Three Essays in Contest Theory

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  Three Essays in Contest Theory Jean-Fran¸cois MercierDepartment of EconomicsMcGill University, Montr´ealAugust 2016A thesis submitted to McGill Universityin partial fulfillment of the requirements of the degree of Doctor of Philosophyc  Jean-Fran¸cois Mercier 2016  Acknowledgements There are many people I wish to thank. Over the past six years, I have met many great persons who either in a direct or in an indirect way, helped me shape this thesis. I have learned a great deal from them and I wish to express my most heartfelt gratitude. First and foremost, I wish to thank my supervisor, Licun Xue, for offeringme constant advice and support since the beginning. Licun helped me and cheered me up when times were hard, when I thought I would not be able to go through it. This means a lot to me and I will be forever grateful. I want to thank Rohan Dutta and Ngo Van Long for spending time discussingmy research with me and for supporting me throughout my job market year. I also thank Vikram Manjunath who helped me a great deal at an earlier stage of my research. Friends and colleagues played a big role during my years as a PhD student. From helping each other out when studying for our many exams, to reviewing our research papers, we helped each other in all sorts of ways and I amglad we had each other’s back when we needed it. I thank Irakli Japaridzeand Nagham Sayour for being part of my favorite reference group. I alsowish to thank Md. Nazmul Ahsan, Guillaume Lord, Marco Serena,  ´ AlexV´azquez-Sedano, Lei Xu, Douglas Barthold, Chinmay Sharma and Vinh Nguyen.i  I am particularly thankful to Ksenia Kordonsky for sharing my life duringthe earlier part of my PhD. Ksenia has been supportive, caring and loving and I thank her for putting up with my mood swings and for being there for me at the most difficult part of my life. I thank the McGill economics department and its faculty members suchas Hassan Benchekroun, John Galbraith, Jian Li, Fabian Lange, TheodorePapageorgiou, Francisco Alvarez-Cuadrado, Markus Poschke, ChristopherGreen, Chris Ragan, Paul Dickinson, Daniel Barczyk and Maxim Sinitsyn.Outside of McGill, I thank Catherine Gendron-Saulnier, Emre Ergeman,Sebastian Panth¨ofer, Luis Corch´on, Deniz Dizdar, Philipp Denter, Ching-Jen Sun, Peter von Allmen, Derek Lougee, Peter Eccles, Diego Moreno and Takashi Kunimoto. Et finalement, je souhaite remercier, du fond du coeur, ma soeur Julie Mercier, ma m`ere Reine Samson et mon p`ere Denis Mercier. Je me suis toujours consid´er´e chanceux d’avoir grandi en ayant comme mod`eles ma grande soeur et mes parents. J’ai eu la chance d’ˆetre support´e et encourag´e `a toutes les´etapes de ma vie. Les derni`eres ann´ees ont ´et´e particuli`erement difficiles et stressantes mais j’ai toujours eu ma famille `a mes cˆot´es.ii  Abstract In the first chapter, I analyze a model of rent-seeking contest where groups compete non-cooperatively for a group-specific public good. Individuals have private information about how much they value the public good and face afree-riding problem in choosing effort levels. The probability that a group wins depends on the aggregate effort of its members relative to the aggregateeffort of all contestants. For tractability, I restrict effort choices to be binary. I show that, in equilibrium, all contestants can exert positive effort ex post,despite the presence of free-riding incentives. This is in contrast to earlier results for contests with perfect information whereby only one contestant in a group exerts effort. I use simulation to show that when moving a playerfrom a group to a group of equal or greater size, average expected effort in equilibrium decreases. Moreover, Olson’s paradox, which asserts that groups of large size are less effective at winning a contest than small groups, mayor may not hold. Olson’s paradox can hold even though the good is purely public within the winning group. Members of the larger group expect other members to draw large valuations, which explains acute free-riding. In the second chapter, I take the perspective of a contest designer who derivesprofits from aggregate effort exerted by the contestants. I develop a revelationmechanism that enables the contest designer to select a subset of contestantsfrom a pool of candidates in a way that maximizes her profits, even though sheis uninformed about the candidates’ valuations for the contest prize. I prove iii
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