Essays on Almost Common Value Auctions
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ESSAYS ON ALMOST COMMON VALUE AUCTIONS DISSERTATION Presented in Partial Ful…llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Susan L. Rose, M.A. ***** The Ohio State University 2006 Dissertation Committee: Approved by John H. Kagel, Adviser Dan Levin Adviser Lixin Ye Graduate Program in Economics c Copyright by Susan L. Rose 2006 ABSTRACT In a common value auction, the value of the object for sale is the same to all bidders. In an almost common value auction, one bidder, the advantaged bidder, values the object slightly more than the other, regular bidders. With only two bidders, a slight advantage is predicted to have an explosive e¤ect on the outcome and revenue of an auction. The advantaged bidder always wins and revenue decreases dramatically relative to the pure common value auction. Ascending auctions, which reduce to two bidders, are thought to be particularly vulnerable to the explosive e¤ect, which may discourage entry. My dissertation investigates the explosive e¤ect in experimental English clock auctions. The …rst essay, “An Experimental Investigation of the Explosive E¤ect in Almost Common Value Auctions,” uses a two-bidder wallet game to test these pre- dictions. I …nd the e¤ect of an advantage to be proportional, not explosive, con…rming past studies. I develop a behavioral model that predicts the proportional e¤ect and test it against the data. The model has two types of bidders: naïve and sophisticated. Naïve bidders use a rule of thumb bidding function while sophisticated bidders are fully rational and account for the probability that a rival is naïve or sophisticated when best responding. I was able to classify subjects as naïve or sophisticated, and those classi…ed as sophisticated do have a better understanding of the game. However, ii all subjects su¤ered from the winner’s curse, which may have masked the explosive e¤ect and been exacerbated by the structure of the wallet game. The second essay, “Bidding in Almost Common Value Auctions: An Experi- ment,”moves the analysis to a four bidder auction to directly test the entry predic- tions. I used a more intuitive common value structure and controlled for the winner’s curse by using subjects with prior experience in common value auctions. I found that although subjects did not su¤er from the winner’s curse, there is no evidence of an explosive e¤ect. Advantaged bidders won no more auctions than predicted by chance. Entry and auction revenue were una¤ected by the presence of advantaged bidders. iii To my parents iv ACKNOWLEDGMENTS I could not have completed this work without the encouragement and support of many people, particularly my committee members. I am forever indebted to John Kagel for his guidance and his moral and …nancial support. I am grateful to Dan Levin for his enthusiastic encouragement, support and suggestions. I thank Lixin Ye for his advice and comments. I would also like to thank John Ham, Stephen Cosslett and Ji Tao for their pa- tient discussions of econometrics. I thank Johanna Goertz for the use of her data, and Mashiur Rahman for his programming skills. Finally, I’d like to thank Mark Owens, Kirill Chernomaz, Serkan Ozbeklik, Hankyoung Sung and Asen Ivanov for their comments, moral support and help testing software. v VITA May 22, 1969 . Born - Roseau, Minnesota 2001 . .B.A. Business Economics, Moorhead State University 2002 . .M.A. Economics, The Ohio State Uni- versity 2002-Present . Graduate Teaching and Research Asso- ciate, The Ohio State University FIELDS OF STUDY Major Field: Economics Studies in: Industrial Organization Experimental and Behavioral Economics vi TABLE OF CONTENTS Page Abstract....................................... ii Dedication...................................... iv Acknowledgments.................................. v Vita......................................... vi ListofTables.................................... ix ListofFigures ................................... xi Chapters: 1. INTRODUCTION .............................. 1 2. AN EXPERIMENTAL INVESTIGATION OF THE EXPLOSIVE EF- FECT IN ALMOST COMMON VALUE AUCTIONS . 4 2.1 Introduction .............................. 4 2.2 TheWalletGame............................ 7 2.3 Summary of the Avery & Kagel Paper . 8 2.4 TheModel ............................... 9 2.4.1 The Symmetric Auction . 10 2.4.2 The Asymmetric Auction . 14 2.5 Experimental Design . 23 2.6 Experimental Hypotheses . 25 2.7 Experimental Results . 27 2.8 Summary and Conclusions . 46 vii 3. BIDDING IN ALMOST COMMON VALUE AUCTIONS:AN EXPERI- MENT..................................... 49 3.1 Introduction .............................. 49 3.2 Theoretical Considerations . 52 3.2.1 Pure Common Value Auctions . 52 3.2.2 Almost Common Value Auctions . 54 3.3 Experimental Design . 56 3.3.1 General Design . 56 3.3.2 Experimental Procedures . 58 3.4 Results ................................. 59 3.5 Summary and Conclusions . 65 Appendices: A. PROOF OF PROPOSITION 1 . 