Committee Member

The Oﬃce of Graduate Studies has veriﬁed and approved the above named committee members.

ii Acknowledgements Special thanks to the John and Hallie Quinn Research Fellowship for research support during mylastthreeyearsattheFloridaStateUniversity. The Irv and Peggy Sobel Award and the Charles Rockwood award also provided ﬁnancial assistance. I would also like to thank Bob Lemke of Krause Publications for answering my questions about minute details of the baseball card industry and Jeremy Hobbes of Collector’s Attic for providing information on some of the missing baseball card product release dates.

iii Table of Contents

List of Tables v

List of Figures vi

Abstract vii

1. INTRODUCTION 1

2. THEORETICAL MODELS 3

3. INDUSTRY OVERVIEW 13

4. EMPIRICAL RESULTS 35

5. EXPERIMENTAL TEST 44

6. CONCLUSION 68

Appendix A. Instructions for the Experiment 70

Appendix B. Sample Experiment Screen 75

Appendix C. Human Subjects Approval 79

Appendix D. Subject Informed Consent Form 81

References 83

Biographical Sketch 87

iv List of Tables

1 IndustrySummaryStatistics,AllBrands...... 29 2 IndustrySummaryStatistics—LowPriceBrandsOnly...... 30 3 Topps’FinancialInformation...... 32 4 DurationAnalysisResults...... 40 5 Numberoftimesaparticularmarketstructurewasachieved ...... 51 6 Individualresultsforsession4N...... 55 7 Individualresultsforsession4I...... 56 8 Individualresultsforsession3N...... 57 9 Individualresultsforsession3I...... 57 10 Payoﬀs to following an APM strategy given a speciﬁcnumberofsimpleNash players...... 59 11 Signals sent indicating recognition of the APM for session 4N ...... 62 12 Signals sent indicating recognition of the APM for session 4I ...... 63 13 Signals sent indicating recognition of the APM for session 3N ...... 63 14 Signals sent indicating recognition of the APM for session 3I ...... 64 15 Simple Signals Table for session 4N ...... 65 16 Simple Signals Table for session 4I ...... 66 17 Simple Signals Table for session 3N ...... 66 18 Simple Signals Table for session 3I ...... 67

v List of Figures

1 ManufacturerBrandsbyYear,1988-2000...... 25 2 ManufacturerReleasesbyYear,1988-2000...... 25 3 IndustryAggregates,ReleasesandBrands,1989-2000...... 28 4 Time series of baseball card releases by manufacturer from 10/11/2001 — 5/1/2002...... 28 5 Time series of baseball card releases by manufacturer from 5/1/2002 — 11/27/2002 29 6 The hazard rate for all releases using the best response (BR) and halfs definitions...... 39 7 The estimated hazard rate for low-price brands using the best response (BR) and halfs definitions...... 41 8 Hazardratesforthebenchmarkdatasets...... 43 9 Timeseriesoftotalnumberofentrantsfortwo4-subjectgroups...... 53 10 Timeseriesoftotalnumberofentrantsfortwo3-subjectgroups...... 54 11 A sample message sending screen for the experiment ...... 76 12 Asamplechoicescreenfortheexperiment...... 77 13 A sample payoff displayscreenfortheexperiment...... 78 14 HumanSubjectsApprovalform...... 80

vi Abstract

An oft-neglected pattern of behavior in the industrial organization literature occurs when firms time the release of their products so that they are not released on the same date. Because of the potentially collusive nature of this practice, there may be legitimate antitrust concerns. This paper presents a model of this behavior which will be called the alternating periods monopoly (APM). Industry characteristics that increase the likelihood of the APM are developed and conditions are derived in a stochastic demand environment to show when firms would prefer to use the APM to other sustainable methods of collusion. A detailed description of the post World War II baseball card industry is presented using the standard industrial organization structure-conduct-performance paradigm as a guide. The characteristics of the baseball card industry closely parallel those characteristics discussed in the theoretical model. This parallel between the theory and the industry suggests that data from the baseball card industry may be used to determine if the manufacturers are using an APM. Current methods of detecting potentially collusive behavior are discussed in the fourth chapter. The data from the baseball card industry do not meet the assumptions needed to effectively use the current methods, rendering them useless in this particular industry. I propose a new empirical test based on duration analysis to determine if firms are using the APM. Using the time between product release data from the baseball card industry, I estimate hazard rates that show positive duration dependence. I also estimate hazard rates for data sets constructed using the same parameters (number of releases and number of days over which those releases occur) as the baseball card industry, but forcing the firms toreleaseinwaysthatwouldnotbeconsideredtomatchtheAPM.Thehazardratesfor the constructed data show negative duration dependence, which provides evidence that the data from the baseball card industry is consistent with an APM hypothesis. The fifth chapter of the dissertation uses an economic experiment to determine if the APM can arise without free-form communication between subjects. The existence of practices that facilitate collusion has generated a large discussion in the antitrust arena. This experiment allows subjects to communicate their future intentions of entering a market in a particular time period by means of a binary signal, where 1 signals enter and 0 signals exit. The overwhelming evidence provided by the experiment is that subjects cannot use the binary signals to coordinate on an APM, even though it is clear that some subjects are both signaling a willingness to participate in an APM and making entry decisions consistent with an APM. These experiments show that the practice of sending non-binding communication is not enough to foster collusion among all subjects, although the treatments with fewer subjects and higher costs show some evidence that an APM may arise under these conditions.

vii CHAPTER 1

INTRODUCTION

Collusion by firms has long been recognized as an impediment to an efficiently functioning market system. As such, a wealth of literature exists on the topic. Current research on collusive behavior can be classified into five broad categories based upon research technique: case study, empirical/econometric, theoretical, experimental, and computational. Although I have separated the techniques into separate categories, most studies utilize a combination of techniques. This dissertation discusses a particular form of collusion, the alternating periods monopoly (APM), and utilizes all of the techniques mentioned above except for computational methods. The APM occurs when only one firm is active in the market per period, and then firms alternate turns being the active firm in the market. Although such a rotation scheme is not necessarily evidence of explicit collusion, it could be used by firms as a collusive scheme. The primary reason firms may choose to use the APM is that it removes intra-period competition among firms. Perhaps the most famous use of a collusive strategy similar to the APM is the “phases of the moon” bid rotation scheme employed in the electrical switchgear industry in the middle of the 20th century. According to Scherer (1970), this scheme involved:

...dividing the United States into four quadrants, assigning four sellers to each quadrant, and letting the sellers in a quadrant rotate their bids. A ‘phases of the moon’ system was used to allocate low-bidding privileges in the high voltage switchgear ﬁeld, with a new seller assuming low-bidder priority every two weeks. (Scherer, 1970, pgs. 159-161)

To my knowledge little work has been done on the APM outside of the auction literature, as typical economic analysis of timing problems in production center around one of the following: capturing first-mover advantage in the industry, the trade-off between delaying release to produce a higher quality product or releasing early to earn less-discounted profits, and the obsolescence problem. Any attention given to the APM outside of the auction literature is typically fleeting1. An exception is Herings, Peeters, and Schinkel (2001) (HPS). Using an algorithm developed in Herings and Peeters (2000) to solve stochastic games numerically, they show that the alternating periods monopoly is a symmetric stationary equilibrium for a duopoly market with identical firms. Furthermore, in their example they show that regardless of which firm moves first both firms receive higher profits from

1 Tirole (1993) spends two lines on it. Green and Porter (1984) direct the reader to Scherer (1970) for the discussion on the Phases of the Moon. Levin and Peck (2002) explicitly rule this type of equilibrium out in their paper.

1 the APM than from Cournot competition as long as the discount rate is sufficiently high. Chapter 2 of the dissertation extends the HPS results by providing general conditions under which the APM is preferred to other forms of industry behavior. The second chapter of this dissertation begins by developing potential reasons the APM might prove useful in a non-auction setting. Industry characteristics that can stimulate the use of the APM are then discussed. A theoretical model based on the Folk Theorem results of Fudenberg and Maskin (1986) is developed to determine the conditions necessary for firms to profitably participate in an APM. The APM is then compared to other potential collusive schemes, and it is shown that firms will prefer the APM to one where they agree to split the market each period. The third chapter of this dissertation provides a historical overview of the baseball card industry, as well as econometric analysis of the release times of baseball card products. The baseball card industry is chosen because it conforms well to the conditions of the theory discussed in chapter 2. A detailed description of the industry, corresponding to the traditional industrial organization structure-conduct-performance paradigm, is presented. The key turning points in strategic behavior by the firms are highlighted throughout the description. The fourth chapter of the dissertation provides an empirical test to determine if the pattern of release times in the baseball card industry is consistent with the APM. Pre- vious methods of detecting collusion are discussed and dismissed as usable models due to fundamental differences in the baseball card market and the markets for which the previous methods were developed. A new test based on duration analysis is presented. A debate exists as to whether industry practices can facilitate collusive behavior without explicit communication between industry participants. The focus of the fifth chapter is on an economic experiment designed to provide evidence on the debate. Economic experiments on facilitating practices date back to the Grether and Plott (1984) experiments based on the Ethyl case and the Hong and Plott (1982) study of the barge industry. The experiment also tests whether or not the theoretically valid conditions of the Folk Theorem model in chapter 2 are enough to generate APM behavior in practice. The results of the experiment are discussed on a number of levels in this chapter. The primary conclusion is that it is difficult for the APM to arise for groups of 3 or 4 subjects when only binary signals are allowed to be sent. The final chapter of this dissertation discusses the significance of the results of the results for the previous three chapters and highlights the contributions made to the existing knowledge on the topics. Suggestions as to how this knowledge should be used as well as methods of extending the current research are discussed.

2 CHAPTER 2

THEORETICAL MODELS

The infusion of game theoretic analysis into industrial organization in the 1960s and 1970s gave rise to a slew of theoretical models that discussed the type of collusion that may occur given certain industry parameters. In fact, it takes three chapters, Fudenberg and Tirole (1989), Shapiro (1989), and Jacquemin and Slade (1989), in the firstvolumeoftheHandbook of Industrial Organization to provide an overview of the development of game theoretic models and their applications to collusive behavior. Stigler (1964) is perhaps the most famous early paper in this literature, laying a foundation for others. Perhaps the most damaging resultwasproveninFudenbergandMaskin(1986),whichshowsthatanyoutcomewith payoffs greater than the minmax can be supported as a noncooperative equilibrium in an infinitely repeated game. Tirole (1993) has termed this “an embarrassment of riches”, as economists can now explain everything as a noncooperative equilibrium while at the same time explaining nothing. However, early game theorists such as von Neumann undoubtedly would have disagreed with that statement2, preferring to focus on why a particular equilibrium might arise out of a set of equilibria. This section follows the suggestion of von Neumann by laying out a framework in which one might expect a particular equilibrium to arise.

General Characteristics of APM Industries The APM could be a potentially useful collusive strategy in many industries. Consider a comparison of the APM and a collusive agreement where firms agree to equally split the market (ESM) each period. ESM collusion occurs when k firms each produce 1/k of the monopoly quantity each period3. The two generally cited reasons as to why ESM collusive agreements break down are unobservable individual production levels by firms and asymmetric costs across firms. I argue that it is possible an alternating periods monopoly avoids both of these problems. First, in an ESM collusive agreement it is typically the case that firms cannot observe how much other firms produce, which provides the incentive for each firm to cheat on the collusive agreement by producing more than its collusive share each period. In an APM it is easier for firms to observe defection behavior of other cartel members as they must merely observe any production by firms who are not supposed to be active. Similarly, the second reason to cheat on the collusive agreement is also alleviated — if firm A has a cost function such that 10 units of the good is the monopoly quantity, and

2 See Weintraub (1992). 3 Although there are market splitting collusive arrangements where ﬁrms produce diﬀerent amounts of the good each period, I will use the ESM as the benchmark for comparison.

3 ﬁrm B has a cost function such that 25 units of the good is the monopoly quantity, then each ﬁrm can produce its respective monopoly quantity during its time in the market, without any incentive to deviate from that quantity.

Industry Characteristics that Increase the Likelihood of an APM With the general reasons for ﬁrms to use an APM discussed above, a second question to ask is what industry characteristics would be more conducive to the formation of an APM. Since there are a vast amount of possible characteristics I will focus on three, each of which is discussed below. Besides the baseball card industry, other industries which may exhibit all or some of the following characteristics are the movie industry, books, special interest magazines, and other hobby related items.

Preferences for Newness Preferences for newness is a concept based on the principle that people like new things. In the economics literature, preferences for newness have been used primarily to model durable goods markets. Rust (1985) and Porter and Sattler (1999) use preferences for newness as a basis for heterogeneity among consumers. By varying the degree to which consumers prefer new goods, secondary markets evolve for used durables. In both papers only a single unit of a durable good is demanded, as consumers have no use for both an old and a new durable such as a car or washing machine. I apply preferences for newness in a slightly different manner, similar to that of Krider and Weinberg (1998). Preferences for newness imply that consumers would like to purchase goods from a certain class each period (by class I mean a fairly general class of goods like baseball cards or cereal or movies), but that due to the durable nature of the good consumers do not wish to purchase the same brand each period. Preferences for newness also imply that if two goods are equally valued by the consumer in all aspects, and the consumer does not have either of the goods, the consumer would prefer the good that was most recently released. Throughout the paper I will use the term brand to refer to a specific product type (like Fruit Loops ) released by a manufacturer (Kellogg’s). Thus consumers may find a preferred brand of cereal, say Fruit Loops, and purchase that brand eachperiodbecausethe product is physically consumed. Cereal would be a class of goods for which preferences for newness may not exist4. However, if consumers purchase a brand of baseball cards, say a brand like 2002 Topps Ten which is one brand of cards from Topps, it is still physically in the consumer’s possession next period. If the consumer desires to continue purchasing baseball

4 This comment is not meant to imply that people prefer to eat stale cereal or that brands cannot change over time. I simply wish to point out that cereal has often been treated as a good (dating back to at least Schmalensee (1978)) where it is assumed the same consumer will purchase his preferred brand of cereal every period.

4 cards in the next period, the consumer will not necessarily wish to purchase 2002 Topps Ten again5. As another example, consider movie-goers: while there are certainly some people who attend the same movie multiple times, it is much more likely that a movie-goer wishes to view a movie every time period, but not the same movie. Thus, the movie-goer has preferences for newness for the product class of movies6. Preferences for newness, in effect, forces the firm to develop new brands if it wishes to sell to a particular consumer multiple times7. Formally, define preferences for newness as follows. Consider a good yτ ,wherethe superscript τ denotes the period in which the good is produced. For simplicity, assume that τ goods are differentiated only by means of production date or vintage. Let Ut (y ) be the τ τ consumer’s utility for y at time t.Foragivenτ, Ut (y ) is assumed to be a strictly increasing, continuous, concave function of yτ . To compare utility across products of different vintages, fixaquantitylevelofyτ as yτ . Then, yτ (0, ), it is assumed that consumers derive more utility from a vintage the more closely∀ ∈ it is consumed∞ to its production date and that at a particular date the consumer will derive more utility from the most recently produced vintage. Equations (1) and (2) describe these relationships more precisely.

U (yτ ) >U (yτ ) n (1, 2, 3,...) (1) τ τ+n ∀ ∈

τ τ n U (y ) >U y − n (1, 2, 3, ...) (2) τ τ ∀ ∈ A special case of preferences for newness¡ could¢ be called “strong preferences for newness”. Rust (1985) describes consumers who have strong preferences for newness as the set of consumers who place a higher value on newer products than other consumers. My deﬁnition of strong preferences for newness is slightly stronger than Rust’s, in that I assume that τ Ut (y )=0 t =6 τ.Foranyt>τ,itisasiftheproductisoldnews. Fort<τ,thevintage does not exist,∀ and hence the consumer cannot purchase it. Thus, a consumer has no utility for a product of a given vintage after its release date. Although preferences for newness alone are not enough to generate a pattern of temporal product spacing, they provide the stimulus as to why ﬁrms repeatedly face innovation costs

5 There are two reasons why a consumer might wish to continue purchasing the same brand of cards again. The first is the investment motive. The second is if the cards are “consumed” by some natural disaster (fire, mom throws them out). Both of these possibilities are neglected in this analysis. 6 I suggest that viewing a movie in a theater is a durable good, albeit in a different sense than physically owning a video cassette or a DVD of the same movie. While the movie in the theater cannot be viewed without multiple purchases, one’s memory is not wiped clean of the characters and plotline in the movie when the movie concludes. It is in this sense that I suggest that viewing a movie in a theater is a durable good. 7 An episode of The Simpsons, Lisa vs. Malibu Stacy, depicts a humorous, yet hauntingly realistic, example of preferences for newness involving the “new” Malibu Stacy doll — which is identical to the previous version of the doll save for a new hat. The episode first aired on April 17, 1994.

5 during short time periods and why so many brands of a product are released sequentially throughout time.

Innovation Costs Related to the concept of preferences for newness are innovation costs incurred by firms. If the firm is constantly developing new brands, it is likely that the firm is constantly incurring innovation costs8.LetΠm be the monopoly profit, I be the innovation cost, k be the number of firms and N be the number of periods the market will meet. If firms collude using an ESM strategy then each firm will have to pay the innovation cost each period, and an individual Πm firm’s undiscounted monopoly profits would be given by ( k I)N.Iffirms use an APM Πm I − strategy of release then each firm receives ( k k )N. Although this simple example neglects discounting, it is easy to show that firms prefer− the APM in this environment since they only N have to pay the innovation cost k timesasopposedtoN times in the ESM.

Production Technologies Production technologies are another factor that could effect the viability of the APM. With some products, such as baseball cards, it is not difficult for a manufacturer to stop production and restart when it is his turn to produce or to produce continuously and warehouse the product. Alternatively, consider the market for milk. Although producers may want to use an APM monopoly, it seems unlikely that each manufacturer could shut down his cows until it was his turn to produce again. This makes it unlikely that an APM would be used because the production technology and the fact that the products are perishable would not allow it. Also, consider the railroad industry. It seems unlikely that an APM would work well due to the networking among rail lines necessary to serve consumers. If a consumer wishes to take a trip and the rail company “in” that period does not have access to lines to complete the trip the consumer may find alternative methods to using the railroad, defeating the purpose of the APM.

Folk Theorem Model A vast literature exists that provides a theoretical basis for determining the conditions under which collusive behavior may occur. Most of these results rely on the structure of a standard folk theorem described by Fudenberg and Maskin (1986). The folk theorem requires that ﬁrms have a discount rate high enough to support a noncooperative outcome over the minmax outcome in repeated market games. The folk theorem also relies on ﬁrms using a

8 This analysis also applies to industries where ﬁrms are not developing new products. In these cases it is more useful to consider the innovation cost as a recurring entry cost.

6 trigger strategy in case other firms deviate from the agreed upon collusive outcome. Trig- ger strategies are strategies where firms cooperate initially, and if no deviation is observed, continue to cooperate. Once a deviation is observed firms enter a reversionary period where they play a Cournot game to punish the defector from the collusive agreement. The reversionary period may be either a finite number of periods or may last forever, depending on the structure of the game. The seminal paper in the literature on sustainable collusion, Green and Porter (1984), extends standard folk theorem results for repeated games by introducing a model with sto- chasticdemand. Firmsproducethecollusiveoutput level unless the market price falls below some trigger price p¯. There are two possible reasons that explain how the price may fall below p¯.Thefirst is due to the stochastic demand factor. Even if all firms are producing their respective collusive shares there may be a large enough negative demand shock to cause price to fall below p¯. The second occurs when firms cheat on the collusive agreement by producing more than their respective collusive shares in any given period. Regardless of the reason, if price falls below p¯, firms behave noncooperatively for a specified period of time, then return to producing the collusive output level. Rotemberg and Saloner (1986) and Staiger and Wolak (1992) are other papers that use the structure of the Green and Porter model. Although the focus of these papers is primarily on how price wars develop in periods of high and low demand, the underlying models apply to how firms can maintain a collusive agreement in the face of unobservable individual production levels by reverting to punishment periods.

Baseline Results Using the standard folk theorem argument developed by Fudenberg and Maskin (1986), it can be shown that a discount rate exists to support the APM over a default equilibrium, which I will assume is the Cournot level. It should be noted that the innovation cost discussed in the previous section is ignored when deriving the necessary condition, thus providing a “maximin” discount rate9 that will support the APM over the Cournot equilibrium. As I have demonstrated above and HPS shows numerically, the introduction of an entry cost each period will only make the APM a more attractive strategy. HPS also shows that if per period entry costs are too high, Cournot competition involves losses for both firms and a collapse of the industry, while the APM allows both firms and the industry to remain active. Suppose an industry consists of k risk-neutral firms facing stochastic market demand in m each period. The demand shocks are iid mean zero shocks. Let E Πi,t be the expected monopoly profittofirm i at time t and let E Πc be the expected profittofirm i should i,t £ ¤ 9 The discount rate is maximin in the sense that it£ is the¤ lowest discount rate able to support the APM over the ESM without adding more complexity (e.g. innovation costs) to the model. With these additional assumptions the discount rate necessary to support the APM will fall, making the discount rate found in the model without the added complexity the maximum of the minimums.

