Essays on Bounded Rationality in Applied Game Theory Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Matthew Thomas Jones, B.S., M.A. Graduate Program in Economics The Ohio State University 2012 Dissertation Committee: James Peck, Co-Advisor (Chair) Dan Levin, Co-Advisor John Kagel c Copyright by Matthew Thomas Jones 2012 Abstract Departures from fully rational behavior due to cognitive limitations or psychological phe- nomena are typically referred to by economists as boundedly rational behavior. In this dis- sertation, I study how bounded rationality impacts cooperation in repeated games, herding behavior and bidding in online auctions. The methods I use include theoretical modeling and empirical analysis of data collected in controlled laboratory experiments as well as data from the field. This research contributes to the understanding of the consequences of bounded rationality in strategic interactions. In the first chapter, I investigate whether cooperation in an indefinitely repeated pris- oner's dilemma is sensitive to the complexity of cooperative strategies. I use an experimental design which allows manipulations of the complexity of these strategies by making either the cooperate action or the defect action state-dependent. Subjects are found to be less likely to use a cooperative strategy and more likely to use a simpler selfish strategy when the complex- ity of cooperative strategies is increased. The robustness of this effect is supported by the finding that cooperation falls even when the defect action is made state-dependent, which increases the complexity of punishment-enforced cooperative strategies. A link between subjects' ACT scores and the likelihood of cooperating is found, indicating that greater cog- nitive ability makes subjects more likely to use complex strategies. Behavior when subjects play multiple simultaneous games is compared to their behavior in isolated single games, ii providing evidence that the additional cognitive cost of playing multiple games also limits cooperation within this environment. Despite numerous applications, the importance of capacity constraints has so far received little attention in the literature on herding behavior. I attempt to address this issue in my second chapter by constructing a simple model of herding with capacity constraints and studying behavior in this environment experimentally. The model predicts and experimental results confirm that capacity constraints can attenuate herding, with the size of the effect dependent on the penalty of choosing an option after its capacity has been reached. For subjects earlier in a sequence of choices, behavior without a capacity constraint does not differ markedly from that observed in comparable experiments despite the fact that preceding choices are made by computers with fixed, commonly known choice rules rather than other humans. For subjects later in a sequence of choices, I find evidence that whether they respond rationally to the capacity constraint is dependent on factors such as the depth-of-reasoning involved in the fully rational equilibrium and the subject's cognitive ability. The third chapter of this dissertation is a study of data on bidding behavior in eBay auctions of Amazon.com gift certificates. I find that 41.1% of winning prices in these auctions exceed the face value, which is an observable upper bound for rational bidding because Amazon.com sells certificates at face value. Alternative interpretations are explored, but bidding fever seems to be the most plausible explanation for the observed behavior. iii Acknowledgments I would like to thank Dan Levin and James Peck for their invaluable guidance and sup- port. I am also very grateful to John Kagel for his advice and feedback. This work also benefitted from the comments and assistance of Michelle Chapman, Caleb Cox, P.J. Healy, Asen Ivanov, Mark R. Johnson, Gary Kennedy, Matthew Lewis, Brandon Restrepo, Michael Sinkey, John Wooders, Lixin Ye, participants of the microeconomics brownbag seminar and the theory/experimental reading group at Ohio State, and seminar participants at the 2011 ESA International Meeting, the 2011 PEA Conference, Kent State University, the Univer- sity of Memphis and the Federal Trade Commission. This work is supported by the NSF under Grant No. SES-1121085. Any opinions, findings and conclusions or recommendations expressed are those of the author and do not necessarily reflect the views of the NSF. iv Vita October 13, 1984 . Born - Pittsburgh, Pennsylvania May 2007 . .B.S. in Economics and Mathematics - Saint Vincent College August 2008 . .M.A. in Economics - The Ohio State University 2007-present . .Graduate Teaching/Research Asso- ciate - The Ohio State University Publications Research Publications Jones, M.T. (2011). Bidding fever in eBay auctions of Amazon.com gift certificates. Eco- nomics Letters 113(1), 5-7. Fields of Study Major Field: Economics v Table of Contents Page Abstract . ii Acknowledgments . iv Vita............................................. v List of Tables . viii List of Figures . x 1. Strategic Complexity and Cooperation: An Experimental Study . 