69 B. PROOF OF PROPOSITION 2 . 72 C. INSTRUCTIONS FOR TWO PLAYER AUCTIONS . 76 C.1 INSTRUCTIONS -SYMMETRIC . 76 C.2 INSTRUCTIONS-ASYMMETRIC . 79 D. INSTRUCTIONS FOR THE FOUR PLAYER AUCTIONS . 83 Bibliography .................................... 87 viii LIST OF TABLES Table Page 2.1 Summary of Experimental Sessions . 23 2.2 Test of Nash and Expected Value Models in the Symmetric Auctions 29 2.3 Estimates for the Asymmetric Auctions . 29 2.4 Comparison of Bidding in the Symmetric Auctions with Regular Bid- ders in the Asymmetric Auctions . 30 2.5 Comparison of Sealed Bid and English Clock Mechanism . 32 2.6 Means of the Clustering Variables . 36 2.7 Criteria for Classifying Subjects in the Asymmetric Auctions . 38 2.8 Symmetric Auctions by Type . 40 2.9 Sophisticated Players of Symmetric Auctions over Regions I & III . 40 2.10 Compare Actual to Predicted Percentages Won by Region . 41 2.11 Asymmetric Auctions with Classi…cation Dummies . 42 2.12 Asymmetric Auctions with Advantage Dummy by Type . 44 2.13 Compare Actual to Predicted Percentgaes Won By Region . 44 2.14 Compare Bidding in Symmetric and Asymmetric Auctions by Classi- …cation................................... 45 ix 3.1 First Price Auctions (standard error of the mean in parentheses) . 60 3.2 Pure Common Value English Auctions . 62 3.3 Bidding in Almost Common Value Auctions . 63 3.4 Predictions of Behavioral Bidding Model for Almost Common Value Auctions.................................. 65 x LIST OF FIGURES Figure Page 2.1 Sophisticated Best Responses to Naive Bidding Function . 12 2.2 Sophisticated Player’sBest Response to an Opponent of Unknown Type 15 2.3 Sophisticated Regular versus Naive Advantaged . 18 2.4 Sophisticated Advantaged versus Naive Regular . 20 xi CHAPTER 1 INTRODUCTION The use of auctions to sell publicly owned resources (such as spectrum rights) is growing. Understanding how auctions work both theoretically and practically is crucial to the proper design of such auctions. Many resources being sold through auctions(…shing, mineral or spectrum rights) can be modeled using a common value auction. In a common value auction, the value of the object for sale is the same to all the bidders, but the bidders are uncertain of the exact value. For example, when companies bid on an oil lease, they don’tknow exactly how much oil is under the ground. Instead, the conduct geological surveys to estimate the amount of oil beneath the ground and bid based on their estimate. The standard common value auction model assumes that all the bidders involved are symmetric. An almost common value auction relaxes this assumption slightly. One of the bidders (the advantaged bidder) places a slightly higher value on the object than the other regular bidders. In the oil lease example, one of the bidders may have a lower cost structure than its competitors. This di¤erence represents a private value advantage. Bikhchandani (1988) has shown that when there are only two bidders present, even a small epsilon advantage causes an explosive e¤ect on the outcome 1 and revenue of an auction. The advantaged bidder always wins and seller revenue is dramatically decreased. The intuition behind this result is clear. In a pure common value auction with two bidders, if a tie occurs each party is indi¤erent between paying their own bid and winning the object, and losing the object. Such indi¤erence is impossible in the almost common value case. If such a tie occurs, the advantaged bidder prefers to increase her bid to insure winning, while the regular bidder prefers to lower his bid and lose the object. It is not unlikely that one bidder may have a known private value advantage. Even in auctions with more than two bidders, the private value advantage may have a serious impact on an auction. The existence of private value advantages have been blamed for the less than anticipated revenue raised by the Los Angeles PCS license auction1, and for the seemingly low takeover price in the Glaxo-Wellcome merger2. Klemperer (1998) raises serious concerns about the use of ascending auctions in cases where a private value advantage exists. First, a known advantage may cause other bidders to not participate in an auction, thus reducing competition and driving prices down. Second, ascending auctions always reduce to just two bidders, the case in which the explosive e¤ect occurs. Avery and Kagel (1997) tested the explosive e¤ect in an experiment using a two bidder wallet game. They found the e¤ect of the advantage to be proportional, not explosive. The …rst essay of this dissertation presents and tests a model that explains the proportional e¤ect. In the model, there are two types of players: naive and 1 Paci…c Telephone was widely believed to have had a private value advantage due to their famil- iarity with the region and their existing customer database. See Klemperer (1998) page 760. 2 See Klemperer (1998) page 763. 2 sophisticated. Naive players use a rule of thumb bidding function and bid the their signal plus the unconditional expected value of their opponent’ssignal.