7 all k firms follow the default behavior and produce the k-firm Cournot quantity at time t. Both the participation and incentive compatibility constraints, equations (3) and (4) respectively, must be satisfied if the firms are to choose the APM over Cournot behavior. Also, the incentive compatibility constraint insures that firms will not attempt to deviate from the APM. Deviation occurs by producing in another firm’s slot, and the deviation d profit is denoted E Πi,t . It is assumed that if a firm deviates from the APM that it is observable to all firms and that all firms will follow Cournot behavior from that point in time. This is a harsh£ punishment¤ but it also helps establish the maximin discount rate necessary to support the APM. Thus, the APM strategy, as developed here, is for firms to follow a set order of releasing products coupled with the active firm producing its monopoly quantity, and, if deviation occurs, all firms will produce the Cournot quantity every period. It should be noted that both constraints focus on the firm that is scheduled to release in th k 1 the k spot in the rotation, as shown by the δ − terminfrontoftheLHSofeachequation. The intuition behind basing the condition on the firm in the last spot in the rotation is that if firm i is willing to participate when placed in the last spot, it would certainly be willing to participate if it was slotted earlier and received a slightly less discounted payoff stream.

∞ ∞ k 1 k t m t c δ − δ E Π δ E Π i (1, 2, ..., k) (3) i,t ≥ i,t ∀ ∈ t=0 t=0 X ¡ ¢ £ ¤ X £ ¤ ∞ ∞ k 1 k t m d t c δ − δ E Π E Π + δ E Π i (1, 2, ..., k) (4) i,t ≥ i,0 i,t ∀ ∈ t=0 t=1 X ¡ ¢ £ ¤ £ ¤ X £ ¤ Although equations (3) and (4) differ by the first term on the RHS, both yield the same necessary condition in order for a discount rate to exist that will ensure the APM is an equilibrium strategy. Although the exact form of the deviation payoff is unspecified, the proof of existence of a discount rate to support the APM is unchanged and only the magnitude of the discount rate necessary to support collusion changes. The condition is given by equation (5).

E Πm >kE Πc i (1, 2, ..., k) (5) i,t i,t ∀ ∈ £ ¤ £ ¤ Proposition 1 If equation (5) is satisfied for all firms, then a discount rate δ∗ (0, 1] exists ∈ such that every for δ [δ∗, 1) such that the APM is an equilibrium strategy. ∈ Proof. The Limit of Means criterion, established in Aumann and Shapley (1994), is a sufficient condition for such a δ∗ to exist. The Limit of Means criterion states that the sequence S (vs) of real numbers is preferred to the sequence (ws) if and only if lim inf (vs ws) /S > i i i − i s=1 s m X th 0.Define the sequence (vi ) as a sequence of zeros followed by E Πi,s every k period. £ ¤ 8 s c c m c Define (wi ) as E Πi,s ,E Πi,s ,... .Letε = E Πi,s kE Πi,s > 0.Everyk periods s s − ε the firm receives ε if (vi ) is chosen instead of (wi ); thus, on average, the firm receives k > 0 ¡ £ ¤ £ S ¤ ¢ £ ¤ £ ¤ ε ε each period. Thus, limS /S = > 0. Since the limit of means criterion is →∞ k k s=1 not sensitive to a change in aX payo¡ ¢ff in a single¡ ¢ period, the RHS of equations (3) and (4) are evaluated identically by the Limit of Means criterion, proving that such a δ∗ exists to m c support both equations if E Πi,s >kE Πi,s . QED Proposition 1 formally de£ fines¤ the condition£ ¤ necessary to support the repeated game strategy. Intuitively, firms will participate in an APM only if the additional gain is not discounted too much. This proposition implies that for any identical firm duopoly case with linear demand in the form of a bQ, constant marginal costs, and a default payoff that is Cournot, the discount rate must− be greater than 0.8 in order for the APM to be preferred to Cournot behavior10. This discount rate is not overly restrictive as the time periods considered are usually very brief11.

Comparison of Sustainable Collusive Arrangements Neither the APM nor the ESM is Pareto superior in terms of expected payoffsifcollusion holds. This can be verified by realizing that all firms, in expectation, receive the same amount of undiscounted expected profits in either the APM or the ESM, assuming no punishment periods for ESM. However, the first firm to release in the APM receives its share of the profits sooner in the APM than in the ESM, while the last firm to release in the APM receives its share of the profits sooner in the ESM than in the APM. One potential flaw in comparing the APM and the ESM is that the ESM as proposed in Green and Porter (1984) is not sustainable if it is assumed that firms cannot observe each others exact production levels and demand is stochastic, unless there is credible commitment by the firms to revert to Cournot behavior for a specified amount of time if the price in the market drops too low. Since neither the APM nor the ESM without reversions is Pareto superior in expected payoffs, I compare the APM with a sustainable version of the ESM. The sustainable ESM is a modified version of the Green and Porter model, where the key element to the sustainability of that model is that firms enter reversionary noncooperative periods with positive probability. 1 Thebasicoutlineofmodelsofthistypeisthatk firms in the industry agree to produce k of the monopoly quantity each period. However, the market price fluctuates based upon both

2 10 (a c) This can be verified by noting that for two firms the Cournot profits per firm are −9b . The monopoly 2 2 2 2 (a c) (a c) (a c) + (a c) profitis −4b . For the second firm to prefer the APM over the Cournot outcome, δ −4b −9b δ −9b . Solving for δ gives δ 0.8. ≥ 11The discount rate≥ necessary to support the APM in a 4-firm industry with linear demand, constant marginal costs, and identical firms is actually lower, at 0.765.

9 the amount produced in a period as well as a stochastic factor. Assume the market price has distribution function F (p (Q)) and disturbances are iid across time and independent of the market quantity, Q.Atriggerprice,p¯, is determined by the firms, and if the price falls below p¯ firms play a Cournot game for T periods. Even though production levels are unobservable between firms these models are sustainable versions of the ESM because firms commit to entering the punishment phase regardless of the reason price falls below p¯.Thus, 1 the incentive to deviate by producing more than k of the monopoly quantity each period is removed. Let F (¯p) be the probability that the price is below the trigger price. I have suppressed the argument to the demand function since, in equilibrium in the sustainable ESM, all firms 1 m will produce k of the monopoly quantity in each collusive period. Again, letting E [Πi ] c be the expected monopoly profitperperiodandE [Πi ] be the expected k-firm noncollusive profit per period, the expected equilibrium lifetime profits of any firm in the sustainable ESM model are given by equation (6). It should be noted that I have set the number of reversionary periods the firms will play, T , equal to one in setting up the lifetime profit function12.

j m E[Πi ] t k 1+ ( F (¯p)) m ∞ E [Π ] j − i + δ  Ã t=1 !  (6)  k j X  j=1 c t 1 t   +E [Π ] ( 1) − F (¯p)  X  i −   Ã t=1 !    X    ¡ ¢  Since equation (6) is somewhat cumbersome, I use a simplified version to show that if a discount rate exists that supports the APM over Cournot behavior, then all firms prefer the APM to the sustainable ESM model. Let x (0, 1]. Since equation (5) must hold for the APM to exist, firms prefer that they spend∈ more time in the collusive state than in the noncollusive state, which implies that firms prefer lifetime profit functions with larger probabilities of being in the collusive state. For equation (6), it can be shown that firms attain their highest probability of being in the collusive state in the third period13, with that probability being 1 F (¯p)+ F (¯p)2 .SinceF (p) [0, 1), there exists some − ∈ x 0,F (¯p) F (¯p)2 such that firms will prefer the lifetime profitfunctionwherethe ¡ ¢ probability∈ of− being in the collusive state is (1 x) to the lifetime profitfunctionwherethe ¡ ¡ ¢¢ − 12Although the choice of T should be endogenously determined by the discount rate and payoffs, a choice of T =1assumes that discount rates are high. Since the theoretical lower bound of the discount rate necessary to support the APM is .765 for 4 firms with linear demand, constant marginal cost, and competitive Cournot payoffs this restriction is not unreasonable. Also, a punishment period of length 1 maximizes the payoff stream. 13Technically firms prefer the Green and Porter case where there is no chance of reversion to Cournot to the cases where there is some positive chance to reversion to competition, but since the case with no reversion is not sustainable it is omitted.

10 probability of being in the collusive state is 1 F (¯p)+ F (¯p)2 .Thus,iftheAPMcanbe shown to be preferred to the simpliﬁed version− of the sustainable ESM (equation (7)), by transitivity it can be shown to be preferred to the actual¡ sustainable¢ ESM (equation (6)).

E [Πm] ∞ E [Πm] i + δj i (1 x)+E [Πc](x) (7) k k − i j=1 X ·µ ¶ ¸ It can then be shown that the APM will be preferred by the last ﬁrm in the rotation to the ESM when there is stochastic demand if:

k 1 m m δ − E [Π ] δ E [Π ] E [Πm] i + i (1 x)+E [Πc](x) (8) 1 δk i ≥ k 1 δ k − i − − ·µ ¶ ¸ Proposition 2 Ifequation(5)issatisﬁed for all ﬁrms, x (0, 1] a δ∗ exists such that for ∀ ∈ every δ [δ∗, 1) the inequality in equation (8) holds, showing the APM is preferred to the sustainable∈ ESM.

Proof. The Limit of Means criterion is a sufficient condition for such a δ∗ to exist and it is m m s E[Πi,s] E[Πi,s] defined in the previous proof. Define the sequence (vi ) as a sequence of k , k , ... . s µ ¶ Under the Limit of Means criterion, this sequence (vi ) is evaluated identically to the sequence m th of payoffs generated by the APM, which is a sequence of zeros followed by E Πi,t every k period. Define (ws) as: i £ ¤ E[Πm ] E[Πm ] i,s (1 x)+E Πc (x) , i,s (1 x)+E Πc (x) ,... . k − i,s k − i,s µµ ¶ µ ¶ ¶ E[Πm ] Let ε = E Πm kE Π£ c ¤> 0 so that E Πc = i,s£ ε¤. Using substitution, (ws) i,s − i,s i,s k − k i E[Πm ] E[Πm ] becomes £i,s ¤x ε , £i,s ¤ x ε ,... . Every£ period¤ the firm receives x ε if (vs) is chosen k − k k − k k i µ S ¶ s ε ε instead of (wi ).Thus,limS x /S = x > 0, x (0, 1]. →∞ k k ∀ ∈ s=1 QED X ¡ ¢ ¡ ¢ Given that neither the ESM without a reversionary period nor the APM are Pareto superior methods of collusion, proposition 2 provides a powerful result. If demand is stochastic and firms are risk-neutral, then the APM is preferred to the sustainable ESM by even the last firm to produce in the APM rotation. Note that this proposition still requires a discount rate high enough to support the APM. Intuitively, because there is positive probability of receiving the Cournot payoff with certainty in some periods the undiscounted profits for all firms are lower in the sustainable ESM than they are in the APM. Assuming a discount rate of one and a four-firm industry, the fourth firm in the APM would receive a profit vector m of (0, 0, 0,E[Πi ]). In the sustainable ESM there is no guarantee that the firm receives a

11 m sum of undiscounted profits over four periods equal to E [Πi ] due to the probability of a reversionary period. It should also be noted that this analysis forces one firm to release last every k periods. However, if firms were to rotate their rotation scheme it is possible that even less patient firms would prefer the APM to the ESM. Consider the duopoly market where firms release in a pattern of 1,2,1,2,... forever. It was shown above that the discount rate necessary to support that release pattern over Cournot competition in a linear demand industry with constant marginal costs was .8. Now consider a release pattern of 1,2,2,1,1,2,2,1,... forever. In this case, the minimum discount rate such that both firms prefer the APM over Cournot competition is around .61. This change in the order of the rotation every k periods provides both an increase in the number of potential users of the APM as well as a drawback in detecting users of the APM. The increase in the number of potential users of the APM comes from the lower discount rate necessary to support the APM over Cournot competition. The drawback is that equilibria will exist for virtually any pattern in which firms release in different periods. Since there is no structure placed on the sequence of releases by the equilibrium, attempts to distinguish collusive behavior from noncooperative behavior are futile if those tests are based on the observed sequence of releases.

12 CHAPTER 3

INDUSTRY OVERVIEW

This chapter of the dissertation begins with a historical overview of the post-World War II baseball card industry. The traditional industrial organization structure-conduct-performance (SCP) paradigm is presented first. The baseball card industry is used in this study for a variety of reasons, although the primary motivation is that the industry conforms well to the theory. Following the historical overview14, existing empirical methods for detecting collusion are reviewed and rejected as possible methods to determine if the release pattern of baseball card brands is consistent with the APM. A new method, based upon duration analysis, is proposed. The results from the duration analysis show that the release pattern is consistent with the APM. Prior to World War II, baseball cards were primarily used as premiums or advertising tools for tobacco and candy products. Information on the use of baseball cards as advertising tools in the tobacco and candy industries prior to World War II can be obtained from a number of different sources, including Kirk (1990) and most of the annual comprehensive baseball card price guides produced by Beckett publishing. I define the baseball card industry as the producers of nationally distributed picture cards of major league baseball players, licensed by Major League Baseball (MLB) and either the Major League Baseball Players Association (MLBPA) or major league baseball players themselves. Before beginning the overview of the industry, there are a few other definitions that the reader may find useful. A case is the unit of cards that a manufacturer sells to its customers, who are typically wholesalers, major retail chains, and major hobby stores. Cases are comprised of a fixed number of boxes of cards, although the number of boxes may vary depending on the manufacturer and brand of the product. Boxes of cards are typically sold by the wholesalers to smaller hobby stores, or by retail chains to consumers. Boxes of cards are made up of packs of cards. Packs are the smallest packaged individual unit that a consumer can buy. Packs consist of the individual cards of a particular brand, and may contain base cards, inserts, or parallels. Base cards are designated by the manufacturer’s checklist for the brand and typically make up the bulk of the cards in a pack. Insert cards are cards available in packs at a lower rate than base cards, often with a completely different design than the base cards in the set. Most insert cards are part of a small insert set, which is theme based and may include baseball all-stars, rookie prospects, or even the favorite players of the owner of the manufacturing company. A parallel card is a type of insert card that is identical to a base card from a brand except for some change in the border, lettering, or glossiness of the base cards in the pack. Parallel

14Many of the details in the historical overview are from the author’s personal experience as a collector in the industry since 1985. Murphy (2002) was used to collect quantitative information for years prior to 1980 while Beckett (2003)t was used for quantitative information for years after 1980.

13 cards are usually inserted at a lower rate than regular base cards. Other types of insert cards will be discussed as needed within the following sections. A brand of cards is determined by the brand name given to the cards made available in a pack by the manufacturer. For those familiar with the hobby, a brand of cards is what one would call a set of cards. Note that a release of cards is not the same as a brand of cards, since brands may be released in series of cards at different points in time throughout the year. Thus one brand may have two or more series, and hence more than one release. Typically, the packs from one series do not contain the cards available in another series. Recently, most brands of cards have one series — that is there is one release of a brand of cards. However, with some larger brands of cards (larger in the sense that there are a larger total number of cards that make up the brand), the manufacturer chooses to release a portion of the brand at one point in time in the year, and other portions of the brand at a later date in the year. The first release of the brand would be the first series, the second release the second series, and so on. Releases will be considered to consist of only those cardsthatareavailableinpacksatthetimeoftheirrelease,whilebrandsmayconsistof cards that are released at different dates.

Structure

Entry into the baseball card industry is regulated by MLB and the MLBPA. Within the last twenty years, minor changes have occurred in the structure of the industry. The requirements to become a manufacturer, the change in the number of ﬁrms, and the production process and supply chain are described in the following three sections.

Requirements

Since ﬁrms must be granted licenses by MLB and the MLBPA to produce cards that appeal to collectors on a national basis, the industry is regulated by those two entities. A card that appeals to collectors will have a player’s likeness depicted on the card and the Major League Baseball logo of the player’s team, past or current. It should be noted that not all manufacturers secure licenses from both sources — one manufacturer, Michael Schechter Associates (MSA) has never acquired a national license from MLB. MSA has acquired licenses from the MLBPA, airbrushing out any part of the team logos on the players’ uniforms that appear in the picture so as not to infringe on any of MLB’s trademarks. However, these cards are not fully embraced by consumers; as such MSA and similar manufacturers will be excluded from this description. A new ﬁrm can only enter the market if it obtains a license15, and the licensors have not been generous in handing out licenses. A few companies that

15Although the courts may see this diﬀerently. See Major League Baseball Properties vs. PaciﬁcTrading Cards for a ruling (since vacated) on this matter.

14 have applied for full licenses and been denied are Classic, Frontline, and Action Packed. As for the general terms of the license, MLB has a standard royalty rate of 11% for national retail product licenses, as well as minimum annual guarantees which vary depending on the different product classification. The MLBPA has similar requirements. According to O’Shei (1997), the MLBPA also has to approve the final product, and will oftentimes make suggestions to the manufacturers about the design and price of the product.

Number of firms Following the lead of earlier industries, Bowman Gum Company (Bowman) and the Leaf Gum Company (Leaf) released the first sets of post-war baseball cards in attempt to boost sales of chewing gum in 1948. While Leaf discontinued production after one year, Bowman produced card sets from 1948 to 1955, at which time the company was purchased by Topps Chewing Gum Company (Topps). Topps first produced a card set in 1951, although it was more a game than what we would now consider a traditional set of picture cards. In 1952 Topps produced its first “true” set, and competed head-to-head with Bowman for four years. After Topps’ purchase of Bowman in 1955, the company held a virtual monopoly in the sale and production of cards depicting current major league baseball players for the next 25 years. Its primary competitor was the Fleer Corporation (Fleer); however, since Topps had exclusive licenses with most of the players in major league baseball, Fleer did not provide much competition. Fleer made minor headway by signing Ted Williams to an exclusive contract, but for the most part Fleer was relegated to producing cards of players no longer activeinmajorleaguebaseball. TheFTCfiled suit against Topps on February 8th, 1962, charging Topps with monopolizing the baseball card industry. Although the FTC action in 1962 failed, Fleer filed a lawsuit in June of 1975 accusing Topps of illegal restraint of trade. Fleer won this case16, and was granted licenses by MLB and the MLBPA to produce baseball cards in 1981. At the same time, another company, the Donruss Company (Donruss), was also granted licenses to produce cards in 1981. Following the production of cards by all three manufacturers in 1981, an appeals court overturned the previous decision17, ruling that Topps did have the monopoly right to the production of baseball cards with confectionery products as well as the monopoly right to sell baseball cards without tieing them to another product. After the appellate ruling, Fleer packaged its baseball cards with stickers while Donruss packaged its cards with puzzle pieces. Since Fleer and Donruss were not attempting to sell more stickers or puzzles, this change signified the end of baseball cards as a promotional tool, and the birth of the baseball card industry as a stand alone industry. The three manufacturers produced card sets for seven years with little competition. The years 1981-1987 were the expansion years of the baseball card industry, fueled primarily by investors stockpiling cards. Although there were numerous unlicensed card sets issued

16See Fleer Corp. v. Topps Chewing Gum, 1980 17See Topps Chewing Gum v. Fleer Corporation, 1982

15 during this time, there was only one other manufacturer granted a license by MLB. The manufacturer was Optigraphics, Inc. (hereafter called Pinnacle, which is the name under which the company made its biggest impact), which produced the Sportflics brand of baseball cards. Sportflics was introduced in 1986, and were actually quite different from traditional baseball cards. Sportflics cards actually had three pictures that showed up on the card front depending on how the card was tilted when held. Some of the cards, if moved quickly enough, showed a player “in action”, either swinging the bat, pitching, or fieldingaball. Since they were so different from the traditional cards, Sportflics were viewed more as a novelty than a mainstream brand, and their inclusion as a competitor to Topps, Fleer, and Donruss is borderline. However, in 1988 Pinnacle produced the Score brand of baseball cards, adding a fourth manufacturer and a fifth brand of cards as they continued to produce Sportflics cards in 1988. The Score brand of cards differed from the other brands, as Score card fronts featured crisp photographs of action shots of players instead of posed pre-game shots, and card backs featured colored pictures of players as well as the more traditional information on card backs such as player statistics and some text about the player. In 1989, MLB and the MLBPA granted licenses to a fifth manufacturer, the Upper Deck Company (Upper Deck). Upper Deck was the first company created solely to produce sports cards. Upper Deck would revolutionize the hobby by introducing high quality cards — no longer were cards printed on heavy cardboard, but on high quality card stock. From 1989 until 1995, the baseball card industry would consist of five producers — Topps, Fleer, Donruss, Pinnacle, and Upper Deck. An additional license was granted to Pacific Trading Cards, Inc. (Pacific) in 1993, but it was not a full license. Pacific could only produce cards that were bilingual (English/Spanish) in nature, and Pacific released at most two brands a year from 1993 to 1997. There are a few changes to the number of manufacturers of baseball cards that occurred after 1995. The first was the acquisition of Donruss by Pinnacle in April of 1996, which reduced the number of fully-licensed manufacturers from five to four. The next change occurred in May of 1998, when Pacific was granted a full license to produce cards, returning the number of fully-licensed manufacturers to five. However, Pinnacle would file for bankruptcy in July of 1998, reducing the number of manufacturers to four, and the brand names of Donruss and Leaf would be acquired by a non-licensed company, Playoff,Inc.(Playoff). Although Playoff was allowed to release one product that Pinnacle had already manufactured in 1998 (Leaf Rookies & Stars), it could not purchase the license to produce cards and it was not granted a license by MLB and the MLBPA until February 2001. However, the number of fully-licensed manufacturers did not return to five in 2001 as Pacific decided not to renew its license to produce baseball cards. There was an additional license granted to Wizards of the Coast18 in 2001, but the cards they produced were similar to the first Topps cards

18Wizards of the Coast specializes in producing cards for games to be played with dice. Their most °R popular game to date is a non-sports product, Magic The Gathering .