1 1.1 Introduction . 1 1.2 Theoretical Background . 6 1.3 Experimental Design . 9 1.4 Research Questions . 12 1.5 Results . 15 1.5.1 Aggregate Cooperation . 16 1.5.2 Strategy Inference . 23 1.5.3 Regression Analysis . 29 1.6 Conclusion . 37 2. An Experiment on Herding with Capacity Constraints . 39 2.1 Introduction . 39 2.2 Related Literature . 42 2.3 Model . 46 2.3.1 Risk-Neutral Bayesian Nash Equilibrium . 48 2.3.2 Bounded Rationality . 50 2.4 Experimental Design . 53 vi 2.5 Experimental Questions and Results . 56 2.5.1 Effects of the Capacity Constraint . 62 2.5.2 Subjects Satisfying Basic Rationality . 66 2.5.3 Rationality vs. Bounded Rationality . 72 2.6 Conclusion . 80 3. eBay Auctions of Amazon.com Gift Certificates: A Study of Bidding Fever in the Field . 82 3.1 Introduction . 82 3.2 Data . 83 3.3 Interpretation . 84 3.4 Alternative Interpretations . 87 3.5 Regression Analysis . 88 3.6 Conclusion . 90 Appendices 92 A. Appendix to Strategic Complexity and Cooperation: An Experimental Study . 92 A.1 Directed Graph Representations of Selected Automaton Strategies in Each Treatment . 92 A.2 Instructions and Screenshots . 94 A.2.1 Phase I Instructions . 94 A.2.2 Phase II Instructions . 97 B. Appendix to An Experiment on Herding with Capacity Constraints . 105 B.1 Derivation of RNBNE . 105 B.2 Derivation of Level-k Strategies . 107 B.3 Risk Aversion . 109 B.4 Instructions and Screenshots . 110 Bibliography . 119 vii List of Tables Table Page 1.1 Treatments . 11 1.2 Repeated Game Lengths . 12 1.3 Frequency of Cooperation . 18 1.4 Summary of Stage Outcomes . 19 1.5 Candidate Automaton Strategies . 24 1.6 Maximum Likelihood Estimates of Strategy Prevalence . 25 1.7 Probits Reporting Marginal Effects of Treatments and History of Play . 30 1.8 ACT and SAT-ACT Concordance Score Summary Statistics . 32 1.9 Probits Reporting Marginal Effects of ACT Percentile, Separated by Treatment 33 1.10 Probits Reporting Marginal Effects of ACT Percentile, Treatment Interactions 36 2.1 Summary of Strategies by Treatment and Setting . 60 2.2 Predicted vs. Actual Effects of Treatment and Setting on Strategies . 63 2.3 Mean Strategies, First Round and Last Round in Each Setting . 65 2.4 Effects of Treatment/Setting on Strategies of Subjects Satisfying Basic Ratio- nality . 68 2.5 Cost Level in Trial Rounds and Rounds 1-6 of MIXED/ORDERED . 69 viii 2.6 ACT and SAT-ACT Concordance Score Summary Statistics . 71 2.7 Probits Reporting Marginal Effects of ACT/Major on Satisfying Basic Ratio- nality . 72 2.8 Transition Matrix Showing Player 3 Best-Fitting Theory Across Settings . 77 2.9 Transition Matrix Showing Player 4 Best-Fitting Theory Across Settings . 77 2.10 Relationship Between Test Scores/Major and MSD Scores - OLS Regressions 79 3.1 Descriptive Statistics . 83 3.2 Summary of Overbidding . 84 3.3 Overbidding by Time and Day of Week . 85 3.4 Overbidding and Winning Bidder's Rating . 86 3.5 OLS Regression - Dependent Variable: Percentage Overbid . 89 ix List of Figures Figure Page 1.1 Payoff Tables . 10 1.2 Cooperation by Round . 17 1.3 Cooperation by Round: NOSWITCH/NOSWITCH-R . 22 2.1 RNBNE Strategies for Players 3 and 4 . 49 2.2 Level-k Strategies of Player 3 . 51 2.3 Level-k Strategies of Player 4 . 52 2.4 Computer Player Strategies . 54 2.5 Player 4 Strategies in NAIVE-MIXED . 55 2.6 Distribution of Strategies by Treatment/Setting/Preceding Player Choice . 57 2.7 Distribution of Strategies by Treatment and Setting . 61 2.8 Distribution of BR Subjects' Strategies by Treatment and Setting . 67 2.9 Strategies with No Capacity Constraint, Rounds 1-6 of MIXED/ORDERED 70 2.10 Player 3 Mean Squared Deviation from Equilibrium . 74 2.11 Player 4 Mean Squared Deviation from Equilibrium . 75 A.1 Always Defect (AD) . 92 x A.2 Always Cooperate (AC) . 93 A.3 Grim Trigger (GT) . 93 A.4 Tit-for-Tat (TFT) . 94 A.5 Screen 1 (Single Game Rounds) . 99 A.6 Screen 2 (Single Game Rounds) . 100 A.7 Screen 3 (Single.