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Essays on Social Norms University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2017 Essays On Social Norms Nicholas Janetos University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Economics Commons Recommended Citation Janetos, Nicholas, "Essays On Social Norms" (2017). Publicly Accessible Penn Dissertations. 2358. https://repository.upenn.edu/edissertations/2358 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2358 For more information, please contact [email protected]. Essays On Social Norms Abstract I study equilibrium behavior in games for which players have some preference for appearing to be well- informed. In chapter one, I study the effect of such preferences in a dynamic game where players have preferences for appearing to be well-informed about the actions of past players. I find that such games display cyclical behavior, which I interpret as a model of `fads'. I show that the speed of the fads is driven by the information available to less well-informed players. In chapter two, I study the effect of such preferences in a static game of voting with many players. Prior work studies voting games in which player's preferences are determined only by some disutility of voting, as well as some concern for swaying the outcome of the election to one's favored candidate. This literature finds that, in equilibrium, a vanishingly small percentage of the population votes, since the chance of swaying the election disappears as more players vote, while the cost of voting remains high for all. I introduce uncertainty about the quality of the candidates, as well as a preference for appearing to be well-informed about the candidates. I find that high levels of voter turnout are supported in equilibrium even when the number of players in the game is large. This resolves the empirical puzzle of why the chance of swaying the election should matter, given that it is very small. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Economics First Advisor Steven Matthews Subject Categories Economics This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/2358 ESSAYS IN SOCIAL NORMS Nicholas Janetos A DISSERTATION in Economics Presented to the Faculties of the University of Pennsylvania in Partial Fulllment of the Requirements for the Degree of Doctor of Philosophy óþÕß Steven Matthews, Professor of Economics Supervisor of Dissertation Jesus Fernandez-Villaverde, Professor of Economics Graduate Group Chairperson Dissertation Committee Steven Matthews, Professor of Economics Andrew Postlewaite, Harry P. Kamen Professor of Economics and Professor of Finance Aislinn Bohren, Assistant Professor of Economics ESSAYS IN SOCIAL NORMS © Copyright óþÕß Nicholas Janetos is work is licensed under the Attribution-NonCommercial- ShareAlike ¦.þ International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ r To my parents, who gied me intellectual curiosity and a love of the unknown iii Acknowledgments I would like to thank the friends, family, teachers, and colleagues who supported me during my graduate career. In particular, I thank my colleagues Selman Erol, Dan Hauser, Ami Ko, Yunan Li, and Laura Liu, for much fruitful discussion and feedback. I especially thank my co-author, Jan Tilly, for his endless enthusiasm and inventiveness. I thank the faculty at the University of Pennsylvania for fostering an atmosphere of in- tellectual pursuit and excitement. In particular, I thank Aislinn Bohren, David Dillenberger, Sangmok Lee, George Mailath, Mallesh Pai, Andrew Postlewaite, Alvaro Sandroni, Rakesh Vohra, and Yuichi Yamamoto for their time and eorts. I would especially like to thank my advisor, Steven Matthews, whose energy and dedication has made me a better researcher and writer. Nicholas Janetos Philadelphia, PA April Õó, óþÕß iv ABSTRACT ESSAYS IN SOCIAL NORMS Nicholas Janetos Steven Matthews My dissertation studies equilibrium behavior in games for which players have some pref- erence for appearing to be well-informed. In chapter one, I study the eect of such prefer- ences in a dynamic game where players have preferences for appearing to be well-informed about the actions of past players. In the main result, I nd that such games display cyclical behavior, which I interpret as a model of ‘fads’. I show that the speed of the fads is driven by the information available to less well-informed players. In chapter two, I study the eect of such preferences in a static game of voting with many players. Prior work studies voting games in which player’s preferences are determined only by some disutility of voting, as well as some concern for swaying the outcome of the election to one’s favored candidate. is literature nds that, in equilibrium, a vanishingly small percentage of the population votes, since the chance of swaying the election disappears as more players vote, while the cost of voting remains high for all. I introduce uncertainty about the quality of the candidates, as well as a preference for appearing to be well-informed about the candidates. I nd that high levels of voter turnout are supported in equilibrium even when the number of players in the game is large. is resolves the empirical puzzle of why the chance of swaying the election should matter, given that it is very small. v Contents List of Figures viii IntroductionÕ Õ Fads and imperfect information¢ Õ.