16 in 1951 in that they were cards created for a pencil and paper version of a baseball game played with dice. In summary, the number of baseball card manufacturers from 1948 to 1955 was two, a single firm from 1956 to 1980, and there have been between three and six firms from 1981 to the present, depending on how one counts partial licenses. The reason for this limited number of firms is that licenses are granted by MLB and the MLBPA, and is not the focus of this study. However, most models of collusion require a small number of firms and stability among firms, which has clearly been present in the baseball card industry. Also, newcomers to the baseball card market, such as PacificandPlayoff, had been competing with the other manufacturers in the football and basketball card markets, so it is not as if they were completely new entrants.

Production process and supply chain The actual production of baseball cards is a fairly simple process for most types of cards. The principle steps are photographing the players, developing the brand’s theme, designing the cards, obtaining the statistics and text necessary for the card backs, the physical production of the cards, and ﬁnally, the shipment from manufacturer to wholesaler or retailer. Most of these processes are easily understandable, and the most diﬃcult part of the process is developing the brand’s theme. The brand’s theme is crucial to the survival of the brand, although once the brand has etched itself into the marketplace the development of the theme plays a lesser role in the production process. As former Topps PR man Marty Appel states in Portantiere (1996):

“You hear people say there’s too much stuﬀ being produced, that it’s too confusing, and to a large degree it’s true. However, Topps feels that if you have a message behind each product, like we do, you should be successful”.

A similar statement is made in Topps’ annual reports, as one of Topps’ goal is “to ensure that each brand of sports card has its own unique positioning in the marketplace”. Thus the theme and design of the brand can be viewed as deﬁning the brand, as well as most of the innovation in producing a new brand. As for the production of cards, Topps’ website, www.topps.com, reports that the process of producing a set, from inception to shipment, is about six months. Upper Deck provides a slightly longer estimate, saying that the entire process of developing a brand takes about forty weeks. However, Upper Deck also states that the printing of the cards takes about one week19. Also, manufacturers do not need to physically produce the cards in-house in order to remain proﬁtable. Upper Deck currently manufactures its own cards, but Topps

19This length of time was provided in Geschke (1996). Brands produced at the time of the interview were typically of lower quality and higher print runs than brands being produced in 2003.

17 has recently switched to outsourcing production. For cards that require special card stock, Topps supplies the company with the special card stock. The supply chain of cards follows a typical manufacturer-wholesaler-retailer-consumer design. Manufacturers are typically prohibited in their licensing agreements from selling directly to ﬁnal consumers, so they sell to either wholesalers, major retailers (such as Wal- Mart), or major sportscard stores. The wholesalers will then sell to small hobby stores that have not been awarded a direct dealership with a manufacturer. Wholesalers are typically not permitted by their contractual agreements with the manufacturers to sell products directly to consumers. Once hobby stores have obtained the product, they basically have the freedom to do as they please with the product. They may sell the sealed product directly to consumers, store the sealed product and attempt to sell it a later date, open the sealed product and attempt to sell the cards individually to consumers, or even open the sealed product and keep the cards for their own personal collection. Once the consumer receives the sealed product, he essentially becomes a hobby dealer, in the sense that all the ownership rights of the pack of cards that the hobby dealer had are now transferred to the consumer. Thus, if a manufacturer continually releases a product because it has a high secondary market value, the manufacturer may face competition from previous purchasers of the product (wholesalers, retailers, and consumers) who have kept the product unopened. Competition from previous purchasers of the product may have played a key part in shaping the strategic behavior of the manufacturers in the late 1990s. Although the supply chain opens up interesting topics for economic analysis, the model in section assume that the manufacturers sell directly to consumers. Another interpretation of the model in section is that it applies to the manufacturer-wholesaler relationship, where the wholesaler, acting as simply a middleman, assumes the preferences of the ﬁnal consumer.

Conduct The second link in the standard industrial organization paradigm is conduct. I begin with a discussion of major innovations in the industry since 1990, followed by a description of pricing policies used by the manufacturers. I then discuss brand release policies at both the aggregate and individual ﬁrm level. The individual ﬁrm level data discussed in section is the data used in section to show that the timing of brand releases is consistent with an APM. Finally, I discuss various means through which manufacturers may communicate.

Innovations When Upper Deck was granted a license in 1989 there was a vast increase in the quality of cards produced. Upper Deck produced high quality, or premium, cards and released them on a national basis in pack form. Previously, high quality cards were released on a limited basis and were only available in factory set form (80s Topps Tiﬀany and Fleer Glossy cards).

18 The impact of Upper Deck is noticeable in Topps’ cards. Comparing Topps cards from 1952 to cards from 1990, little difference is seen in the quality of the card. In the later years, the photos were crisper and the cards were cut more evenly, but the overall quality of the cards did not change dramatically. Following the introduction of Upper Deck, cards became glossier, more colorful, and were printed on higher quality card stock. The 1990s saw a variety of innovations in the sportscard industry as manufacturers attempted to increase sales. The first major innovation was by Upper Deck in 1990, when they randomly inserted 2500 serial numbered Reggie Jackson certified autograph cards into the Upper Deck Hi Series product. The concept of an insert card was taken to a new level with this innovation. As far back as the 1960s Topps had offered insert items (usually not cards, but tattoos or posters) in its packs, and Fleer had been inserting its all-star players set in its product since 1986, but none of those inserts caught the attention of the collectors like Upper Deck’s serial-numbered autograph card. In 1991 Donruss became the first manufacturer to provide serial numbers for a set of insert cards, its Elite series, so that collectors would know the production run. Serial numbering appealed to collectors so much that there have been entire brands of cards which had the base cards serial numbered. In 1992 Topps and Donruss both introduced parallel cards, Donruss with its Leaf Black Gold and Topps with its Topps Gold. In 1994 Fleer introduced die-cut cards to the baseball card market. These cards are the same size as a standard baseball card, but the cards would be die-cut to enhance the look of the card. The earliest cards were Fleer’s Hot Gloves in 1994, in which the card was die-cut to look like a baseball glove. Topps would use laser etching in 1996 to produce its Topps Laser brand, where all the base cards were laser cut and laser etched. The biggest change in the industry would occur in 1997 when Upper Deck introduced the concept of a game-used jersey card in the first series of its Upper Deck brand. A game-used jersey card is a standard sized baseball card with a piece of the depicted player’s jersey embedded into the card. While the price per card of packs was increasing due to increasing amounts of autographs, parallel cards, serial numbered cards, die-cut cards, and laser etched cards, the introduction of the game-used cards corresponded to an even greater increase in price per pack. The process of embedding the jerseys into the cards is much more complex than changing color schemes or adding serial numbers, and the players jerseys also needed to be purchased. Once collectors warmed to the idea of game-used jersey cards, their popularity and supply increased dramatically. The concept has been extended to include game-used base (not to be confused with base cards, these are cards with a piece of a game-used base embedded in them), glove, hat, and bat cards. Most of the other changes in the industry consisted of combinations of the above changes — serial numbering game-used cards, making die-cut and parallel versions of game-used cards, having a player autograph a card that had a game-used piece embedded in it, and embedding more than one game used piece (either fromthesameplayerordifferent players) onto the card were some of the extensions of the previous concepts introduced. Another major innovation by Upper Deck are cut autograph cards. Although Babe Ruth is an immensely popular with collectors and an important

19 player in baseball history, it is impossible to get Ruth to currently autograph cards due to the fact that he is deceased. While companies could purchase a Babe Ruth game-used bat, chopitupandembeditintoacardwithapictureofRuthonit,theycouldnotproduce cards with autographs of Ruth. To circumvent this problem Upper Deck introduced the concept of a cut autograph, which is simply cutting out a player’s signature from an item he signed years ago. Such autographs are generally obtained from cancelled checks or reputable autograph collectors. The signature is cut out of the autographed item and then embedded into the card in a fashion similar to the game-used items. A brief description of this process can be found in Creager (2002) in regards to a card that features cut autographs of the first five members of the National Baseball Hall of Fame. Although innovations occur in the industry with some regularity, it should be noted that companies do not gain a lasting advantage from innovating. This is due to the ability of other companies to quickly adjust their products by incorporating the new innovations. The mid 1990s Beckett magazines contain numerous references to this imitation. Two such references can be found in Broome (1996) and Leer (1996). The first has a quote from baseball card dealer Candy Greenholtz, “When card companies come up with new bells and whistles, others seem to follow”, while Leer’s statement came in a question and answer session among hobby dealers concerning the amount of imitation seen in the products. In an attempt to stop imitation and solidify its market position, Upper Deck filed suit to stop other manufacturers from producing cards with game-used materials embedded in them. Although this lawsuit failed, it may have been a cause of contention among the manufacturers. This contention is discussed further in chapter 4.

Pricing policies

From the years 1948-1973, cards were sold primarily through retail outlets in penny, nickel, or dime packs, which reﬂected the suggested retail price (SRP) for a pack of cards. The number of cards per pack was typically such that the price per card of a pack averaged a penny per card, although in the 1950s Topps’ nickel packs had six cards per pack, and the packs also contained one stick of gum. Not surprisingly, there is some evidence of competition in the early 1950s, before Topps purchased Bowman. Bowman had been charging a penny per card in a pack, but Topps entered the market by packaging six cards for a nickel. Bowman subsequently increased the amount of cards in its nickel packs to seven in 1954 and nine in 1955, before being purchased by Topps. Topps would retain the policy of packaging cards at the rate of six cards for a SRP of ﬁve cents until 1961, when it began packaging the cards at a SRP rate of a penny per card. From 1961 to 1973, the SRP of a pack of cards would remain at a penny per card, although Topps would discontinue the use of penny packs and replace them with dime packs. Presumably Topps made this change to lower costs, as the number of packs that would need to be produced with this new system would be less than it was in the old system if the production numbers stayed the same, meaning Topps would

20 have to purchase less wrappers to package the cards in and also produce less gum to insert into the packs. In 1974, Topps lowered the amount of cards per pack to eight while keeping the SRP of a pack at ten cents. This marks the firsttimethattheratioofSRPperpacktocardsper pack exceeded one penny. For the remainder of the 1970s, Topps would vary both the SRP of a pack of cards and the number of cards per pack. Cards per pack would vary between eight and fifteen, while the SRP would vary between ten cents and twenty-five cents. In 1981, with the introduction of Fleer and Donruss, Topps would settle on a SRP of thirty cents and a pack size of fifteen cards. The other manufacturers initially packaged more cards in a pack for the same price, but from 1982 to 1984, all three manufacturers followed astandardpolicyoffifteen cards per pack for about thirty cents. From 1985 to 1992, SRPs for the basic brands of cards either rose slightly each year (around five cents per pack per year) or remained the same, and the number of cards per pack was typically held at fifteen. The only company that did not follow this pattern was Upper Deck, which charged a higher price for its cards due to the higher quality of the cards. After 1992 it becomes difficult to compare pack prices for a few reasons. First, all the manufacturers were releasing multiple brands at this point in time20. Second, the quality of the cards was changing rapidly, even for the basic brands, and as such comparisons with the pack prices in the 1980s become virtually meaningless. Some evidence on the increase in pack prices and price per card from 1993-1997 can be found in Keifer (1997). Although the data in the article does not adjust for quality differences, price per card increased from 13 cents in 1993 to approximately 30 cents in 1996, with the biggest increase between the 1994 and 1995 releases. The primary reason for this increase was due to the MLBPA strike in 1994, which drove borderline fans out of the hobby, leaving only hard-line collectors. The demand shock also had a different effect on products of differing quality. In the basic brands therewastypicallyadramaticincreaseinthepackpricewhilethenumberofcardsperpack was held constant. For example, Topps increased the price of its pack by 50 cents, from 79 cents in 1994 to $1.29 in 1995 without increasing the number of cards in a pack. However, in the premium brands slight price increases tended to be accompanied by a lower amount of cards in the pack, driving up the price per card. Another exogenous demand shock occurred in 1998, this one positive, due to the pursuit of the single season home run record. Although the demand shock was perceived by many as a large positive shock, pack prices did not increase greatly. Instead, manufacturers released more brands, perhaps signifying a shift in strategic behavior from price and quantity strategy to brand release strategy.

Release policy — 1955-2000 During Topps’ monopoly years, it would typically release one brand of cards in a few series throughout the year. Some of these series of cards were printed in diﬀerent quantities than

20SeeFigure1.

21 the others (although in most cases the cards included in a series were printed at the same rate), with the latest series typically produced in the lowest amounts due to the time of its release after the baseball season. In 1974 Topps changed its release strategy. No longer were cards released in series, but all at once. From 1974 until 1992, Topps would release brands in this fashion, with two small exceptions in 1974 and 1976, when Topps issued its first traded sets. A traded (or update) set features players who made a significant contribution during the season and were not included in the regular set of Topps or players who were traded during the season in their new uniforms. In 1974 and 1976, traded cards were only available in packs that could be purchased later in the year, while the regular cards were available in packs that could be purchased any time throughout the year. The Beckett Almanac of Baseball Cards and Collectibles 7 states that although the traded cards from 1974 and 1976 were released later than the base cards (April of 1976 for the 1976 Topps brand), they are printed in about the same quantity as the base cards from that brand. For all other years from 1974—1992, all cards in the Topps brand for a given year were available in all of that brand’s packs. By looking at the advertisement on a Topps wax box in 1974, it appears as if Topps believed that making all cards available in a pack, “Keeps Topps baseball exciting and selling all season long”. When Fleer and Donruss first produced cards in 1981, they followed the same release strategy as Topps. Both companies had one brand and one release, in which all the cards for the brand were available in the packs of that release. Other than the production of Fleer and Donruss cards, the major hobby news that occurred in 1981 was that Topps brought back the traded set concept that originally debuted in 1974. However, when Topps released the traded cards through hobby stores in factory set form, not in packs. This marks the first time in which a manufacturer released a major product without releasing it in retail outlets. Throughout the 1980s the manufacturers followed a fairly standard releasing schedule — all of them would release their primary products between November and February. For example, 1989 Score was available in late November of 1988. Near the completion of the baseball season, around the middle of October, the companies would release their traded or update products, always in factory set form. Between the release of their primary product in November—February and the release of their traded set the following October, companies would release products for other major sports and entertainment as well as other baseball products. These other baseball products have been given the name “oddball” products by collectors. These products differ from the regular issues in a number of ways. The actual physical size of the card may be different (either larger or smaller), the number of cards in the set is smaller, the quantity of cards produced is smaller, and the sets contain only star players or rookies. Oddball products also consist of products that are not cards, such as stickers, coins, and tattoos, that were produced in an attempt to reach a wider audience. All three manufacturers released oddball products in pack form as well as in factory set form throughout the 1980s, and the production of oddball products may be viewed as an early attempt at producing multiple brands by the manufacturers.

22 In 1989, Topps became the first manufacturer to release two different major brands21 in pack form on a nationwide basis when it brought back the Bowman brand of baseball cards. This introduction of a second major brand, coupled with the change in quality brought about by the entrance of Upper Deck, would change manufacturers’ release strategies during the 1990s. The manufacturers began by releasing a second product which would compete with the basic Upper Deck brand. The second product would be a higher quality set with a lower print run. Donruss would release the Leaf brand in 1990, Fleer would release Ultra in 1991, Topps would release Stadium Club in 1991, and Pinnacle would release Pinnacle in 1992. Upper Deck would actually release a less expensive product in 1994, called Collector’s Choice, to compete with the lower priced brands. Figure 1 is a time series of the number of brands produced by manufacturer from 1988 to 2000. Figure 1 shows that the number of brands the manufacturers have been producing has been increasing, with a few exceptions, since 1988. A few comments need to be made concerning the construction of the data for figures 1-3. The years correspond to the year as designated by the manufacturer and not the actual calendar year of the release date. The reason for this categorization is two-fold. First, I do not have the actual release date for all products during this time period, so the best information I have is the manufacturer’s designation of the product year. Second, the brands most likely to be released in November or December of the calendar year and designated as a product for the next calendar year (e.g. 1989 Score being released at the end of 1988) were also the brands which were most likely to have another series issued. Since this later series would be released during the calendar year designated as the product year by the manufacturer, it would be inconsistent to consider two series of the same brand as being issued in different years. For most of the years the graph covers, the process of counting brands by the calendar year designated by the manufacturer just shifts the beginning of the calendar year from January to mid-November, as once one manufacturer released a brand for the upcoming year no other manufacturers would release a brand for the current year22. Also, although Pinnacle acquired Donruss in 1996, I do not have information as to which brands were released by which company, so I have included all brands in 1996 that were previously Donruss created (Donruss, Leaf, and Studio) as Donruss brands in 1996. Finally, after Pinnacle’s bankruptcy in 1998 and Playoff’s acquisition of the Donruss and Leaf brand names, Playoff released at least one product near the end of the 1998 calendar year, Leaf Rookies and Stars. Since Pinnacle was responsible for the design and name of the brand I have included Leaf Rookies and Stars as a Pinnacle product. Most of the trends in Figure 1 appear to be increasing at a constant rate, with a few

21Optigraphics, the company that would become Pinnacle, had released Score and Sportflics in both 1988 and 1989, but as has already been mentioned the inclusion of Sportflics as a competitor to the other brands is borderline at best. The Sportflics brand is viewed by many to be similar to the oddball products previously mentioned. 22This practice changed around the year 2000, which is why the figures only show brands and releases until 2000.

23 exceptions. The most notable exceptions are Pinnacle from 1996 to 1997, Pacificfrom1997 to 1998, Topps from 1997 to 1998, and Upper Deck from 1998 to 1999. The increase in Pinnacle brands is due to its acquisition of Donruss in 1996, while the increase in Pacific brands is due to its acquisition of licensing from MLB and the MLBPA in 1998. Topps’ and Upper Deck’s increases in brands are most likely driven by the increased demand for baseball related products following the chase of Roger Maris’ single season home run record by Mark McGwire and Sammy Sosa in 1998. This increase in brands is likely due to the overproduction of cards in the 1980s and the softening secondary market for those cards produced in the late 1980s. During the 1980s, investors and speculators were still active in the baseball card market, and companies could produce mass quantities of cards throughout the year that would be stockpiled by the speculators. Seeing a secondary market transaction for a lot of 100 of the same card was not uncommon for most products of the late 1980s and early 1990s. However, once the speculators exited the market, only the collectors remained. Most collectors had little use for multiples of the same card, so, in an effort to regain the sales lost by the exiting speculators, manufacturers turned to producing additional brands. The same collectors who purchased one brand could now be brought back into the market with subsequent brands, increasing sales. Another possible reason for the increase in brands was to solve the durable goods monopoly problem that exists in baseball cards. By producing another brand, manufacturers may have found a credible method of shortening the lifespan of a product. There is evidence that most new entrants to the baseball card market experienced this type of problem. In 1981, both Donruss and Fleer were produced based upon collector demand. As the year progressed, if their product sold out they would print more to meet demand. After realizing that they were alienating their customers due to the adverse effects on prices in the secondary market, both Donruss and Fleer discontinued this practice in 1984. In 1990, the Score brand of cards sold particularly well during the first half of the year. As a result, management started the printing presses and flooded the market throughout the second half of the year. The result was so devastating that when Jerry Meyer became CEO of the manufacturers of Score, the company name was changed to Pinnacle. In addition, Pinnacle began to stamp cases of product with a serial number to restore collector confidence. There are also rumors that Upper Deck followed a similar practice of overproducing specificcardsintheearlyyearsof its existence23. While the precise reason for the shift to increasing the number of brands is unclear, it is certainly clear that the focus of manufacturers shifted from selling as much as they could of one brand to selling all they had produced of one brand as quickly as possible. Whilelookingatthenumberofbrandsprovidessomeinsightastothecompanies’production strategies, it may be more informative to look at the number of releases companies hadfrom1988to2000asUpperDeckbegantoreleaseitsbrandsinseriesin1989. Other

23For more information on Upper Deck’s policies, see Williams (1995).

