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University of Arkansas, Fayetteville ScholarWorks@UARK Theses and Dissertations 8-2014 Essays in Pro-social Behavior Joshua R. Foster University of Arkansas, Fayetteville Follow this and additional works at: http://scholarworks.uark.edu/etd Part of the Behavioral Economics Commons Recommended Citation Foster, Joshua R., "Essays in Pro-social Behavior" (2014). Theses and Dissertations. 2228. http://scholarworks.uark.edu/etd/2228 This Dissertation is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of ScholarWorks@UARK. For more information, please contact scholar@uark.edu, ccmiddle@uark.edu. Essays in Pro-social Behavior Essays in Pro-social Behavior A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics by Joshua Foster Bentley University Bachelor of Science in Economics, 2009 August 2014 University of Arkansas This dissertation is approved for recommendation to the Graduate Council. Professor Cary Deck Dissertation Director Professor Amy Farmer Professor Jeffrey Carpenter Committee Member Ex Officio Member Professor Salar Jahedi Committee Member ABSTRACT This dissertation examines individuals’ actions to improve social outcomes when unrecoverable investments are necessary. Situations involving non-pecuniary and pecuniary investments are considered. In the former, the prerequisite of real effort - a non-pecuniary, unrecoverable investment - is examined when said effort determines an individual’s ability to procure their preferred social outcome. Theoretical predictions over an individual’s effort provision are based on their revealed preferences for the social distribution of wealth according to the general axiom of revealed preference (GARP). Laboratory experiments reveal that individuals’ effort provisions do not support the assumption of stable preferences (transitivity) of wealth distribution. Specifically, individuals who reveal a preference for egalitarian outcomes do not exert enough real effort toward said outcomes when all of the wealth can be distributed directly to them. In the latter, pecuniary situation, auction formats that require all bidders to pay their bid (i.e., all-pay auctions) are studied as a way of funding public goods, specifically in the context of charity auctions. An innovative theoretical variation of the war of attrition is designed. This variation requires bidders to make unrecoverable upfront investments in the auction in order to participate, and the amount of one’s investment dictates how much one can potentially bid in the auction. In addition, an empirical analysis of this theoretical variation is provided via laboratory experiments. These experiments seek to highlight the bidder-specific and mechanism-specific characteristics that may lead to greater success in charitable fund-raising. The results suggest that auction mechanisms with an incremental bidding design outperform mechanisms with a lump-sum bidding design. ACKNOWLEDGMENTS Foremost, I would like to express my deepest appreciation to my advisor, Cary Deck, who has guided and supported me in establishing my academic career. I would also like to thank my committee members, Amy Farmer, Jeffrey Carpenter and Salar Jahedi for the time they spent assisting me improve this dissertation. This is the only part of my dissertation on which I could not solicit their feedback, and I am confident that it has suffered as a result. I would also like to thank the economics department and the Walton College, respectively. I will forever be grateful for the eagerness from the economics faculty to assist in my academic development, particularly that which I’ve received from Bill Curington, Andrea Civelli, Javier Reyes, Fabio Mendez and Andy Horowitz. I would like to thank Susan Yell for her tremendous administrative support and warm smile, both of which helped me through my final year. Finally, I would like to thank my best friend, Shannon Lee Rawski, for her enduring love and support - you are my constant. DEDICATION To my parents, the greatest teachers I have ever had. TABLE OF CONTENTS 1 Chapter 1: Putting Social Preferences to Work 1 1.1 A Model of Effort Provision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Experiment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 9 1.3 1.4 The Dictator Games and the Effort Task . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 Dictator Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.2 Effort Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Chapter 2: Wars of Attrition with Unrecoverable Upfront Investments 27 2.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2 Theoretical Overview of the War of Attrition . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.1 N Participants, K Prizes, and Complete Information . . . . . . . . . . . . . . . 35 2.2.2 N Participants, K Prizes, and Incomplete Information . . . . . . . . . . . . . . 37 2.3 The All-pay Auction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.4 The War of Attrition with Unrecoverable Upfront Investments . . . . . . . . . . . . . 41 2.5 2.6 2.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4.2 Equilibrium Analysis: Contest Stage . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4.3 Equilibrium Analysis: Endowment Stage . . . . . . . . . . . . . . . . . . . . . 44 Wars of Attrition with Unrecoverable Upfront Investments for Charity . . . . . . . . 46 2.5.1 Equilibrium Analysis: Contest Stage . . . . . . . . . . . . . . . . . . . . . . . . 48 2.5.2 Equilibrium Analysis: Endowment Stage . . . . . . . . . . . . . . . . . . . . . 50 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3 Chapter 3: Bidder Behavior in All-pay Auctions for Charity 54 3.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2 Theoretical Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.1 Bucket Auction Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.3 Equilibrium Analysis: Auction Stage . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2.4 Equilibrium Analysis: Endowment Stage . . . . . . . . . . . . . . . . . . . . . 68 3.3 Experiment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.5 3.4.1 Auction Currency Endowment Strategies . . . . . . . . . . . . . . . . . . . . . 76 3.4.2 Bidding Behavior, Individual Contributions & Participation . . . . . . . . . . 78 3.4.3 Behavioral Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Bibliography 89 A Putting Social Preferences to Work 95 A.0.1 Subject Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 A.0.2 Screenshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 A.0.3 IRB Approval Notification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 B Bidder Behavior in All-pay Auctions for Charity 104 B.0.4 Subject Directions for the Bucket Auction . . . . . . . . . . . . . . . . . . . . . 104 B.0.5 Exit Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 B.0.6 IRB Approval Notification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 LIST OF FIGURES 1-1 Revealed Preference Based on Binary Dictator Game . . . . . . . . . . . . . . . . . . . 6 1-2 Histograms of Actual Vs Reported Numbers in Effort Task . . . . . . . . . . . . . . . 16 1-3 Kernel-weighted Local Polynomial Smoothing CDFs of Effort Task Errors by State of the World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2-1 Timing of Decision Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2-2 Expected Revenue Increases with the Redemption Value (θ) . . . . . . . . . . . . . . 52 3-1 Timing of Decision Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3-2 Expected Revenue Increases with the Redemption Value (θ) . . . . . . . . . . . . . . 71 3-3 Auction Currency Bought in $ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3-4 Average Contribution by Mechanism in $ . . . . . . . . . . . . . . . . . . . . . . . . . 79 3-5 Participation Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 LIST OF TABLES 1.1 Dictator Games (a) and Potential States of the World (b) . . . . . . . . . . . . . . . . . 10 1.2 Effort Task Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Random Effects Probit of Subject Choice in Dictator Game . . . . . . . . . . . . . . . 15 1.4 Random Effects Estimates of Altruistic Dictator Decisions in the Effort Task . . . . . 18 1.5 Random Effects Estimates of Selfish Dictator Decisions in the Effort Task . . . . . . . 21 1.6 Random Effects GLS of Time Completing Effort Task . . . . . . . . . . . . . . . . . . 23 2.1 Payout from Winning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.1 Payout from Winning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2 Effort Task Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.3 Session Groups for Auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4 Endowment & Revenue Predictions by Mechanism (in $) . . . . . . . . . . . . . . . . 75 3.5 Summary of Survey Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.6 OLS Estimate of Survey Responses on Aggregate Contributions . . . . . . . . . . . . 84 3.7 Probit Estimate of Auction Exits on Survey Responses in 2 Bidder Auctions . . . . . 85 3.8 Probit Estimate of Auction Exits on Survey Responses in 6 Bidder Auctions . . . . . 86