Õ Introduction......................................¢ Õ.Õ.Õ Previous literature.............................. Õþ Õ.ó Illustrative example.................................. Õì Õ.ì Static stage game.................................... óÕ Õ.ì.Õ Equilibria of the stage game........................ óì Õ.¦ Dynamic game..................................... ìÕ Õ.¦.Õ Equilibria of the dynamic game...................... ì Õ.¦.ó Instrumental preferences for conformity................. ¦þ Õ.¢ Matching game application............................. ¦ì Õ.¢.Õ Comparative statics............................. ¢þ Õ.ä Extensions....................................... äó Õ.ä.Õ β players are valued............................. äó Õ.ä.ó rα rβ ..................................... ä¦ Õ.ß Conclusion....................................... ä¢ < ó Voting as a signal of education äÉ ó.Õ Introduction...................................... äÉ ó.Õ.Õ Prior literature................................ ßÕ ó.ó Model.......................................... ߢ ó.ó.Õ Assumptions on the information structure............... Õ ó.ó.ó Firm beliefs.................................. ó ó.ì Analysis......................................... ì ó.ì.Õ Useful facts and notation.......................... ¦ ó.ì.ó Voter turnout in large games........................ ¢ ó.ì.ì Constructing equilibria........................... ó.ì.¦ Heterogeneous costs............................. Éó ó.ì.¢ Numerical example with continuous costs and nite N ........ É¢ ó.¦ Conclusion.......................................ÉÉ vi Appendices ÕþÕ Bibliography.......................................... Õ¦ vii List of Figures Õ.Õ Two equilibrium path realizations of the pooling (top) and periodic (bot- tom) equilibria..................................... Õß Õ.ó Construction of simple static equilibria....................... ó Õ.ì Outcome paths in stationary equilibria...................... ¢Õ Õ.¦ Stationary equilibria and their corresponding linear strategies......... ¢É Õ.¢ Outcome paths as a function of time........................ äÕ ó.Õ An example of the conditional distributions induced by a rotation order when γþ γÕ γó.................................... É ó.ó When there are no signaling concerns, more informed players than unin- formed players> > vote................................... É ì Equivalence of the inference problems between a player with uniform beliefs over calendar time, and a player with stationary beliefs over the state..... ÕÕó ¦ Numerical simulation of equilibrium non-stationary distribution....... Õ¦¦ ¢ Numerical simulation of equilibrium non-stationary distribution, part ó... Õ¦¢ ä Numerical simulation of equilibrium non-stationary distribution, part ì... Õ¦¢ ß Numerical simulation of equilibrium non-stationary distribution, part ¦... Õ¦ä viii Introduction Fads are a pervasive economic phenomenon, and large industries (advertising, branding, etc.) exist with the goal of inuencing which products are âĂŸin vogueâĂŹ by inuencing who is perceived to be choosing which actions. In chapter one, ‘Fads and imperfect informa- tion’,I provide a framework to analyze such behavior, grounded in rational agents, and based on asymmetric information. I model fads as an equilibrium outcome of a dynamic game with imperfect information. e game has high- and low-type players who dier from each other in two ways. First, all players want to match the actions of high-types and want not to match the actions of low-types. Second, the high-type players have access to better infor- mation about the actions chosen by players in the past—although no player has any special ability to identify which types chose which actions. e high-type players are interpreted as a well-connected âĂŸin-groupâĂŹ, and the low-type players as an âĂŸout-groupâĂŹ. For example, the high-type players may be interpreted as people who live in Manhattan, the low-types as people who live in a rural area, and the actions as some choice between styles
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