24 20 Donruss 15 Fleer Pacific 10 Pinnacle Topps 5 Upper Deck Wizards 0

8 0 2 4 96 8 0 198 199 199 199 19 199 200

Figure 1: Manufacturer Brands by Year, 1988-2000

Donruss 20 Fleer 15 Pacific Pinnacle 10 Topps Upper Deck 5 Wizards

2 4 990 99 99 000 1988 1 1 1 1996 1998 2

Figure 2: Manufacturer Releases by Year, 1988-2000

25 companies would follow this strategy. Figure 2 shows the number of releases by manufacturer from 1988 to 2000, where the same three caveats that apply to the construction of the brand data also apply to the release data. The release data shows a similar pattern as the brand data, although the levels of releases are higher than the levels of brands due to the fact that some manufacturers released their brands in more than one series. Figure 3 shows the number of releases and brands in the baseball card industry from 1989 to 2000. The graph begins in 1989 since no manufacturers released their product in series between 1981 and 1988. The gap between releases and brands increases until 1996, at which time the gap begins to shrink. As the gap grows wider it means that the producers were releasing their brands in larger numbers of series, and as the gap grows smaller it means that the producers were releasing less series of their brands. One possible explanation for the increase in the gap between series and brands is similar to the explanation for the increase in brands above. Manufacturers wanted to keep those people who purchased baseball cards at the beginning of the year to continue to purchase during the middle and end of the year. Initially, they broke their products into series, as consumers would need to buy both series to complete their sets or find their favorite players. This would bring in a smoother revenue stream for the manufacturer, keep consumers purchasing the manufacturers’ products throughout the year, and had essentially no extra cost to the manufacturer since all of the design work had to be completed by the time the first series was produced. However, manufacturers began to realize that if the first series did not sell well then any future planned series were unlikely to do well. But those consumers who shun one product from the manufacturer may be willing to purchase a product bearing a different name, leading to manufacturers producing more brands and less products in series. Currently, most of the products produced in series form are the products that already have an established consumer following, such as basic Topps or Upper Deck. The term basic is used in the hobby to refer to the line of the first brand of cards ever produced by the manufacturer. Basic Topps extends back to 1951, while basic Upper Deck extends back to 1989. Additionally, releasing a product in series format can be used to extend any economic profits that result from a brand surpassing expectations. One brand released in 2002, Topps 206, is a new brand from Topps. It quickly rose to the top of most consumers’ want lists, and Topps has released two follow-up series that were not scheduled for release in order to capture any economic profits resulting from the brand being so well received by consumers.

Release policy — 2001-2002 The data presented in this section is the ﬁrm level data used in the empirical analysis in chapter 4. The data consist of the release dates and descriptive statistics of 92 of the 95 baseball card releases24 that occurred between October 12th, 2001 and November 27th, 2002. Of the 92 releases, there were 83 distinct release dates. The most releases occurring on

24Three releases are omitted because speciﬁc release dates could not be veriﬁed.

26 any day was two. No manufacturer had more than one release on a given day. Of the 9 occurrences where two products are released on the same date, 4 of those occurrences were Playoff and Topps, 2 were Fleer and Topps, and there was 1 occurrence each of Playoff and Fleer; Topps and UD; and Fleer and UD. It should also be noted that most of these multiple release dates occurred between the end of the baseball season and Christmas Day, suggesting thattheremaybetimeperiodswhendemandishighenoughtodisruptanyattemptstouse the APM. Figures 4 and 5 show the actual date of the brand release by each manufacturer. The vertical gridlines are placed every 5 days, which is approximately the average length of time between release dates. Brands with suggested retail prices greater than $10 are set slightly above the lower priced brands for each manufacturer. While there are some periods of overlap and some periods without any releases, the general idea that the baseball card industry may be using the APM is supported. In addition to the potential breakdown in the APM during the holiday season, figure 5 also shows that there was a fair amount of overlap in late April of 2002 and early May of 2002. The abundance of releases during this time periodcanbeexplainedbythethreatofaMLBPAstrikethatwouldhaveoccurredinlate August or early September of 2002. Manufacturers, knowing from firsthand experience that the player’s strike of 1994 depressed card sales for nearly 3 years, may have felt pressured to release the brands earlier in the year than they had planned. Perhaps in the manufacturers’ minds, the loss in profits from flooding the market early in the year were not likely as great as the loss in profits that could have occurred if the player’s went on strike. Table 1 provides a summary of descriptive statistics for each manufacturer as well as for the industry. The mean days between releases is found by dividing the number of days in the sample period by the number of releases. The industry column, which looks at the spacing of releases regardless of manufacturer, shows that one baseball card release occurred approximately every 4.5 days, while the mean time between actual release dates is about 5days. Thedifference is due to the 9 occurrences where two products are released on the same day. The columns with the manufacturer names provide descriptive statistics looking solely at that manufacturer’s releases. Note the difference between the average time between each of the individual firm’s release and the average industry release. If one market period in the industry is considered to be 4.5 days, then Fleer and Upper Deck are releasing approximately once every 4 periods, while Topps and Playoff are slightly off the pace. This behavior matches the prediction of the APM in that one release occurs by a different firm approximately every period. The longest lag between releases for the entire industry is 16 days, which occurred between 8/14/2002 and 8/30/200225. One potential problem with using all of the products released is that they may not be close substitutes, as suggested retail prices per pack can vary greatly. For instance, 2001

25The 16-day lag occurred in August of 2002, but there is the possibility that one of the three omitted products was released during that time, which would make the longest lag 15 days, from 9/18/2002 — 10/3/2002.

27 80 70 60 50 Releases 40 Brands 30 20 10 0

1989 1991 1993 1995 1997 1999

Figure 3: Industry Aggregates, Releases and Brands, 1989-2000

10/11/2001 11/30/2001 1/19/2002 3/10/2002 4/29/2002

Figure 4: Time series of baseball card releases by manufacturer from 10/11/2001 — 5/1/2002

28 FL

5/2/2002 6/21/2002 8/10/2002 9/29/2002 11/18/2002

Figure 5: Time series of baseball card releases by manufacturer from 5/1/2002 — 11/27/2002

Table 1: Industry Summary Statistics, All Brands Industry Fleer Playoﬀ Topps Upper Deck Mean days b/w releases 4.52 17.85 24.44 13.79 17.61 Std dev 3.55 10.91 21.53 8.91 12.18 No. of releases 92 21 17 30 24 Min. days b/w releases 0 2 2 1 2 Max. days b/w releases 16 54 86 37 46

29 Table 2: Industry Summary Statistics — Low Price Brands Only Industry Fleer Playoﬀ Topps Upper Deck Mean days b/w releases 6.35 17.85 27.93 15.45 18.50 Std. dev 5.04 10.91 21.97 13.57 13.07 No. of releases 84 21 15 27 22 Min. days b/w releases 0 2 2 5 2 Max. days b/w releases 16 54 86 61 46

Donruss Signature and 2002 Topps Series I were released on the same day. However, the Donruss brand carried a suggested retail price of $49.99 per pack whereas the Topps brand’s suggested retail price was $1.29. Of the 92 brands, 68 have suggested retail prices between $0.99 and $5, 16 have SRPs between $6-$10, and 8 products have SRPs greater than $15, with the highest pack price being $100 for a pack of four cards of 2001 Upper Deck Ultimate Collection. Table 2 provides a summary of industry statistics with only low price brands, which are considered to be those brands with suggested retail prices below $10. The low- priced market period is now about once a week, which seems to be a more reasonable time period on which to coordinate releases than the 4.5 days when all the brands are included. A trend has recently begun that suggests that manufacturers view the scheduled release date as an important one to meet. It has become more and more common for baseball card manufacturers to insert redemption cards into packs of cards. If a consumer receives one of these redemption cards, he can redeem it for the item specified on the redemption card. In the past redemption cards were used primarily for items that were too large to fitintoapack of cards, perhaps an additional set of cards, a particular player’s game-used bat, or a chance to win a trip to a World Series game. Currently, redemption cards are also being inserted forobjectssuchasautographedcardsandrookieor1st-year cards26,bothofwhichfitinthe card pack. The stated reason for issuing redemption cards for autographs is that the player autographing the card did not return the autographed cards to the manufacturer in time for the manufacturer to include them in the packs when the product was scheduled to ship. As for the rookie card redemptions, these are typically redemption cards for unknown rookies that may emerge during the upcoming season, and these types of redemptions are inserted in brands released early in the baseball season (about January to July). The reason for the inclusion of these redemption cards is to ensure that the brands released early in the season donotmissanyofthekeyrookieplayerswhomayhaveanimpactduringtheyear. In either case, manufacturers could avoid inserting redemption cards by delaying the release of the brand. The fact that the manufacturers do not delay the release of the brand implies that there is some reason they find it beneficial to release products on their scheduled release

26Although the deﬁnition of a rookie card has changed over time, rookie cards are generally deﬁned by the hobby as any nationally distributed card of a player released in a year provided that player did not have a nationally distributed card released in an earlier year.

30 date.

Communication Manufacturers can communicate in a variety of ways. Every year since 1985 there has been an annual trade conference for sports cards held in Hawaii at the end of February. Manufacturers, wholesalers, and hobby stores meet to discuss the current and future state of the sports card market. Manufacturers unveil some new products and ideas, and also listen to feedback by major retailers. Manufacturers unveil products to hobby stores through press releases or sample cards, and most of these press releases can be found in one or more of the sports card magazines (Tuff Stuff, Beckett Baseball Collector, Sports Collector’s Digest) in order to inform consumers about upcoming products. These press releases contain information on the number of cards in the release, insert cards and their odds ratios, the suggested retail price of a pack of cards, the number of cards in a pack, how the brand will be distributed (hobby or retail), and the intended release date of the product. Most of that information has been reported in the press releases regardless of the time period, but two major changes have occurred. The first concerns the odds ratios of the insert cards. Due to legal actions brought against the manufacturers they were required to list odds ratios for the inserts cards in the mid-1990s. Also, either manufacturers have not always been as specific about the release dates of their products as they are now or Beckett did not publish the dates in their magazines. The first specific release date reporting by Beckett occurs around the end of 1997 — beginning of 1998. It seems to be that after Pinnacle went bankrupt all of the manufacturers began listing release dates of their products. Upper Deck appears to be thelastofthemanufacturerstofollowthisstrategy,beginninginlate1998. Unfortunately, some of the release dates provided in the periodical are only intended release dates and not actual release dates. This method of communicating through providing intended release datesisthebasisfortheexperimentruninchapter5.

Performance Because there is only one publicly held company that produces baseball cards, information on performance is scarce. The information gathered is from Topps’ annual reports filedwiththe SEC. Table 3 shows the sales figures for Topps’ sports collectibles products from fiscal year 1998 to fiscal year 2002, as well as the contributed margin for sports collectibles products. It should be noted that Topps does not separate its sports collectibles products sales into segments, meaning that the data below is the most detailed that can be obtained. Also, although information exists on sales figures prior to fiscal year 1998, Topps did not separate its sports collectibles sales from its entertainment cards sales, so that data is not included. The table shows that Topps’ sales and the margin from sports collectibles products has been declining since 1998. In each annual report Topps has an explanation for this decline in

31 Table 3: Topps’ Financial Information Fiscal Year Salesa Margina 2002 $118,368 $30,856 2001 $122,918 $36,365 2000 $133,803 $47,408 1999 $124,855 $48,414 1998 $141,324 $41,842 a in thousands of dollars sales. The decline in fiscal year 2002 was due to lower sales of football and basketball products, partially offset by an increase in the sale of baseball products. The increase in fiscal year 2000 was due primarily to an increase in baseball sales following Mark McGwire and Sammy Sosa’s pursuit of the single season Major League Baseball home run record, as well as shipment of basketball products in the first quarter of fiscal year 2000 that would have occurred in the fourth quarter of fiscal year 1999 had it not been for the NBA lockout. Topps’ further states that increases in baseball sales helped to offset the loss in revenue from fiscal year 1998 to 1999 due to the NBA lockout. Thus, for most of this time period baseball sales were rising or at least holding steady. Although there is little information on profits in the industry, some inferences can be made based on how the industry structure has changed. The biggest change was Pinnacle’s bankruptcy in 1998, possibly due to overextension and the contracting baseball card market up to that point. However, this did not deter other companies from seeking licenses from MLB and the MLBPA. Pacific obtained a license in 1998 and Playoff obtained a license in 2001, which suggests that some manufacturers believed the industry to be profitable.

Market Conditions and Consumer Preferences Traditionally, consumers of baseball cards have been children, buying packs of cards with a stick of bubblegum in an attempt to obtain a picture card of a favorite player. In the 1970s the industry began to change, as those children who collected their first cards in the 1950s grew up and attempted to recapture their youth by purchasing cards from their era. As the hobby developed, card prices shot up rapidly. The late 1970s and early 1980s saw an increase in both card stores and publications of price guides, with The Sport Americana Baseball Card Price Guide of 1979 the first major price guide. With the increase in visibility, speculators entered the market and in the 1980s stockpiling of cards, particularly rookie cards, became a major craze. Although the definition of a rookie card has changed over time, it is generally defined by the hobby as the first nationally distributed card of a player in a brand of cards, as long as that player has not had a card in a brand of cards from the manufacturer of that brand or another manufacturer in an earlier

32 year. Rookie cards are a staple in the hobby, and their appeal to collectors has driven some recent changes in when manufacturers release products. Examplesmaybethebestwaytoexplaintherookiecardconcepttothosewhoarenot familiar with it. In 1983, Topps, Donruss, and Fleer all released their first cards of Tony Gwynn, so all three cards are considered rookie cards. In 1984, Fleer and Donruss both released a card of Kevin McReynolds, so they were considered his rookie cards. Topps, however, did not have McReynolds under license then, and would not release its first card of McReynolds until 1988. The 1988 card is NOT considered a rookie card by today’s standards, although it is considered his First Topps Card (FTC), a label which had more importance in 1988 than it does today. Moving forward a few years to when manufacturers were releasing more than one brand of cards in a year, consider the case of Vladimir Guerrero. In 1995, Guerrero had cards produced in two different brands, Bowman and Bowman’s Best. Both cards are considered rookie cards even though the brands are both produced by Topps. Any Guerrero card after 1995, regardless of which manufacturer produces it, is NOT considered a rookie card. The change in release strategy was triggered by Pinnacle’s bankruptcy and Playoff’s purchase of the Donruss and Leaf brand names. Due to legal action by MLB and MLBPA, Playoff was prohibited from releasing a product that Pinnacle had already produced in 1998, Leaf Rookies & Stars, until December of 1998. Because of its late release date, which was after the four current manufacturers had already released their basic 1999 products, Playoff was able to include rookie cards of some players, notably Troy Glaus and J.D. Drew, both of whom had few other cards released during 1998. About the same time, Upper Deck released a product called Upper Deck Black Diamond which contained the first Upper Deck issued J.D. Drew card and its second Troy Glaus issue. However, Upper Deck made the mistake of labeling the product with a 1999 date, and even though the two products were released within days of one another in December, collectors decided that the Playoff product contained rookie cards of those players and the Upper Deck product contained 2nd year cards. Duetothisdesignationbythehobby,thesecondarymarketvaluesofthecardsgreatlydiffer, and the Playoff product is heralded as one of the top products of the 1990s, while the Upper Deck product is just another brand. Perhaps because of this occurrence, when Upper Deck released its Black Diamond product in 2000 it released it in two series. The second series was released in December of 2000 and was called Upper Deck Black Diamond Rookie Edition. Thus, the practice of squeezing in releases at the end of a calendar year after releases for the following calendar year had already been released was born. While the rookie card craze shows some evidence of preferences for newness by collectors, more evidence on can be found by looking at the monthly surveys in Beckett Baseball Card Monthly 27 (Beckett). Each month Beckett lists the top 5 items that are the hottest on the market according to surveys of dealers and consumers, and in 18 consecutive monthly

27The magazine recently changed its title to Beckett Baseball Collector and has subsequently changed to Beckett Baseball.

33 issues from August 2000 to January 2002 only two brands were able to sustain the highest ranking for more than one month, 2001 Topps Heritage (4 months at number 1) and 2000 Greats of the Game Autographs (2 months). In all, there are 56 products listed in the possible 90 spots throughout the 18 month span, showing an incredible amount of turnover as consumers move from product to product. Also, there are an abundance of anecdotal stories describing the preferences for newness of consumers of baseball cards. In an article on refractors, a particular type of parallel card produced by Topps, Broome (1996) begins with, “The baseball card hobby has been marked by a ﬁckle collector base that collectively jumps from one "hottest issue of the week" to the next”. Those sentiments are echoed by veteran card dealer Kit Keifer in Broome (1996):

“There is always going to be more demand for a current year’s product, at least for a couple of weeks,” Keifer says, half joking. “The window of opportunity for new sets seems to be getting smaller and smaller. With chase cards (inserts), dealers and collectors have preconceived notions of supply. More often than not, they are wrong.”

This evidence on consumer behavior fits preferences for newness as they are defined in chapter 2. It also suggests that traditional models and empirical analysis that neglect preferences for newness may provide results based on an incorrect specification of consumer preferences.

34 CHAPTER 4

EMPIRICAL RESULTS

Papers that attempt to detect whether or not observed industry behavior is collusive tend to fall into two categories. Papers such as Baker and Bresnahan (1985) and Nevo (2001) constitute a first category. These papers analyze residual demand within the beer and cereal markets respectively. These residual demand techniques rely on cross-sectional price and quantity data to determine the substitutability of goods within the product category when prices change. While useful in industries where the same goods are consumed over time, these techniques are not particularly useful in industries with preferences for newness because they rely on estimating cross-price elasticities between brands. One of the keys to the residual demand analysis is that all (or most) brands are available at the same time periods, allowing for the consistent estimation of these elasticities. In the baseball card industry (and, more generally, industries with preferences for newness), there may not be much available data on simultaneous sales of products released a few time periods apart. Even if the data were available residual demand analysis relies on decomposing price- cost margins into three pieces: the amount due to product differentiation, the amount due to multi-product firm pricing, and the amount due to potential collusion. Note that there is nomentionofhowmuchoftheprice-costmarginisduetothelengthoftimetheproducthas been on the market, which would be a crucial element in analyzing whether or not pricing behavior is collusive in markets for goods where consumers exhibit preferences for newness. Papers such as Porter and Zona (1993) and Bajari and Ye (2002), which attempt to determine whether collusive bidding has occurred in procurement auctions, constitute the second category. The collusion detection methods in these papers rely on participation in each auction by cartel and non-cartel members. Using the bids submitted by all firms and controlling for other factors, it is possible, under conditions of conditional independence of bids and exchangeability, to determine which bids placed in the auction could be collusive. Unfortunately this methodology relies upon not only seeing the winner of the auction (i.e. the sole producer in the APM), but also the bids of other participants. Since information of this type does not exist in the baseball card industry it will be impossible to use this methodology. Due to the limitations of these methods, particularly in regards to goods with preferences for newness characteristics, an alternative approach is used in an attempt to detect potentially collusive behavior. Duration models are used to determine if the release patterns appear to be spaced out over time (i.e. positive duration dependence) or clustered (i.e. negative duration dependence) in the data from the baseball card industry. This method is explained in the following section. While the results found using duration analysis are not as powerful as those made with the techniques described above, the duration analysis

35 technique does not rely on assumptions that may perhaps be unreasonable for the industry in question.

Duration Analysis In order to determine whether brands are randomly introduced into the market I estimate a set of duration models to test for duration dependence. Duration dependence can be defined as the impact the length of a spell has on the timing of the end of the spell. If data exhibits positive duration dependence it means that as more time passes it is more likely the spell will end, while negative duration dependence means that as more time passes it is less likely the spell will end. A third type of duration dependence, constant, means that the length of the duration has no impact on the probability it will end. In the baseball card industry, as well as others, positive duration dependence implies that the probability that a new release occurs is increasing since the time of the last release, while negative duration dependence implies that the probability is decreasing. Thus positive duration dependence is consistent with the notion that firms are waiting to release products, while negative duration dependence implies clustering of products. A more intuitive method of determining whether positive or negative duration dependence is occurring is to look at the hazard function. For a distribution function, F (t),andits f(t) associated density function, f (t), the hazard function is defined as h (t)= 1 F (t) .The hazard function evaluated at t tells the probability of an event occurring given that− we have observed a duration of length t. Anincreasinghazardfunctionreflects positive duration dependence while a decreasing hazard function reflects negative duration dependence. It is also possible to have constant duration dependence, which is shown by a hazard rate independent of t. Constant duration dependence would imply that product releases occur randomly, and that the length of the duration has neither an increasing nor decreasing effect on when a new release will occur. The exponential distribution function, 1 exp ( λt),is an example of a distribution function with a constant hazard rate, which in this− case− is λ. In order to determine which type of duration dependence exists in the data, I have chosen to model the data using the Weibull distribution function. The Weibull function is chosen because the hazard function can display increasing, decreasing, or constant duration dependence depending on the shape parameter. Equations (9) and (10) show the Weibull distribution and hazard functions respectively. The variable λ is the scale parameter (also known as the baseline hazard because if α =1the hazard rate reduces to λ)andα is the shape parameter. A test of α =1vs. α =16 is equivalent to testing whether the Weibull can be statistically distinguished from the exponential model, which provides a test as to whether the hazard rate is constant. Additionally, the Weibull distribution can establish positive duration dependence if α is statistically greater than 1.

P (t)=1 exp( λtα) (9) − −

36 α 1 h (t)=λαt − (10) Another form of the Weibull considers the impact independent covariates have on dura- 0 tion dependence. The baseline hazard is typically specified as λi =exp(xiβ) to ensure that probabilities remain positive. The rationale for specifying the baseline hazard as a function of independent covariates is to account for possible time-independent heterogeneity among manufacturers that may cause their baseline hazard rates to differ. In the baseball card industry, it could be that different manufacturers are following different release strategies, and that looking at overall industry behavior obscures this. It is also possible that products with the same prices are released in clusters while releases in general are not, and clustering of like priced products would suggest competition. These possibilities are examined below.

Duration Analysis Results The data used in the analysis is the data from the section on release policy — 2001-2002 in chapter 3. Readers may wonder if measuring time in days is the most relevant measurement of time, as it raises questions about the behavior of the baseball card consumer. Although it pertains to the movie industry, there is an interesting story reported by The New York Times (pg. C.1.) on October 11, 2002 about a breakfast between Jeffrey Katzenberg, a Dreamworks studio founder, and Harvey Weinstein, co-chairman of Miramax Films in relation to two Leonardo DiCaprio films, Gangs of New York and Catch Me if You Can. Both were scheduled to open on Christmas Day 2002. In the end, Weinstein altered his release date and Miramax “chose” to release Gangs of New York just five days earlier, on December 20th. This small change in release date was apparently all that was needed to alter expected profits enough to satisfy both parties, suggesting that what may look like trivial changes in release dates are actually quite important. Second, while it may not be realistic to think that consumers walk into the baseball card store each day, it should be noted that there are a variety of online stores at which consumers may shop. Many major card stores now use either Ebay, a baseball card specific web site like www.beckett.com, or their own web site to sell products. Thus, it is possible that consumers are “visiting the store” more often than once every market period, even if they are not visiting a traditional brick and mortar location. Finally, aggregation of the data into a larger time denomination such as weeks poses at least two problems. A first problem is how to aggregate the data in terms of larger time denominations. Choosing a day of the week to begin the week is purely arbitrary, and different choices of the starting day for each week could lead to vastly different results. choosing the day that begins the week is arbitrary and could dramatically alter the “observed” industry release pattern. Second, aggregation reduces the amount of available information, and in particular reduces the size of the lags between releases in a potentially harmful way. Consider two products that are released 12 days apart. If the data are aggregated it could look like the products are released in consecutive weeks. Now

37 consider two products released 1 day apart. When aggregated, this data could also look like the products were released in consecutive weeks, even though it is much more likely that the first two products are released in what would be considered a different time period than the second two. It seems that aggregating the micro data could lead to obscuring potentially useful information, as Engle (2000) suggests. For all of these reasons the durations are left as days. The results of estimating duration models using the Weibull distribution are below. Be- fore proceeding, there is one small adjustment made to the data in order to allow estimation of the Weibull distribution. One problem with estimating the Weibull model is that observations cannot be recorded as zero as the log-likelihood function will be undefined. Since there are several occurrences of two brands released on the same day it is unclear how to record the interval between releases. Two approaches are taken to circumvent this problem. The first approach assumes that both releases are reactions to the previous release, so the value assigned to each release should be the time since the last previous release, which results in the same length of time recorded for each observation. I call this method of assigning the duration the best response (BR) definition. Another method of recording the duration for two products released on the same day would be to track down the hour of release for each brand, and then assign a fractional amount to the release that occurs later in the day. Since it is not feasible to track down the hour of the release, a value of 0.5 is assigned to one of the releases that occurs on the same day, and the following release has its duration adjusted downward by 0.5. I call this method of assigning the duration the halfs definition28. Using the BR definition, the shape parameter (α) is 1.5458; using the halfs definition resultsinanestimateofα of 1.3138. Estimates of λ are 0.07 and 0.12 for the best response and halfs assignment methods respectively. Both methods yield statistically significant results at the 5% level for both parameters and both result in positive duration dependence. The halfs definition implies a slightly steeper climb at the beginning of the hazard function followed by a flatter rise than the best response definition, as shown in figure 6. The hazard rates at 4.5 days, which is the average amount of time between releases in the industry, are approximately equal with either method, at 24.5% for the BR definition and 26% for the halfs definition. In an effort to see whether industry behavior obscures firm behavior, I estimated all possible individual firm, 2-firm, 3-firm, and 4-firm combinations, for a total of 15 models29. To construct the data set for any combination of firms, simply remove all products released by any firm not included in the combination and recalculate the durations between the remaining releases. One reason to test all combinations is to see if any combinations provide results that are qualitatively different than other combinations. In particular, if individual firm models yield hazard rates that are different than the overall industry model this may suggest

28Since assigning a value of 0.5 is arbitrary, models with other fractional assignments were also estimated. The general result remains unchanged using those other fractional assignments. 29The 16th combination is the null set, which is not tested for obvious reasons.

38 0.4 0.35 0.3 0.25 0.2 h(t) 0.15 0.1 0.05 0 12345678910 BR Time (days) Halfs

Figure 6: The hazard rate for all releases using the best response (BR) and halfs definitions. that an individual firm is using a release strategy that is masked by industry behavior. A second reason to test all combinations is to try to discern if any set of firms in the industry is behaving differently than the industry as a whole. For example, suppose the industry as a whole displays positive duration dependence but a 2-firm combination displays negative duration dependence. This implies that while the industry behavior matches the APM, the firms in the 2-firm combination typically release close to one another, which may be viewed as one firm trying to force the other out of the industry or take its market share by competing on a head-to-head basis. Table 4 shows the estimated results for the models where all brands were considered. I find that all 15 combinations returned a hazard rate that was increasing, and in 12 of the 15 cases the hazard rate was significantly different than 1 at a minimum of the 5% level. The only insignificant results occur in the model for Playoff alone, Upper Deck alone, and the Topps and Upper Deck combination, although Upper Deck alone and the Upper Deck and Topps combination are significant at the 10% level. Estimating the model for Playoff alone may result in insignificant parameter estimates because Playoff was the newest entrant into the baseball card market, resulting in fewer observations. It is also reasonable to assume that Playoff had less knowledge about the industry, and that part of this time period was spent learning. The reasons for the insignificant results in Upper Deck alone and Upper Deck and Topps are unclear, although it is possiblethataceaseanddesistordersentbyUpper Deck to other manufacturers regarding the production of game-used memorabilia cards lead

39 Table 4: Duration Analysis Results Combination λ SE λ α SE α No. of obs All BR 0.070∗∗∗ 0.022 1.546∗∗∗ 0.147 91 All halfs 0.124∗∗∗ 0.031 1.314∗∗∗ 0.124 91 Fleer (F) 0.005 0.005 1.777∗∗∗ 0.288 20 Playoff (P) 0.016 0.018 1.255 0.291 16 Topps (T) 0.011 0.009 1.652∗∗ 0.279 29 Upper Deck (UD) 0.014 0.012 1.448∗ 0.315 23 F,P 0.015 0.009 1.680∗∗∗ 0.209 37 F,T 0.030∗ 0.018 1.555∗∗∗ 0.227 50 F,UD 0.036∗ 0.019 1.422∗∗ 0.207 44 P,T 0.019∗ 0.010 1.665∗∗∗ 0.174 46 P,UD 0.039∗ 0.020 1.339∗∗ 0.161 40 T,UD 0.066∗∗ 0.029 1.284∗ 0.174 53 F,P,T 0.029∗∗ 0.013 1.724∗∗∗ 0.189 67 F,P,UD 0.036∗∗ 0.017 1.605∗∗∗ 0.200 61 F,T,UD 0.086∗∗∗ 0.031 1.321∗∗ 0.149 74 P,T,UD 0.065∗∗∗ 0.023 1.418∗∗∗ 0.147 70 The asterisks refer to significance levels for a 2-tailed test of λ=0 and a 1-tailed test of α>1. is significant at 1%, is significant at 5%, and is significant at 10% ∗∗∗ ∗∗ ∗ to some break down of the APM. Perhaps Upper Deck was angered by the indifference with which the order was received by the other manufacturers and began to release products close to their’s to try to compete head-to-head. It is also possible that Topps, in response to the order, began going head-to-head with Upper Deck by releasing its products close to Upper Deck’s. One factor that could lead to a potential bias in the results is the different individual pack prices. Although the baseball card industry seems narrowly defined already, the difference in pack prices suggests that not all of the brands released are in direct competition, as the example in chapter 3 with 2001 Donruss Signature and 2002 Topps Series 1 suggests. It seems questionable to consider these two products as close substitutes since their prices differ so much, with the former product targeted for adults and the latter for children and set collectors. After removing all products with a SRP greater than $15 per pack, the results did not change much. The shape parameter, α, dropped to 1.520 for the best response definition and 1.306 for the halfs definition. Both methods yielded parameters significantly different than one at the 5% level. The scale parameter, λ, dropped to 0.062 for the best response definition and 0.113 for the halfs definition. Both methods yielded scale parameters significantly different than zero at the 1% level. Figure 7 shows the hazard functions for the low price brands for the best response and halfs definitions. Using the best response

40 0.35 0.3 0.25 0.2

h(t) 0.15 0.1 0.05 0 12345678910 BR Time (days) Halfs

Figure 7: The estimated hazard rate for low-price brands using the best response (BR) and halfs definitions. definition,wecanseethatthereisa15%chancethatafirm will release a low price brand one day after another low price release has occurred. By the sixth day (about one market period for low releases) that probability has risen to 24%. Using the halfs definition, there is about an 8% chance that a firm will release a product one day after the other firm, with the probability increasing to 26% by the sixth day. In an attempt to control for possible heterogeneity in release strategies across manufacturers, I estimated the duration model for the industry using suggested retail price and dummy variables for the manufacturers as independent covariates. Even with these controls positive duration dependence still exists, and the coefficients on the independent covariates are not significantly different than zero. These results are consistent with the results from the individual firm models above, suggesting that all firms are involved in behavior that matches the APM. All of these results are amazingly consistent in that regardless of which way the data is analyzed it exhibits positive duration dependence. These results are consistent with the APM described above. The individual firm results and the results with independent covariates suggest that all firms are using a similar strategy of waiting at least a few days after a release has occurred to release another product, and that industry behavior is obscuring little in the way of individual firm strategies. There is also some possible evidence of competition between the two largest manufacturers, Topps and Upper Deck, although it is

41 tenuous.

Benchmark comparisons Benchmark models are estimated in order to compare the hazard functions resulting from the observed data with researcher constructed release patterns that are known not to exhibit the features of the alternating periods monopoly. Two data sets are constructed using the baseball card industry data as a guideline. Assume that there are 92 releases that occur, and that those releases occur in a period of 411 days. This will create 91 observable durations, with the average duration length equal to 4.5 days. Also, to simplify the analysis, assume that there are 4 firms and each firm releases 18 products30. The first benchmark data set is constructed by assuming that all four firms release a product on the same day. Due to the problem of including durations of 0 in the maximization of the log-likelihood function, three firms are assigned a duration value of 0.33. There is then a duration of 17.7 days, after which all of the firms again release on the same time. The duration of 17.7 days is the necessary amount of time to keep the average duration at 4.5 days. This duration of 17.7 days is assigned to the first firm to release its product, and then the next three durations are again recorded as 0.33. This results in a data set that consists of 69 durations of length 0.33 days and 22 durations of 17.7 days. The second benchmark data set is constructed by assuming that the four firms release their products on successive days. This is still a fairly competitive market in terms of when products are released, but it avoids the problem of “observing” a duration of length 0. Three firms are assigned a duration of 1 day, and the fourth firm is assigned a duration of 15.5 days. Again, this duration of 15.5 days is the necessary amount of time to keep the average duration length near 4.5 days. The process is then repeated, producing a string of durations similar to the first benchmark data set. The second benchmark data set consists of 69 durations of length 1 and 22 durations of 15.5 days. Due to the nearly degenerate nature of these benchmark data sets the Newton-Raphson algorithm used to obtain estimates for α and λ for the actual baseball card industry data cannot be used for the benchmark data sets. The reason is that the variance-covariance matrix of the parameter estimates for the benchmark data sets is nearly singular. Thus, a grid search is used to obtain estimates for the parameters of α and λ.Forα,theshape parameter of the Weibull distribution, the grid search is performed over the range of values (0.01, 1.50), increasing by hundredths. For λ, the scale parameter, a range of values from (0.01, 1.05), also increasing by hundredths, is used. Interior solutions are found in both of the benchmark data sets, and the value of the likelihood function is decreasing at the boundary points. In the data set where it is assumed that firms release products on the same day, the shape parameter (α) and the scale parameter (λ) are estimated as 0.52 and 0.66 respectively. In the consecutive days of release benchmark

30It could just as easily be assumed that one ﬁrm releases all 92 products.

42 0.4

0.3

0.2 h(t)

0.1

0 12345678910 Same Day Time (Days) In A Row

Figure 8: Hazard rates for the benchmark data sets data set the parameters α and λ are 0.76 and 0.37 respectively. Of particular interest is the shape parameter, α. Notice that it is less than 1 for both benchmark data sets, implying that the hazard rates will be decreasing. Figure 8 depicts the hazard rates for both of the benchmark data sets. The important conclusion drawn from this exercise is that an industry in which ﬁrms cluster the release of their products will exhibit negative duration dependence. This is the opposite of the result obtained from the estimation using the actual baseball card industry data, as the actual data produced hazard rates that were increasing and statistically diﬀerent than 1. It should also be noted that a pattern of randomly spaced releases can also be rejected. If the time between releases were purely random then the hazard rate would be constant, which would imply that the shape parameter, (α), would need to be equal to 1. Recall that α is statistically greater than 1 in all but one industry combination using the actual data from the baseball card industry. It can now be concluded that the pattern of baseball card industry releases is consistent with the alternating periods monopoly.

43 CHAPTER 5

EXPERIMENTAL TEST

An economic experiment is designed with two objectives in mind. The firstobjectiveis to provide a test of the empirical validity of the requirements of the Folk Theorem model described in chapter 2. While the requirements are theoretically valid, it remains to be seen whether the APM strategy will be used in practice. The benefit of running the experiment is that the payoffs can be constructed to match the theoretical requirements. In addition to the theory testing objective, an often debated aspect in the collusion literature is whether or not collusive schemes require explicit communication among members of an industry. Alternatively, the question may be stated as: Do industry practices exist that facilitate collusion? The experimental economics literature suggests that explicit communication is important for collusive outcomes to occur. Thus, the second objective of the economic experiment is to determine whether or not the APM can arise without explicit communication if subjects are allowed to signal their intentions using a multiple-periods ahead signaling mechanism, similar to announcing that a firm intends to release a product at a particular time.

Prior Experimental Research There is a vast literature on the effects of communication on coordination (or collusion) in experimental economics. Papers are categorized into two groups. The first group focuses on coordination experiments and is used to develop some stylized facts on what should be expected with different design treatments. The second group consists of market experiments. Although the market experiment approach is not used, these papers are discussed brieflyto provide evidence that subjects do discover the APM in market experiments.

Coordination Experiments One of the earliest uses of experiments involved a repeated Prisoner’s Dilemma game. The goal of the experiments was to determine if subjects could learn to cooperate even though defection was the Nash equilibrium of the stage game. Since those early experiments the literature on coordination and cooperation experiments has increased dramatically, as various extensions have been added to the Prisoner’s Dilemma game, as well as coordination experiments with other popular games. One set of papers, all involving Amnon Rapoport and featuring a similar experimental design, are based on the market entry game of Selten and Guth (1982). The number of subjects is usually 20, and the games are typically structured such that there is a pure

44 strategy Nash equilibrium for some number c<20 subjects to enter the market each period, where c represents the market capacity. If more than c subjects enters the market, then all subjects who enter receive a payoff less than they would have if they remained out. The value of c is randomly drawn each period. In this first paper, Sundali, Rapoport, and Seale (1995), a treatment with no feedback and a treatment with feedback were run. In the no feedback treatment they find that there is positive correlation between c and the number of entrants, but no evidence of tacit coordination. They find similar results for the treatment with feedback. The remaining papers extend the treatments. Rapoport, Seale, Erev, and Sundali (1998) is primarily interested in testing hypotheses of loss aversion by allowing for losses as well as gains if subjects remain out of the market. This addition of losses does little to change the results from the initial paper. Erev and Rapoport (1998) adds information about other players’ payoffs. They find that this information increases entry slightly, suggesting a relative or peer effect. Rapoport, Seale, and Winter (2000) allows playerstoenteroneoftwomarketswithpotentiallydifferent capacities or to stay out of the market. The most recent paper, Rapoport, Seale, and Winter (2002), adds asymmetric payoffs to the players, where one player gains a larger amount from entering than another player. While these asymmetric payoffs should alleviate the coordination problem, it does so only slightly. The main result gained from this framework is that subjects typically choose close to the pure strategy single-period Nash equilibrium level of entry. However, no tacit coordination seems to evolve. Multiple experiments attempt to determine how an equilibrium is selected from a set of equilibria. The results of these experiments show that subjects may choose a strategy that is not the actual APM strategy. Using a stag hunt game where subjects can choose high effort or low effort, Van Huyck, Battalio, and Beil (1990) find that as the number of subjects in a group decreases the payoff dominant equilibrium (all choose high effort) becomes more likely to emerge. Also, when there is no harm from choosing high effort it typically emerges in the experiment. However, when choosing high effortiscostlysomegroupsconvergetowards the secure equilibrium, which is for each subject to choose low effort. Cooper, DeJong, Forsythe, and Ross (1990) look for equilibrium selection in coordination games. By varying the payoffsinoff-equilibrium cells of the game matrix they find that subjects do not always choose the Pareto dominant Nash equilibrium. Perhaps the most closely related paper to this dissertation is Dickhaut, Ledyard, McCabe, and Mukherji (2002). A pair of subjects play a Shapley game, which has no pure strategy Nash equilibrium to the stage game. While there is a mixed strategy Nash equilibrium to the stage game, the payoffs to the mixed strategy Nash equilibrium are much lower than if the subjects could coordinate intertemporally. The authors’ primary treatment is whether or not they allow interface-to-interface communication between each pair of subjects. In the treatments with communication, each subject is essentially allowed into a chat room with the other subject in his pair. Subjects are allowed to discuss any topics, including coordination and punishment strategies. This interface-to-interface communication greatly increases the

45 amount of cooperation between subjects. While this is not an unexpected result, it is important in two respects. First, unlike many of the market experiments discussed in the following section, the only possible method of coordination is intertemporal. Second, it is commonly believed that face-to-face communication is needed to establish intertemporal cooperation schemes in non-market experiments31. However, it may simply be that allowing free-form communication of any type, either face-to-face or written, is all that is needed. The key seems to be that if one person realizes that coordination must occur intertemporally and can explicitly tell the other person, then coordination becomes more likely.

Market Experiments Although a market experiment is not used, there have been instances of individual behavior in some market experiments that are consistent with the APM. This behavior can be seen in market experiments as early as Fouraker and Siegel (1963). In one of their quantity experiments32, number 10, group number 43 falls into a fairly stable pattern of one subject producing 25 units and another subject producing 8 units. Although this is more of a quasi- APM than a true APM, group 43 did almost as well in terms of profits as a set of subjects (groups 40 and 41 of experiment 10) who were able to produce one-half the monopoly quantity each period33. Instances such as these are scattered throughout market experiments, and can be seen in Davis and Holt (1998) and Isaac, Ramey, and Williams (1984). In Davis and Holt (1998), a group of subjects discuss possible collusive strategies and settle on the APM even when the payoff stream generated is suboptimal when compared to another collusive strategy such as ESM34. Isaac, Ramey, and Williams (1984) is a posted-offer market experiment where subjects are allowed to verbally communicate between rounds of the experiment. The market parameters are such that there are four sellers in the conspiracy sessions and the monopoly quantity is three units. One group’s collusive strategy involved rotating the seller who would not sell a unit each period. Isaac and Smith (1985) suggest that firms in their predatory pricing experiment may follow an APM. However, the de facto equilibrium that emerges from their experiment is the Stackelburg equilibrium and the necessary conditions derived in section are not met for the large firm. Other market experiments testing for collusion include Isaac and Plott (1981), Isaac and Walker (1985), and Cason and Davis (1995). In Isaac and Plott (1981), a double oral auction mechanism is used. In each session, either buyers or sellers are given the opportunitytoverballycommunicatebeforeeach round. In most periods, the group that

31An earlier paper, Brown-Kruse, Cronshaw, and Schenk (1993), also uses anonymous freeform communication in spatial markets and obtains this result. 32The exact page number is 271. 33The diﬀerence is partially due to the fact that group 43, by focusing on a rotation of 25 units and 8 units each period, produced slightly more than the monopoly level of 30 units. 34The APM is suboptimal to ESM due to increasing marginal costs of production for the experimental units.

46 is allowed to communicate begins by making collusive offers, but by the end of the period offers tend to move towards the competitive level. It should be noted that both sides of the experiment used human subjects, so there may have been some strategic demand withholding by the side of the market that was not allowed to collude. Isaac and Walker (1985) test the effect of verbal communication in both a single unit and multi-unit first-price sealed-bid auction. Subjects receive independently drawn values each period, and are allowed to discuss anything other than the quantitative value, side payments, or physical threats. While some groups began with a bid rotation scheme similar to the APM, most groups switched to a scheme where they qualitatively signalled their value. While both schemes were stable, the qualitative signaling scheme allows subjects to extract a higher level of monopoly profits each period in a setting where values are randomly drawn each period. Thus, the switch should not be seen as evidence against the APM as it is constructed in chapter 2, as all firms receive the same shock in the APM theory developed in that chapter. One of the treatments in Cason and Davis (1995) allows nonbinding pre-period price signaling in a multi-market experiment. Sellers in the experiment were able to participate in three markets, with one of those three markets a low-cost market. Even with the additional of multiple markets, most “collusive” regimes existed only because one or two sellers tolerated defections by the third group member. The price signals sent did not lead to collusive schemes. Kwasnica and Sherstyuk (2002) find a result similar to the APM in their experimental study of collusion in multiple unit auctions with complementarities. They find that experimental subjects are able to collude using bid rotation in two-bidder two-object simultaneous ascending auctions with large complementarities. Bidders would take turns submitting the minimum bid each round in order to avoid competing away the complementarity. The use of an APM is similar to using bid rotation to capture complementarities, where the complementarity in the oligopoly can be defined as the amount each period by which one-firm monopoly profits exceed the sum of monopoly profits when k firms agree to split the market. As the experiments show, the APM should be a real concern of antitrust authorities. Although none of these market experiments is explicitly designed to capture the APM, they all show evidence that some subjects are considering it as a possible collusive mechanism.

Experimental Design The experiment is designed to test if the APM can arise without verbal or written communication between subjects. The experiment is a simple choice experiment where subjects choose whether to be “in” the market during a period or “out” of the market. There are a few reasons that a choice experiment is used in place of a market experiment in which the subjects would select a production level. First, Bru, Gomez, and Ordonez (2002) have run a set of repeated quantity choice experiments and show that there is no consistent pattern of convergence of quantity at the aggregate level. Some groups seem to be converging towards the competitive level, while others seem to be converging towards the monopoly level.

47 This lack of convergence is one reason for a simple choice experiment. Second, a market experiment would involve subjects learning about the supply and demand parameters in the experiment. Since learning the market is a time intensive process, the choice experiment allows for more repetitions of the stage game by removing this learning process. Finally, a choice experiment gives the APM its best chance at evolving as there is no other method of collusion that can evolve. If the APM fails to evolve it is either because subjects understand how the APM can increase payoffs but still choose not to use it because the costs of forming an APM are too high or because they do not understand the dynamics that would lead to the APM. There are two factors that are investigated, creating four possible treatments. The first factor is the number of subjects in a group, with either 3 or 4 subjects in each group. The second factor is the payoffs to the subjects. In the first treatment subjects received Cournot payoffsfroma3-firm or 4-firm industry with linear demand, depending on how many subjects were in the group. In the second treatment subjects received the Cournot payoffsfroma 3-firm or 4-firm industry, minus a fixedcostwhichcanbeviewedasaninnovationcost. The treatments are referred to as 4N, 3N, 4I, and 3I, where the number stands for the number of subjects in a group while the letter N corresponds to the treatment with no innovation costs and I corresponds to the treatment with innovation costs. The payoffs are determined as follows. If a subject chose NOT to enter the market in a particular period then that subject received 100 Experimental Currency Units (ECUs) regardless of the decisions of the other subjects35. The payoffs to those subjects who entered the market were derived from the k-firm linear demand Cournot profit function for k (1, 2, 3, 4). Letting P (Q)=a bQ be the inverse demand function and each firm’s ∈ − (a c)2 constant marginal cost be c,thek-firm linear demand Cournot profit function is: − 2 . (k+1) b (a c)2 − Since the term b is independent of k, it is set equal to 14, 400. In the 4N and 3N treatments this yields a payoff of 3600 ECUs if only one subject enters, 1600 ECUs each if two subjects enter, 900 ECUs each if three subjects enter, and 576 ECUs each if four subjects enter. For the 4I session, each subject in a 4-subject group received the Cournot payoff corresponding to the total number of subjects who entered minus an innovation cost of 450 ECUs for entering. In the 3I session, a 3-subject group received the Cournot payoff minus an innovation cost of 700 ECUs for entering. Subjects in the innovation costs treatments are notgivenatwo-partprofit function comprised of the Cournot profit and the innovation cost; instead, they are simply shown the profit net of the innovation cost. The different innovation costs depending on the group size are used to drive the payoff when all k firms entered close to the 100 ECUs a subject received when remaining out of the market without changing the dominant strategy Nash equilibrium of the stage game. The hope is that a payoff near the one subjects receive when staying out of the market will spur more attempts at achieving

35Thechoiceof100ECUsinsteadof0ECUsreﬂects a general opportunity cost for participating in the experiment.

48 the APM. The exchange rate was 5000 ECUs for $1 for the 4N and 3N treatments and 4000 ECUs for $1 for the 3I and 4I treatments. The experiment was designed using the Z-Tree software36. There were a total of four sessions run, one for each treatment. Between 6 and 12 subjects participated in each of those four sessions. Subjects were seated at a computer terminal and were randomly and anonymously placed into groups of 3 or 4 depending on the treatment. Subjects knew the total number of members in their group and were told that while the other members of their group would remain anonymous, the group members would remain the same throughout the duration of the experiment. They were also told that the experiment would last at least 80 periods, and that after 80 periods there was an 85% continuation probability after each period. This randomly determined endpoint provides the stimulus to ensure that subjects do not view the game as one with a fixed endpoint. Subjects went through three screens in the experiment: the message-sending screen, choice screen, and payoff display screen, which appeared after all subjects had made their decisions for a period and showed each subject his earnings for the period as well as his total earnings37. The message-sending screen allowed subjects to send non-binding binary messages (1 for “IN” and 0 for “OUT”38) to their group members for each of the next 10 periods. To send messages subjects had to toggle between the IN and OUT buttons, and when their messages were set for the 10 periods they simply had to hit the submit button to submit all the messages at once. To aid the subjects, a box appeared that showed the signal they sent for a specific period when they sent their last set of messages. The last piece of information that the subjects receive on this screen is the history of actual decisions made by each group member in the previous rounds. The history screen is provided based on the results of Duffy and Feltovich (2002). They investigate whether actions or words more effectively enable coordination, and find that the result depends on the type of game. They find that observation and communication increases the frequency of cooperation, and in Prisoner’s Dilemma games actions speak louder than words. Also, the APM is based upon the knowledge that one firm can observe when the other has produced, providing another reason for the inclusion of the history screen. The choice screen is the screen where subjects make their decision whether to be IN or OUT. Subjects make this decision by pressing the button that corresponds to their choice. The choice screen also contained three other pieces of information. The payoff table is displayed in the lower left-hand corner. Subjects were informed that all other group members observed the same payoff table and that this payoff table would not change throughout the experiment. A history of actual decisions box is displayed in the upper right-hand corner. This box is similar to the box on the message-sending screen, although the box on the choice screen also contained the message sent by each player immediately

36The software package is described in Fischbacher (1999). 37The actual instructions for one version of the experiment are included in Appendix A. 38It should be noted that to the subjects the choices were A and B, not IN or OUT.

49 prior to their actual decision for that period. Thus, if a subject sent a message of IN for period 10 immediately prior to making his decision for period 10, the message of IN for period 10 would appear in the history of actual decisions box in period 11, regardless of the messages sent for period 10 in periods 1-9. This information was included so that subjects could determine if other group members were adhering to the signal they most recently sent for that period. Finally, in the lower right-hand corner of the screen were the messages sent by each subject in the group. These messages were only for the most recent round of messages sent.

Entry Decision Results The results of the experiment have been broken into entry decision results and individual signaling results. Although the APM did not arise in any treatments, the treatments where the innovation costs were implicitly added did reduce the number of times all players chose to enter the market. The results from the signals sent by the subjects are particularly interesting in that they shed light on the subjects thought process. Due to the binary nature of both the entry decision and signaling data, most of the results presented rely on visually spotting patterns that appear within the data. While this initial approach lacks statistical rigor, it should be noted that subjects in the experiment must use the same approach when viewing the data if they are to coordinate on an APM, without the added benefit39 of knowing to look for APM patterns. Thus, if the researcher withouttimeconstraintsspecifically looking for APM patterns in the data cannot find them while scanning the data, it is highly unlikely that time-constrained subjects will find those same patterns. While visually spotting patterns is a firststep,itispossiblefortheresearchertofind cases that he believes show evidence of the APM but which are really random strings of data. Thus in an attempt to statistically quantify subjects decisions, two definitions of randomness are used. The first definition of randomness can be described as whether or not subjects flipped a coin to determine if they should enter or remain out in any given period. Given an underlying population composed of two categories, the binomial sign test can be used to determine if the proportion of observations in one of the two categories is equal to a specific value. The second definitionofrandomnessisbasedonthefactthataseriesofbinarydata generated by a random process can be expected to have a certain number of runs. A run is defined as a sequence within a series in which one of the alternatives occurs on consecutive trials. If subjects are behaving in a nonrandom matter, then there will either be too few or too many runs in the series of entry decisions. These tests will be described in more detail when applied.

39Whether or not knowing to look for APM patterns can be considered a beneﬁt to subjects participating in the experiment is a diﬃcult question to answer, as one may be inclined to dismiss possible rotation schemes that are not precisely APM.

50 Table 5: Number of times a particular market structure was achieved Session Group #Mon #Duo #Tri #Quad #Zero MEI 1 0 11 46 25 0 27.7 4N 2 2 22 37 21 0 34.9 3 0 4 32 46 0 15.5 4I 1 0 17 34 29 0 28.0 2 3 24 44 9 0 41.7 3N 1 6 44 31 1 33.9 2 7 29 46 − 0 27.8 − 3I 1 5 66 12 0 47.4 2 18 51 14 − 0 53.6 −

Group Results Table 5 shows the number of times each of the market structures (monopoly, duopoly, triopoly, 4-firm oligopoly, and zero-firms) were achieved by each group. In the two sessions with 4 subjects, the modal market structure is triopoly except for group 3 in the 4N session. While the APM with all group members is never approached in these sessions, the fact that the modal market structure is triopoly does suggest that subjects are attempting to create an APM by staying out of the market during some periods. The introduction of the innovation cost provides no clear-cut evidence in the 4 subject groups as to whether or not the APM can arise. Although group 2 in session 4I was able to avoid reaching a market structure with 4 subjects all but 9 times, group 1 in session 4I has market structure numbers similar to those of groups 1 and 2 in session 4N. Since both the 4N and 4I sessions ran for 82 periods this difference cannot be due to a difference in number of periods. In the two sessions with 3 subjects, the modal market structure is duopoly for all groups except group 2 in the 3N session. However, note that triopoly was the market structure in about 15% of the periods in the 3I sessions, whereas it was reached in about 46% of the periods in the 3N sessions. Also, group 2 in session 3I had 18 periods of monopoly market structure, which almost matches the total from the rest of the sessions combined, regardless of cost structure and group size. This suggests that in the 3 subject groups the innovation cost appears to play a larger role in fostering collusion, although it is not quite enough to generate a true APM. Once again, there was not a large difference in the number of periods, as the 3N and 3I sessions ran for 82 and 83 periods respectively. The last column of table 5 provides the Monopoly Effectiveness Index (MEI)40.Since the payoffsdiffer between sessions, a straightforward comparison of the total payoffs received by each group throughout the session would inherently favor those sessions without the

40This measure is described in Isaac, Ramey, and Williams (1984).

51 innovation costs. Let ΠM denote the total profiteachgroupwouldhavereceivedinthe experiment if the market structure had been a monopoly each period, ΠC denote the total profit each group would have received in the experiment if all the subjects in a group entered each period, and ΠA denote the total profit actually received by each group throughout the ΠA ΠC ( − ) entire experiment. The MEI is then (ΠM ΠC ) 100. This standardization allows more accurate comparisons as to how well the subjects− ∗ performed in capturing the monopoly profits throughout the experiment. In the 4N sessions the MEI values were 15.5, 27.7 and 34.9, while in the 4I sessions the MEI values were 28.8 and 41.7. Although slightly higher in the 4I sessions, the MEI shows that the introduction of the innovation cost did not significantly alter subjects ability to capture available profits. However, when comparing the 3N and 3I sessions subjects are able to capture a much larger share of the available profits. Subjects in the 3I session capture about 50% of the joint profit maximization level compared to only 30% in the 3N sessions. Thus, the introduction of a fourth subject seems to hinder cooperation. This is not unusual, as similar results about the effect that increasing the number of subjects has on the stability of collusive behavior can be seen in Isaac and Reynolds (2002). One other possibility is that the groups were learning to play the APM as time passed. The plots of the market structures over time show results similar to Bru, Gomez, and Ordonez (2002) in that different groups tend to follow different paths or in some cases no discernible path at all. Figures 9 and 10 show the plots of four groups, two 4-subject groups and two 3-subject groups, in the experiment. For example, group 2 of session 4I tends to show an increase in the number of participants per period over time. The market structure starts as a duopoly/triopoly, then moves to a fairly stable triopoly, and finally results in a 4-firm oligopoly. Group 1 of session 4N follows a slightly different pattern — it begins by fluctuating between triopoly and 4-firm oligopoly, then from periods 38 to 73 it fluctuates between duopoly and triopoly, and finally returns to 4-firm oligopoly at the end of the session. Group 1 of session 3N begins as a fairly stable duopoly for the first 26 periods, reaching triopoly status in only periods 3 and 6, and then essentially fluctuates between duopoly and triopoly for the remainder of the game. Group 2 of session 3N begins quite erratic, enters a long period of triopoly behavior from periods 24 to 50, then seems to fluctuate, although it comes close to reaching a fairly stable duopoly at the end of the session.

Individual Attempts at the APM It is possible that the market structure results in the previous section are determined by purely random actions and that no subject was attempting to play an APM. Looking at the individual entry decisions of some of the subjects shows that this is untrue. For example, subject 2 in group 1 of the 4I session began by playing a 4-subject APM for the ﬁrst 28 periods of the experiment, followed by 32 periods of playing a 2-subject APM, and ﬁnishing with 18 periods of always entering. Subject 1 in group 1 of the 3I session played a 3-subject

52 Figure 9: Time series of total number of entrants for two 4-subject groups

53 Figure 10: Time series of total number of entrants for two 3-subject groups

54 Table 6: Individual results for session 4N 4N Subj #Enter %Enter #Truth Binomial Runs Test

1 62 75.6 40 4.64∗∗∗ 2.95∗∗∗ Group 1 2 64 78.0 68 5.08∗∗∗ 1.27 3 81 98.8 32 8.83∗∗∗ 0.16 4 53 64.6 68 2.65∗∗∗ 1.58

1 70 85.4 33 6.29∗∗∗ 2.47∗∗ Group 2 2 42 51.2 76 0.11 2.67∗∗∗ 3 52 63.4 66 2.32∗∗ 1.43 4 77 93.9 46 7.84∗∗∗ 3.44∗∗∗

1 75 91.5 42 7.40∗∗∗ 0.59 Group 3 2 71 86.6 30 6.52∗∗∗ 0.02 3 82 100.0 4 8.94∗∗∗ − 4 60 73.2 33 4.09∗∗∗ 5.45∗∗∗ The asterisks refer to signiﬁcance levels of a 2-tailed test is signiﬁcant at the 1% level, at 5%, and at 10% ∗∗∗ ∗∗ ∗

APM throughout the first 60 periods of the experiment and then followed that by playing a 2-subject APM for the remainder of the experiment. Group 1 of session 3I is described in more detail in the next section. Subject 2 of group 1 in session 3N also began with a 3-subject APM, and although she abandoned that strategy in round 28 would return to play it later in the experiment. There are a few other examples that can be found scattered throughout the data that show that some subjects were actually playing an APM strategy, but that the other subjects either did not want to join, could not coordinate on how to join, or did not understand how joining could increase one’s payoff. Tables 6-9 show both the actual number of times an individual subject chose to enter as well as the percentage of times that the subject entered. In the 4N session, subjects entered an average of 65.75 times or about 80% of the time. Of the 12 subjects who participated in the session, 4 of them entered in at least 90% of the periods. In the 4I session, subjects entered an average of 58.9 times, which is 73.4% of the time. There were 2 of the 8 subjects, one in each group of the session, who entered over 90% of the time. While the APM did not arise in the 4I session, the added innovation cost appears to have increased efforts to coordinate on an APM. The results in the sessions with 3 subjects per group were similar to those with 4 subjects. In the 3N session, subjects entered an average of 65 times, which is about 79% of the periods. Only 1 of the 6 subjects entered over 90% of the time. In the 3I session, subjects entered an average of 55.8 times, or 67.2% of the periods. Again, only 1 of the 6 subjects entered over 90% of the time. Again, the innovation cost reduces the number of periods in which subjects enter, which is consistent with the hypothesis that subjects will attempt more coordination

55 Table 7: Individual results for session 4I 4I Subj #Enter %Enter #Truth Binomial Runs Test

1 70 87.5 40 6.71∗∗∗ 0.78 Group 1 2 41 51.3 62 0.22 1.36 3 79 98.8 50 8.72∗∗∗ 0.16 4 62 77.5 67 4.92∗∗∗ 0.94

1 61 76.3 71 4.70∗∗∗ 1.26 Group 2 2 75 93.8 45 7.83∗∗∗ 1.38 3 61 76.3 45 4.70∗∗∗ 1.87∗ 4 22 27.5 65 4.02∗∗∗ 1.95∗ The asterisks refer to significance levels of a 2-tailed test is significant at the 1% level, at 5%, and at 10% ∗∗∗ ∗∗ ∗ in the innovation cost sessions. It is interesting to note that the percentage of players who enter in at least 90% of the periods changes very little from session to session when group size is held constant. This suggests that there may be some players who refuse to play any strategy other than the dominant strategy Nash Equilibrium to the stage game. This topic is explored in more detail in the next section. Another possible factor that could hinder the development of the APM is the truthfulness of the subjects. Recall that, in addition to the history of past decisions made by all other subjects of the group, the choice stage screen also displayed the last signal sent for a particular period, providing subjects with a gauge of the trustworthiness of others. The fifthcolumnof tables 6-9 show the total number of times each subject acted truthfully. A subject behaves truthfully if he follows the last signal he sends for a period. For example, there will be ten period 10 signals sent, one for each of the first ten periods including period 10. The subject is marked as truthful if the signal he sent for period 10 during the period 10 signaling stage is identical to his actual decision. All signals sent for period 10 prior to the period 10 signaling stage (the signals for period 10 sent in the first9periods)areignored.Itshouldbe noted that 100% truthfulness may not occur even if an APM would occur, as there may be some periods early in the session where subjects intend to follow one decision for the period, but upon seeing the signals of others reverse their decision. Comparing the 4N session to the 4I session, subjects truthfully revealed their intentions an average of 44.8 times in the 4N session and 55.6 times in the 4I session. In the 3N and 3I sessions, subjects truthfully revealed their intentions 55.2 and 64 times respectively. The innovation cost sessions show movement towards more truthful revelation, an indication that at least some subjects are responding to the incentives provided. Note that the group that exhibited the least amount of truthful revelation, group 3 of session 4N, achieved the lowest MEI at 15.5 and that the group with the greatest amount of truthful revelation, group 2 of session 3I, achieved the highest MEI at 53.6. The correlation

56 Table 8: Individual results for session 3N 3N Subj #Enter %Enter #Truth Binomial Runs Test

1 72 87.8 20 6.85∗∗∗ 0.82 Group 1 2 51 62.2 74 2.21∗∗ 0.84 3 64 78.0 80 5.08∗∗∗ 2.58∗∗∗

1 81 98.8 44 8.83∗∗∗ 0.16 Group 2 2 63 76.8 71 4.86∗∗∗ 0.25 3 59 72.0 42 3.98∗∗∗ 1.91∗ The asterisks refer to signiﬁcance levels of a 2-tailed test is signiﬁcant at the 1% level, at 5%, and at 10% ∗∗∗ ∗∗ ∗∗

Table 9: Individual results for session 3I 3I Subj #Enter %Enter #Truth Binomial Runs Test

1 35 42.2 81 1.42 3.52∗∗∗ Group 1 2 83 100.0 27 9.11∗∗∗ − 3 55 66.3 65 2.96∗∗∗ 1.70∗ 1 47 56.6 73 1.21 1.18 Group 2 2 58 69.9 66 3.62∗∗∗ 3.43∗∗∗ 3 57 68.7 72 3.40∗∗∗ 1.36 The asterisks refer to significance levels of a 2-tailed test is significant at the 1% level, at 5%, and at 10% ∗∗∗ ∗∗ ∗∗ coefficient between the percentage of truthful revelation by subjects in a group and the group’s MEI is 0.86, suggesting a strong direct relationship. A t-test of the hypothesis that the true correlation coefficient is equal to zero is rejected at the 1% level for both directional and non-directional tests, as the t-statistic is 4.12. This relationship between MEI and truthful revelation suggests that subjects were more willing to sacrifice profits in the current period for profits in the future periods if the other members of their group could be trusted. The finaltwocolumnsoftables6-9providestatisticaltestsforthetwodefinitions of randomness defined at the outset of the experimental results section. The first test statistic reported is for the binomial sign test. The binomial sign test is used if the underlying data is comprised of two categories, such as the entry decision data, and it determines if the proportion of observations in one of the two categories is equal to a specificvalue,π.The null hypothesis of the test is that the proportion of the chosen category is equal to π.The test statistic reported below is for π =0.5. Of the 32 subjects spanning the 4 sessions, there are only 4 subjects for whom the null hypothesis cannot be rejected. While these 4 subjects may appear to be flipping a coin to decide their entry decisions, further inspection shows that they are actually those subjects who were most likely to be playing an APM for a portion of the session. Playing the APM reduced the number of entry decisions by

57 the subjects to make it appear as if they were playing a 50/50 split. For the remaining 28 subjects, all but one had a proportion of entry decisions that was statistically greater than 50%. While these subjects were inclined to enter more often than not, it is still possible that the pattern of entry decisions was random. The second test statistic reported is for the single sample runs test41. This test can be used to determine if the distribution of a series of binary events in a population is random. A run is defined as a sequence within a series in which one of the alternatives occurs on consecutivetrials. Thesinglesamplerunstesttakestheobservedproportionsfromthe sample as the underlying proportions of the population and uses those proportions to cal- culate a distribution of runs that should occur if the data were generated randomly. Thus, the null hypothesis is that the data is random. For large sample sizes, a normal distribution approximation is used. When reviewing the statistical significance of the test it is important to remember that the observed proportion of the events is considered the true proportion. Thus, a subject such as subject 1 of group 2 in session 3N, who is almost assuredly acting nonrandomly since he entered in 81 of 82 periods, appears to have randomly distributed data. This is because the expected value of the number of runs when the underlying proportions of the data are 98.8 and 1.2 and the number of trials is 82 is approximately 3. With only 1 decision to not enter there are only two possible number of runs that can occur, 2 or 3, so that regardless of whenthesubjectmadehisdecisiontonotenterhecouldneverbeveryfarfromtheexpected value of the number of runs. Of the 32 subjects, there are 12 subjects for whom the null hypothesis is rejected, providing evidence that some subjects have too many or too few runs in their data. Of the 4 subjects for whom the null hypothesis of the binomial sign test was not rejected, 2 of those subjects fall into the group of subjects for whom the null hypothesis of the runs test is rejected. This provides more evidence that these particular subjects are not behaving randomly, as there tends to be a pattern to the entry decisions. While these statistical tests provide some measure of quantitative analysis I believe that they should only be used as a complement to the evidence obtained from visual inspection of the data. Recall that subject 2 in group 1 of the 4I session began by playing a 4-subject APM for the first 28 periods of the experiment, followed by 32 periods of playing a 2-subject APM,then18periodsofalwaysentering,andafinal 2 periods of not entering. This appears to be a very clear case of a subject playing the APM, yet both of the statistical tests suggest that this subject was behaving in a random manner. However, if the single sample runs test is used on only the first 60 periods of the session, then the resulting test statistic is 4.40, which provides evidence that the subject was behaving in a nonrandom manner throughout the first 60 periods of the experiment. This approach of breaking down the data into smaller series is utilized in the next section. 41Sheskin (2004) provides a thorough review of both the binomial sign test and the single sample runs test.

58 Table 10: Payoffs to following an APM strategy given a specificnumberofsimpleNash players 4-subj APM 3-subj APM 2-subj APM Cournot Avg. Payoffs APM SN APM SN APM SN 4N Session 975 — 600 1600 500 900 576 4I Session 862.5 — 450 1150 275 450 126 3N Session — — 1267 — 850 1600 900 3I Session — — 1033 — 500 900 200

Simple Nash Players Throughout the sessions there were some players who were either unaware that dynamic collusion could lead to greater profits or were otherwise predisposed to play the Nash Equi- librium of the stage game each period. Define any player who chose to enter in more than 90% of the periods as a simple Nash player. As described in the next paragraph, simple Nash players can greatly impact the ability of an APM to form, particularly in the 4N and 3N sessions. However, removing these simple Nash players may reveal attempts at an APM by less than the full amount of subjects in a session. Table 10 shows the average payoffs subjects would receive if they followed a 3-subject APM in the face of an extreme simple Nash player who entered every period. In the 4N and 3N sessions, a single simple Nash player is almost enough to thwart any attempt at any type of APM. In the 4N session, the average payoff to following a 4-subject APM is 975. If one subject is a simple Nash player and the three remaining 3 subjects attempt to form a 3-subject APM then the average payoff for those 3 subjects is reduced to 600 ECUs. If 2 subjects are simple Nash players and the remaining 2 subjects attempt to form an APM then the average payoff for those participating in the 2-subject is 500 ECUs. Recall that the minimum payoff that a subject can receive is 576 ECUs if he enters. Thus, a 2-subject APM should not form in a group in the 4N session as it cannot raise profits above the minimum payoff a subject will receive if he enters every time. A 3-subject APM may be able to form in the 4N session, although the profit level received from participating in a 3-subject APM is just slightly above the one would receive from entering each period. The payoffs per period of forming a 3-subject or 2-subject APM in the 3N session are 1267 and 850 respectively, while the payoff obtained from entering each time is at least 900. Thus, one simple Nash player in a 3N group destroys any hope of an APM arising, and in a 4N group there is only a slight possibility that a 3-subject APM might arise. Simple Nash players should not have as much impact in the 4I and 3I sessions. The payoffs per period to each subject average 862.5, 450, and 275 for a 4-subject, 3-subject, and 2-subject APM in the 4I session. The payoff to always entering is a minimum of 126, which occurs if all subjects enter. In the 3I session, the payoffs per period average 1033 and 500

59 for a 3-subject and 2-subject APM. The payoff to always entering is a minimum of 200, again occurring if all subjects enter. Thus, the likelihood of an APM arising in the 4I and 3I sessions increases due to the innovation cost. There are 8 of the 32 subjects who qualify as simple Nash, and 4 of those 8 subjects entered the market either every period or all but one period. All groups except for group 1 in the 3N session and group 2 in the 3I session had at least one player who could be classified as a simple Nash player, although one subject in group 1 of session 3N barely misses the 90% cutoff. Group 3 of session 1 had 2 subjects that qualified as simple Nash players. If the simple Nash players are removed from each group a few instances of the APM arise, albeit with less than the full number of subjects for the group and without the structure used to derive the conditions of the theory. Some of the more interesting APM results are described in the following paragraphs. Perhaps the clearest example comes from group 1 of session 3I. Subject 2 was a simple Nash player who entered every time period. As discussed above, subject 1 played a 3-subject APM for about the first 60 rounds of the experiment. Subject 3 always chose “IN” until round 27, when he began exiting whenever subject 1 would enter. In round 61 subject 1 switched to playing a 2-subject APM, and by round 67 subjects 1 and 3 were in sync and alternated entering and exiting the rest of the game. Table 9 shows that the null hypothesis of the runs test is rejected for both subjects, although subject 3’s data is just barely significant. When the first 21 periods are removed from subject 3’s data, his test statistic rise to 3.18. This is the cleanest APM that arose, and it may in fact have been because player 2 was so attracted to the simple Nash strategy that he never disrupted the attempts of the other two players to lock into a pattern. In session 3N, subject 2 in group 1 was playing a 3-subject APM from the beginning of the experiment. In period 7, subject 3 picked up on this and began exiting whenever subject 2 would enter. This lasted until period 27, when subject 3 entered during one of subject 2’s time slots. Using the single sample runs test for subject 2 over the first 27 periods of the session we find that the null hypothesis can be rejected at the 10% level. For subject 3, the null hypothesis of the single sample runs test is rejected at the 5% level for the string of entry decisions from periods 7-26. In group 2 of the 3N session subjects 2 and 3 play what is essentially a 2-subject APM from periods 67-82. This APM arises even though the average payoff to the 2-subject APM (850ECUs)islessthantheminimumpayoff the subjects would be guaranteed to receive if they entered (900 ECUs). Both subjects have identical amounts of entry and exit decisions, 9and7respectively,andnumbersofruns,14. Thenumberofrunsistoolargetobe considered as generated from a random process. Group 1 of the 4N session provides some interesting patterns involving subjects 1, 3, and 4. From periods 20-26 subjects 2 and 4 settled on a 2-subject APM. Subject 2 breaks the pattern in period 27, possibly realizing because he realized that he would be guaranteed to earn more if he always entered. In period 38, subjects 1 and 4 begin a 2-subject APM

60 that lasts until period 43. The breakdown in the 2-subject APM may be due to subject 3 attempting to join the APM, as subject 3 had been entering every period from 26-42. Subject 4 attempted to start a 3-subject APM when he realized that subject 3 might be interested in joining, but discontinued his pursuit of the 3-subject APM in period 51. An unusual APM for periods 62-73 evolved between subjects 1 and 4 where one subject would enter the market for 3 periods while the other subject remained out. The subjects were able to settle on this rotation for 12 periods until endgame effects took hold and both subjects began entering every period. Unfortunately, while these partial APM schemes are interesting, the sample sizes are too small to perform runs analysis. Over the last 7 periods of play for group 2 in session 4N, subjects 1, 2, and 3 develop a slightly more complex method of extracting profits in excess of 576 ECUs. Although it is only 7 periods, its development can be seen in the previous 7 periods, and likely would have continued had the experiment continued. Subject 2 attempted to coordinate a 3-subject APM, where the subjects would each earn 600 ECUs. Subjects 1 and 3 both entered in the periods in which subject 2 sat out. The result was that subject 2 averaged 600 ECUs per period during this time, while subjects 1 and 3 averaged 633 ECUs. Near the end of session 4N, subject 4 of group 3 attempted to start a 4-subject APM. Perhaps realizing this, subject 2 exited during those periods in which subject 4 entered. Once again, while this partialAPMisinteresting,thesamplesizeistoosmalltoperformarunstest. These results show that some subjects, while not able to obtain the benefits from an APM in which full group participation occurred, were able to increase their payoffs by coordinating on a smaller-scale APM. Most of this behavior occurred in the sessions with innovation costs which were more conducive to fostering smaller-scale APMs. Thus, while the availability of multi-period binary signals may not have been able to generate collusive behavior for the full set of subjects within a group, it may have fostered collusive behavior among a subset of those subjects.

Signal Usage The signals that the subjects sent can be used to determine the degree to which they are trying to communicate with other members of the group. Since there are 1024 distinct signaling strings that can be sent, and only 80-83 periods per session, most of the signal combinations will not be sent by each subject. However, several important signal combinations can be pinpointed and the frequency with which those signals were sent can be observed. I have broken these important signal combinations into two categories — combinations in which the subject is signaling one of the APM patterns and what I will call simple signal combinations. It should be noted that for 29 of the 32 subjects, each subject’s modal choice of signaling combination is included in one of these two categories42.

42Of the remaining 3 subjects, one had a modal sequence choice that can be explained as a variant of an APM strategy, one subject had a sequence of signalling strings that seemed almost entirely random, and the

61 Table 11: Signals sent indicating recognition of the APM for session 4N 4N Sub 4-subj 3-subj 2-subj %APM 1 0 5 0 6.1 Group 1 2 0 0 0 0.0 3 1 0 1 2.4 4 9 0 1 12.2 1 4 2 33 47.6 Group 2 2 16 17 18 62.2 3 6 15 18 47.8 4 0 0 1 1.2 1 0 0 0 0.0 Group 3 2 34 1 5 48.8 3 0 0 0 0.0 4 11 0 1 14.6

APM Signals The APM signaling combinations are quite complex. For instance, a subject participating in a 4 subject group session may send any of the following sequences of binary signals in an attempt to communicate desire to participate in a 4-person APM: 1000100010, 0001000100, 0010001000, and 0100010001. The amount of times that the subject sent ANY one of those signals is counted as an attempt to signal a 4-subject APM. Similar counts have been calculated for signaling combinations which communicate a desire to participate in a 3-subject or 2-subject APM. While these tables will not capture all of the attempts at coordination43, they do provide some measure of the ability of the subjects to realize that a higher payoff can be obtained through intertemporal collusion. Tables 11 and 12 show the amount of times each subject sent signals corresponding to one of the APM sequences. There is not much difference in the signals sent by the subjects in session 4N or 4I, despite the fact that the payoff to each subject when all four subjects chose to enter the market was only 126 ECUs in session 4I, and was 100 ECUs if a subject stayed out of the market for a particular period. In fact, it could be said that the subjects in the 4I session showed less understanding as to how payoffs could be increased by intertemporal collusion. For instance, even though subject 2 of group 1 in session 4I sent 60 periods of signals suggesting either a 4-subject APM or 2-subject APM, there is only one other signaling string between the other 3 subjects of that group that matches any version of the APM. The lack of attempted coordination in the 4-subject innovation cost treatment is puzzling given third subject had an “abbreviated” 2-subject APM, where the subject signalled in for periods 1 and 3 and out for the remainder of the periods. 43See the note on group 2 of session 4N in the discussion of simple Nash players in the previous section.

62 Table 12: Signals sent indicating recognition of the APM for session 4I 4I Sub 4-subj 3-subj 2-subj %APM 1 0 1 0 1.3 Group 1 2 28 0 30 72.5 3 0 0 0 0.0 4 0 0 0 0.0 1 0 0 1 1.3 Group 2 2 0 0 1 1.3 3 11 12 14 46.3 4 45 0 0 56.3

Table 13: Signals sent indicating recognition of the APM for session 3N 3N Sub 4-subj 3-subj 2-subj %APM 1 3 2 1 7.3 Group 1 2 0 38 0 46.3 3 0 0 0 0.0 1 2 7 6 18.3 Group 2 2 0 5 0 6.1 3 0 2 18 24.4

6 that only 10 of a penny is given up if one stays out of the market and the other 3 subjects enter. Tables 13 and 14 show the signal usage in the 3N and 3I sessions respectively. Although it should not arise, I have included the 4-subject APM strings for completeness. There does not appear to be much difference in the APM signals sent between subjects in the 3N session and those in either 4N or 4I. However, it is possible that some subjects, particularly one such as subject 2 in group 1 of session 3N, realized that while a 3-subject APM would raise profits a 2-subject APM would actually reduce profits. Subjects in the 3I session were particularly savvy, with three of the six subjects sending either the 3-subject or the 2-subject signaling string over 70% of the time. A fourth subject, number 3 of group 2, consistently sent signals where he proposed exiting for 1 round and entering for 2. Also, when the signaling data is looked at, it appears that subject 3 in group 1 of session 3I may have convinced subject 1 to abandon his strategy of using the 3-subject APM in favor of a 2-subject APM. In all, 4 of the 32 subjects sent signals for one version of the APM in at least 70% of the periods and an additional 7 subjects sent signals for a version of the APM between 45%-65% of the periods. Thus, about one-third of the subjects displayed some recognition of the APM and actively chose to signal this recognition to the other members of the group. For the remaining two-thirds of the subjects it is impossible to distinguish whether subjects lacked

63 Table 14: Signals sent indicating recognition of the APM for session 3I 3I Sub 4-subj 3-subj 2-subj %APM 1 0 61 15 91.6 Group 1 2 0 1 0 1.2 3 0 7 52 71.1 1 0 71 0 85.5 Group 2 2 0 10 9 22.9 3 0 0 2 2.4 understanding of how payoﬀs could be increased by the APM or if they simply chose not to signal the APM. It is quite possible that those subjects who did not signal the APM behaved by sending random signal combinations, which would inhibit the development of the APM. This claim is investigated in the following section.

Simple Signals In order to investigate whether or not subjects were randomly submitting signal combinations I have tabulated counts for three strings of signals. I will call these simple signal combinations. Those three strings are a sequence of 10 zeros (the no periods signaling string), a sequence of a 1 followed by 9 zeros (first period only signaling string), and a sequence of 10 ones (the all periods signaling string). The no signaling string has two interpretations. The first interpretation is the literal interpretation of the signaling combination, that the subject intends to remain out for the next 10 periods. A second interpretation is that, since the no signaling string was the default string, the no signaling string could also be used by subjects attempting to hide their intentions44. Itispossiblethatsubjectsmayhaveviewed this sequence as a “no information” sequence. The 1st period signaling combination is essentially the same as simple one-period, pre-period communication and does not provide any information as to the subject’s understanding of dynamics. I have included the all periods signaling combination as a simple signal, although some subjects may use the all periods signaling combination as a threat to others. Also, although the endpoint of the session was randomly determined, some subjects were susceptible to end-game effects, and signalled their desire to enter every round in the late rounds. The columns in tables 15-18 contain the total number of times a particular signaling combination was sent, as well as the percentage of periods in which those signaling combinations were sent. Since the all periods signaling combination may be viewed as a sophisticated strategy, I have included two columns for the percentage of total rounds in which a simple signal was sent, one with and one without the

44One subject privately asked how he could choose to “not signal”. My response was that the software was going to send either a zero or a one for each signal depending on how he chose, and he promptly pressed the submit button sending a string of all zeros.

64 Table 15: Simple Signals Table for session 4N 4N Sub # No # 1st %Nosig # All %No,1st signals period &1st per periods &Allper 1 42 0 51.2 0 51.2 Group 1 2 26 56 100.0 0 100.0 3 7 1 9.8 2 12.2 4 22 19 50.0 9 61.0 1 18 0 22.0 8 31.7 Group 2 2 8 8 19.5 2 22.0 3 13 20 40.2 7 48.8 4 37 37 90.2 3 93.9 1 43 37 97.6 1 98.8 Group 3 2 23 1 29.3 3 32.9 3 78 0 95.1 1 96.3 4 56 2 70.7 1 72.0 all periods combination. Tables 15 and 16 show the simple signal combinations for subjects in sessions 4N and 4I. Note that 7 of the 12 subjects in session 4N and 4 of the 8 subjects in session 4I sent signaling combinations of no signal or 1st period at least 50% of the time. Also, every group except for group 2 in session 4I had at least one person send no signal or 1st period at least 90% of the time. Whether these signals were meant to be strategic or simply demonstrated a lack of understanding of the dynamics of the problem is unknown. It is highly unlikely, however, that coordination among 4 subjects would occur without the use of the signaling device, particularly since coordination can only occur intertemporally. Tables 17 and 18 show the simple signaling combination results for sessions 3N and 3I. In the 3N sessions there was still one subject in each group who signalled either no period or 1st period about 50% of the time. While this is dramatically less than the 90% levels that were seen in the 4-subject groups, it still demonstrates either an inability to see or an unwillingness to cooperate on a more proﬁtable strategy. The 3I sessions, however, show a stark improvement in that the number of no period and 1st period signals sent falls below 10% for all subjects. Additionally, while the number of all periods signals increases, especially in group 2 of session 3I, most of these all periods signals were sent near the end of the game, indicating that endgame eﬀects had likely taken hold. Subject 1 sent 7 of her 12 all periods signals after period 76 while the other 5 were sent consecutively from periods 37-41, possibly suggesting a punishment if the others failed to cooperate. Subject 3 sent 11 of his12 all periods signals after period 68. The decrease in simple signals sent in the 3-subject groups suggests that the dynamic collusive possibilities are more obvious in the 3-subject groups,

65 Table 16: Simple Signals Table for session 4I 4I Sub # No # 1st %Nosig # All %No,1st, signals period &1st per periods &Allper 1 40 25 81.3 2 83.8 Group 1 2 18 0 22.5 0 22.5 3 26 42 85.0 1 86.3 4 27 53 100.0 0 100.0 1 1 0 1.3 1 2.5 Group 2 2 32 10 52.5 11 66.3 3 28 1 36.3 11 50.0 4 18 0 22.5 0 22.5

Table 17: Simple Signals Table for session 3N 3N Sub # No # 1st %Nosig # All %No,1st, signals period &1st per periods &Allper 1 8 0 9.8 0 9.8 Group 1 2 13 26 47.6 0 47.6 3 1 19 24.4 0 24.4 1 13 6 23.2 9 34.1 Group 2 2 5 0 6.1 21 31.7 3 38 9 57.3 1 58.9 particularly when the costs of coordination of and non-participation in the APM increase. The simple signals tables show that most subjects were not sending signals in a random manner. The APM signaling combinations represent 9 of the possible 1024 signaling combinations that could be sent while the simple signal combinations represent 3 of those possible 1024 signaling combinations. Call these 12 signaling combinations the “favored signaling combinations”. The favored signaling combinations comprise a little more than 1% of the total number of signaling combinations that could have been sent. Of the 32 subjects, 20 subjects sent a favored signaling combination in at least 75% of the periods, with 12 of those 20 subjects sending a favored signaling combination in 90% or more of the periods. Subject 1 in group 2 of session 4I had the lowest percentage of favored signals sent at 3.8%. The next lowest percentage was 13.2% by subject 2 in group 1 of session 3I. If we group all of the signaling combinations into two categories, the 12 favored signaling combinations and all others, we can use the binomial distribution to provide evidence that subjects were not choosing their signals at random. The probability of choosing 3 favored signaling combinations in 80 trials, which is what the subject who sent the lowest percentage 5 of nonrandom signaling combinations sent, is 1.731 472 × 10− . The probability of choosing

66 Table 18: Simple Signals Table for session 3I 3I Sub # No # 1st %Nosig # All %No,1st, signals period &1st per periods &Allper 1 0 0 0.0 2 2.4 Group 1 2 6 1 8.4 3 12.0 3 5 2 8.4 9 19.2 1 0 0 0.0 12 14.5 Group 2 2 6 0 7.2 1 8.4 3 1 0 1.2 12 15.7

13 nonrandom signaling combinations in 83 trials, which is what the subject who sent the 25 second lowest percentage of nonrandom signaling combinations sent, is 2.199 026 × 10− . Both of these events are highly unlikely if the signals were drawn randomly. 12 It is still possible that the underlying distribution of 1024 favored signaling combinations 1012 and 1024 nonfavored signaling combinations generated the observed data. The binomial sign test45 canbeusedtodetermineiftheobservedproportionofthefavoredsignalingcombina- 12 tionsisequalto 1024 . For subject 1 in group 2 of session 4I, the test statistic that results fromchoosing3favoredsignalingcombinationsin80periodsis1.62. The binomial sign test is evaluated with the normal distribution, and we fail to reject the null hypothesis at the 10% level. For the subject with the second lowest percentage of favored signaling combinations sent, subject 2 in group 1 of session 3I, the test statistic is 9.72. Thus, we reject the null hypothesis at standard significance levels. The remaining 30 subjects have test statistics similar to subject 2 in group 1 of session 3I. These tests show that it is highly unlikely that subjects were choosing their signaling combinations randomly. The signaling results shed some light on the problem of obtaining dynamic collusive behavior without free-form communication. It appears that a major hindrance to intertemporal collusive behavior is the lack of understanding as to how it can increase one’s profits. Taken together, the entry decision results from the actual play and the signaling results show that those subjects who understand that profits can be increased by intertemporal collusion are able to achieve some level of collusion. The signaling results also suggest that the primary use of free-form communication among subjects may not be to establish coordination, but rather to educate those subjects who lack the ability to understand the dynamics.

45The test statistics are calculated using a correction for continuity.

67 CHAPTER 6

CONCLUSION

This dissertation set forth with three goals: build a theoretical model to explain how the alternating periods monopoly is an equilibrium to a market game; provide a case study of an industry and an empirical test to determine if the APM was occurring in that industry; and to provide results from an economic experiment to test the viability of the theoretical conditions of the theory and to determine the possibility of the APM arising without explicit communication between subjects. The primary contribution of chapter 2 is the development of industry characteristics that support the APM as a viable collusive outcome. Mainstream literature has focused on other collusive possibilities, such as equally splitting the market each time period, choice of product location along a product spectrum, and whether collusion implies minimal or maximal product differentiation. While all of these lines of research have provided valuable insights, the use of time itself as a collusive device has been largely ignored. Perhaps part of this neglect stems from the fact that the industries which would participate in an APM type of collusion have been inadequately defined in the theoretical literature. The hope is that the introduction of preferences for newness into consumer preferences and the corresponding innovation costs into producer costs will spur a wide array of research topics. One such research project already underway, Zillante (2004), is to build a model that incorporates temporal spacing, or periods where no firms produce. The model could be used to examine the welfare effects that occur if firms are forced to produce during the same time periods. Chapter 3 provides a detailed description of the post-World War II baseball card industry, utilizing many different aspects of the data. While there are a few existing descriptions of the pre-war industry, this is the only attempt I am aware of that provides an in-depth analysis of thechangeinstrategicbehaviorbythemanufacturers in the industry during the post-World War II era. The most striking aspect of this description is the historical progression of the industry, as the turning points in strategic behavior are clearly seen. A new empirical method of detecting potentially collusive behavior is presented in chapter 4. The new econometric test is proposed based on duration analysis. Results from the baseball card industry show that the observed behavior matches the APM. However, since the technique merely provides evidence that behavior matches a potentially collusive strategy itshouldnotbeseenasadefinitive statement as to whether firms are actively participating in a cartel, but as a starting point for a more exhaustive investigation. Also, it is hoped that this technique will lay the foundation for a more powerful econometric test that will perform better at differentiating collusion from competition. Chapter 5, the economics experiment chapter, provides two key results. The first result is that the conditions laid out as the minimum necessary conditions to support the APM

68 theoretically are unlikely to support it in practice. However, the APM, or at least some version of the APM, becomes more likely to arise as the costs of coordination and participation decrease. The second result is that collusion is difficult even when subjects are allowed to send signals that suggest a dynamic collusive strategy. This result provides one more link between the previous experiments in which one-period non-verbal signaling is allowed and experiments in which verbal signaling is allowed. Depending on one’s view of the world, the belief that facilitating practices exist that allow firms to reach a collusive outcome without explicit discussion is either strengthened or weakened. It is strengthened in the sense that those subjects who already grasp the dynamics of the problem are able to use the signaling device to achieve higher profits. It is weakened in the sense that the signals do not seem to be able to teach dynamics to those who do not understand them. However, if all the decision makers in an industry understand the dynamics of the problem, it may be that the APM could arise. Future research is underway to see if those subjects who appear capable of understanding and implementing the APM can indeed use the signaling mechanism in the experiment to reach an APM that includes full group participation. If those results are similar to the ones in chapter 5 it suggests that free-form communication may be necessary for an APM to form. Thus, if one forms, antitrust authorities may view this as a signal that a particular industry should be scrutinized.

69 Appendix A. Instructions for the Experiment

This appendix includes a sample of the instruction script that subjects were read in the experiment. This particular script is the one used on May 26th, 2004.

Script for AZ 5/26/04 Experiment

Thank you for participating in today’s experiment. I will read aloud from this script to ensure that all sessions of this experiment receive the same information. However, if you have any questions please do not hesitate to ask myself or one of the other experimenters. At this time I ask that you refrain from talking to any of the other subjects. If you violate this rule then the experimenter reserves the right to remove you from the experiment and you will receive only your $7 show-up fee.

How are groups determined?

In today’s experiment the computer has randomly placed subjects into 3 groups of 4. Your decisions and those of the members of your group will determine your payoﬀ.The exact method in which your payoﬀ will be determined will be described momentarily. It is important to note that although the members of the groups will remain anonymous, the other subjects in your group will remain the same THROUGHOUT THE EXPERIMENT.

How are payoﬀs determined?

At this point in time it should be noted that all currency amounts will be denoted in a ﬁctitious currency, called Experimental Currency Units (or ECUs). ECUs will be exchanged at the rate of 50 ECUs = $0.01, or 50 ECUs = 1 penny. Thus, 5000 ECUs = $1. The only number that is not transformed is your $7 show-up fee, which remains ﬁxed at $7 US dollars.

Stages

There are 3 stages in this experiment. The three stages are called: 1. Message sending 2. Choice 3. Payoff display Although the “Choice” stage is the 2nd stage in the actual experiment I will discuss it first as the choice stage determines your payoff for a period. Please turn your attention to your computer screen now, but do not hit any buttons at this time. In the center of the “choice” stage it has your subject ID number for your group. You will retain this identification (P1, P2, or P3) throughout the experiment. Also, your overall subject number is noted, but you can disregard this number — it is essentially there

70 for my benefit as I walk around. Also note that the current period and the remaining time for the particular stage are indicated in a header along the top of the screen. Upper-left The upper-left corner of the “Choice” stage contains two buttons, A and B (although in the demo only B is a button — in the actual experiment both A and B are buttons). In today’s experiment you will be asked to decide between choosing option A and choosing option B in the “Choice” stage of each period. You make this choice by pressing the button in the upper left corner of your screen that corresponds to the choice you wish to make for the current period. You will have 30 seconds to make this decision. Once you have made your choice you will be asked to wait patiently until all other subjects have made their choices. This ensures that all groups proceed at the same pace so that one group does not end up finishing the experiment prior to another group. Your choice, as well as the choices made by theothermembersofyourgroup,willdetermineyourpayoff for that period. Lower-left Your payoff is a function of how many members of the group choose option A and how many choose option B. The table in the lower left corner of your computer screen shows your payoff schedule based on your choice and the choices of the other members of your group. You should note that ALL members of your group (as well as all members of the experiment) see the SAME payoff schedule. The payoffs will NOT change throughout the course of the experiment. Please recall that all payoffs are denoted in ECUs and that 5000 ECUs = $1. Note that any time you choose option B you receive 100 ECUs, regardless of what your fellow group members chose. Your payoff table shows that if only 1 subject in your 4-subject group chooses option A within a particular period then ONLY that subject will receive 3600 ECUs for that period. If exactly 2 subjects in your group choose option A within a particular period then EACH subject who chose option A will receive 1600 ECUs for that period. If exactly 3 subjects in your group chose option A then EACH subject who choseoptionAwillreceive900ECUsforthatperiod.Thisishowyourdecisionsandyour group member’s decisions determine your payoff. Note that when you make a choice of A or B it is ONLY for the CURRENT period, and you may change from choice A to choice B as frequently or infrequently as you like from period to period. Upper-right The box in the upper right-hand corner of the “choice” screen is the “history of play” box. As of right now, the box contains a header row with Period, P1, MesP1, P2, MesP2, P3, and MesP3. Period corresponds to the period in which the decision was made and the columns beneath P1, P2, and P3 correspond to the decisions actually made by that specific subject in your group for that period. As an example, if P1 chooses A in period 1, when you see the choice screen in period 2 you will see the number one, “1”, appear in the cell of the history box that corresponds to column P1 and Period 1. If P1 chose B in period 1, then the number zero, “0”, will appear in the cell of the history box that corresponds to column P1

71 and Period 1. It is important to remember that A = 1 and B = 0 throughout the experiment. Inthedemoitisperiod1anditisasifalltheplayerschoseBinperiod0.Youwillbeable to observe the decisions made by every member of your group for every completed period of the experiment. Again, note that you will only be able to see their decisions in the periods following the current period (you will only be able to see period 1 decisions once we have moved to period 2, you will see period 1 and period 2 decisions when we have moved to period 3, etc.). Eventually a scroll bar will appear that will allow you to scroll up and down the history box — when this occurs you will initially see the most recent periods of play at the bottom of the box, and then you may scroll up to view the prior periods of play. The MesP1, MesP2, and MesP3 columns will be explained after I explain the “messages sent” box in the lower right corner of the screen. Lower-right Finally, the lower right-hand corner of your screen is the “Messages Sent” box. In this experiment you will be able to send binary (0 or 1) messages to your fellow group members. These messages are able to be sent 10 periods in advance for each message — I will explain howthemessagesaresentmomentarily.Notethatthemessagessentboxcontainsthelabels period, P1, P2, and P3. Each cell in the messages sent box corresponds to the most recent message sent by that player for that period. For example, if a 0 appears in the messages sent box corresponding to period 4 and subject P3, this means that subject P3 has sent a message that he or she INTENDS to choose B in period 4. If a 1 appears in the messages sent box corresponding to period 4 and subject P2, this means that subject P2 has sent a message that he or she INTENDS to choose A in period 4. It is important to note that these messages are non-binding, which is why I stressed the word INTENDS — thus neither you nor the other subjects in your group have to follow the messages sent. Again, you will see messages for the next 10 periods, including the current period (the message sending screen, to be described shortly, actually comes first in the experiment). Also, your payoff does NOT depend on the messages that you have sent, nor does it depend on the messages the other members of the group have sent. Your payoff ONLY depends on the actual choices of A and B made by the group members during each period. Finally, return to the history box. When you see MesP1 this shows the message that was sent IMMEDIATELY prior to the actual choice made by that player. As an example, consider period 10. There will be 10 period 10 messages (one for each period from 1-10) that will be sent by each subject prior to the actual choice of A or B for period 10. The message that appears in the history box corresponds to the period 10 message for period 10. That is, if player 1 chooses to send a message of A (or 1) for period 10 prior to making his actual choice for period 10, then when the choice screen appears for period 11 that message of 1 will be recorded under MesP1 for period 10, regardless of the messages sent by player P1 for period 10 in periods 1-9. Note that you will have 25 seconds to reach a decision in the choice stage — if you do not reach a decision within 25 seconds a red “please reach a decision” will flash in the upper-right

72 corner of your screen (it should be flashing now). Although you will never be forced off of the screen, it is asked that you make your decisions in a timely manner so that we can finish all of the intended periods. Throughout the first few periods of the experiment I will allow some excess time as you familiarize yourself with the interface, but after 5-10 periods I will ask that you try to adhere to the 25 second clock. To exit the choice stage, simply click on the button that corresponds to the actual decision that you wish to make for the current period, A or B. In the demo only B is a button — in the real experiment both A and B are buttons. If you have no questions about the choice stage please click on B now to move to the next screen. Note that you will not receive any paymentforthechoicemadeinthisdemo.

Message sending stage

PRIOR to entering the choice stage you will see the “Message Sending Screen”. In this stage you have the ability to send messages about the option you plan on choosing in each of the next 10 periods of the experiment. Again, the top of the screen contains a header with the current period as well as a countdown clock. The first column contains the labels for each row: Period, Choose A, Choose B, Current Choice, and Last Round. The row for “period” corresponds to the period for which you are sending a message. The rows for “Choose A” and “Choose B” will contain buttons in the actual experiment (although they are only boxes now), that will allow you to send a message of A or B for the upcoming periods. Pressing the button that corresponds to Period 1 and Choose A will change the number in the “current choice” row under period 1 to a 1, and pressing B will change the number back to a 0. Remember, a 1 corresponds to a message that you INTEND to choose option A in a particular period, while a 0 corresponds to a message that you INTEND to choose option B in a particular period. It is important to note that when a new period begins the “Current Choice” will always reset to all zeroes. Is everyone clear on how to send messages for the upcoming 10 periods? The row corresponding to “last round” shows the message that you sent last round for that period. Suppose that it is period 1 and you sent a message of 1 for periods 2 and 9. When the period 2 message sending screen appears, the period labels at the top will shift one spot to the left (so that period 1 is now where period 0 is), as period 0 drops off and period 10 appears. The “Last round” row will also shift, so that if you wish to send the same messages that you sent the previous period you merely need to look below the column to see which message you sent for the last period — you do NOT need to keep track of which periods you sent which messages in, as the software does that for you. Thus, if you sent a message of 1 for periods 1 and 9 you would see a 1 in the first and next to last “last round” columns in period 2, rather than the second and last columns. You WILL need to change your messages from zeroes to ones IF you wish to send the same message for each period. Also note that the cell for “last round” under Mes10 will always be a zero, as you will never have sent a message for that period before.

73 When you have finished making your message selections you can submit your messages by pressing the “Submit” button in the lower right-hand corner of your screen. You will NOT be allowed to change your messages once you have pressed the submit button, but you are allowed to change messages prior to pressing the submit button. When you submit your messages you will see the “Waiting Screen”, which asks you to wait patiently until all subjects in the experiment have finished submitting their messages. Again, note that these messages are non-binding and that they do NOT affect your payoffsinanyway. There is a 45 second countdown clock in the upper right-hand corner of your screen. Once 45 seconds have passed, a message will flash in red asking you to please reach a decision. Although the program will not force you to the next stage, it is asked that you make your message sending decisions in a timely manner so that we can finish all of the intended periods for this session. Again, due to the complexity of the interface I will allow a little excess time during the first few periods. The last piece of information is the history of play box. It is identical to the history of play box in the choice stage except that it only contains the actual decisions by the subjects in your group. If you have no questions about the message sending screen, please hit the submit button to exit the stage now.

Payoﬀ display screen

The payoff display screen simply shows your payoff for the just completed period as well as your total payoff from all the previous periods, including the one just completed. Both the current payoff and the total payoff are denominated in ECUs. You can leave this screen by pressing the OK button in the lower right-hand corner. The timer is set for 7 seconds for this screen — you will exit the screen if 7 seconds elapses.

Length of the experiment

The experiment is intended to run for at least 80 periods. After the 80th period there is an 85% chance that the experiment will continue for an additional period. This endpoint has been previously determined by a random number generator and has been embedded into the software.

Questionnaire

Once the experiment finishes you will be asked to fill in your first and last name for record keeping. This facilitates the payment process for me. Once you have input your name press the “OK” button and please wait patiently until your name is called. Are there any questions?

74 Appendix B. Sample Experiment Screen

Figures 11-13 show sample screens that subjects might see in the second period of the experiment described in section and Appendix A. The samples are from session 4N.

75 Figure 11: A sample message sending screen for the experiment

76 Figure 12: A sample choice screen for the experiment

77 Figure 13: A sample payoﬀ display screen for the experiment

78 Appendix C. Human Subjects Approval

This appendix provides a scanned copy of the Florida State University Human Subjects Committee Approval Memorandum for the economic experiment that provided the results discussed in chapter 5 of this dissertation.

79 Figure 14: Human Subjects Approval form

80 Appendix D. Subject Informed Consent Form

This appendix provides a sample of the form used to obtain subject consent for the economic experiment in chapter 5 of this dissertation.

SUBJECT’S CONSENT FORM

PURPOSE I am being invited to participate voluntarily in this research experiment to study the economics of decision-making. SELECTION CRITERIA I am a randomly recruited student at Florida State University. Certain criteria (such asclassattheuniversity)mayhaveplayedaroleinhowthesetofsubjectswasnarrowed down. Only persons 18 years of age or older may participate, and I affirm that I am 18 years of age or older. PROCEDURE This experiment will last up to 2 hours. I will be assigned to a computer terminal by chance, “like the flip of a coin” or “random arrival.” I will be asked to make decisions at the computer terminal. PARTICIPATION COSTS AND SUBJECT COMPENSATION In addition to the $7 for showing up on time and participating, I have the opportunity to earn additional compensation, which will be based upon my decisions, the decisions of others who are in the experiment, and the rules within which those decisions are made. I am free to ask any questions about the rules as to how my compensation will be determined. Any compensation I receive as a result of my participation in this experiment may be reported for taxation purposes to appropriate federal and state agencies, but the results of the study will remain confidential and will not be forwarded to tax authorities. I am free to withdraw from the experiment without additional compensation and without incurring the ill will of the experimenters at any time. If I do so, I may keep my $7.00 show-up fee. RISKS AND BENEFITS There are no known health risks or health benefits for this experiment beyond those from any other typical activity in a Florida State University classroom or computer lab. CONFIDENTIALITY The confidentiality of any personal information will be protected to the extent allowed by law. To the extent allowed by law, our rule is that only the researcher and any research assistants conducting this experiment may know what my earnings are (subject to tax reporting requirements above) and only researchers affiliated with the experimental economics research group at Florida State University may have access to the data with my name. My name will not be reported with any results related to this research. CONTACTS

81 I can obtain further information from Arthur Zillante at 850-644-7074. If I have questions concerning my rights as a research subject, I should call the Human Subjects Committee oﬃce at 850-644-8836. BEFORE GIVING MY CONSENT, THE METHODS, INCONVENIENCES, RISKS, AND BENEFITS HAVE BEEN EXPLAINED TO ME AND MY QUESTIONS HAVE BEEN ANSWERED. I MAY ASK QUESTIONS AT ANY TIME AND I AM FREE TO WITHDRAW FROM THE PROJECT AT ANY TIME WITHOUT CAUSING BAD FEEL- INGS. MY PARTICIPATION IN THIS PROJECT MAY BE ENDED BY THE INVESTI- GATOR OR BY THE SPONSOR FOR REASONS THAT WOULD BE EXPLAINED, BUT WHICH WILL CARRY NO BAD EFFECTS BEYOND THIS EXPERIMENT. SHOULD CURRENTLY UNKNOWN INFORMATION DEVELOP DURING THE COURSE OF THIS STUDY THAT MAY AFFECT MY WILLINGNESS TO CONTINUE IN THIS RE- SEARCH PROJECT, IT WILL BE GIVEN TO ME AS SOON AS IT BECOMES AVAIL- ABLE. THIS CONSENT FORM WILL BE FILED IN A LOCKING FILE CABINET IN THE RESEARCHERS OFFICE WITH ACCESS RESTRICTED TO AN AUTHORIZED REPRESENTATIVE OF THE FLORIDA STATE UNIVERSITY ECONOMICS DEPART- MENT. I DO NOT GIVE UP ANY OF MY LEGAL RIGHTS BY MY CONSENT. A COPY OF THIS CONSENT FORM WILL BE GIVEN TO ME UPON REQUEST.

______Signature and date

______Witness

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86 Biographical Sketch

Arthur Louis Zillante was born in Danbury, Connecticut on November 13, 1976 to Louis and Carol Zillante. He moved to Port St. Lucie, Florida at the age of 4 and would spend his childhood and teenage years there, graduating from Port St. Lucie High School near the top of his class in 1994. He received an Associate of Arts Degree from Indian River Community College in August of 1996. He entered the Florida State University in August of 1997 and would earn a Bachelor of Science Degree in Economics in April 1999. He received a Master of Science Degree in Economics from the Florida State University in December 2001. During his graduate studies at the Florida State University he would earn the Irv and Peggy Sobel Award for outstanding ABD graduate student in the Economics Department in 2002, the Charles Rockwood Award for outstanding instructor among graduate assistants in the Economics Department in 2003, and a university level Outstanding Teaching Assistant Award in 2004. He received a Doctor of Philosophy Degree from the Florida State University in December 2004. He accepted a post-doctoral position associated with George Mason University that is sponsored by the International Foundation for Research in Experimental Economics for the 2004-2005 academic year, where he will contribute to the development of the Vernon Smith Workshop Series at George Mason University.