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Essays on Signaling and Social Networks A ESSAYS ON SIGNALING AND SOCIAL NETWORKS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF ECONOMICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Tom´asRodr´ıguezBarraquer May 2011 © 2011 by Tomas Rodriguez Barraquer. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/wj208kq6898 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Matthew Jackson, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Kyle Bagwell I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Giacomo DeGiorgi I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Muriel Niederle Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Approved for the University Committee on Graduate Studies iv Preface Over the last few decades some analytic tools intensely used by economics have pro- duced useful insights in topics formerly in the exclusive reach of other social sciences. In particular game theory, justifiable from either a multi-person decision theoretic perspective or from an evolutionary one, often serves as a generous yet sufficiently tight framework for interdisciplinary dialogue. The three essays in this collection apply game theory to answer questions with some aspects of economic interest. The three of them have in common that they are related to topics to which other so- cial sciences, specially sociology, have made significant contributions. While working within economics I have attempted to use constructively and faithfully some of these ideas. Chapter 1, coauthored with Xu Tan, studies situations in which a set of agents take actions in order to convey private information to an observing third party which then assigns a set of prizes based on its beliefs about the ranking of the agents in terms of the unobservable characteristic. These situations were first studied using game theoretic frameworks by Spence and Akerlof in the early seventies, but some of the key insights date back to the foundational work of Veblen. In our analysis we focus on the competitive aspect of some of these situations and cast signals as random variables whose distributions are determined by the underlying unobservable charac- teristics. Under this formulation different signals have inherent meanings, preceding any stable conventions that may be established. We use these prior meanings to pro- pose an equilibrium selection criterion, which significantly refines the very large set of sequential equilibria. We apply our framework to examine in detail an argument recently espoused in the philosophy and sociology of science literatures to explain v what some authors view as the surprising solitude of String Theory as a mainstream contender to a Theory of Everything. The argument is that this preponderance of String Theory may in part be due to the need of scientists in the early stages of their careers to signal their research ability amidst rising competition. While the standard signaling frameworks suffice to account for the existence of multiple stable patterns of behavior of varying efficiency and informativeness, they do not shed light on the possible role of competition in selecting among these equilibria. The framework that we propose contributes to understanding the prevalence of many forms of conspicuous behavior. In Chapter 2, coauthored with Matthew O. Jackson and Xu Tan, we study the structure of social networks that allow individuals to cooperate with one another in settings in which behavior is non-contractible, by supporting schemes of credible os- tracism of deviators. There is a significant literature on the subject of cooperation in social networks focusing on the role of the network in transmitting the information necessary for the timely punishment of deviators, and deriving properties of network structures able to sustain cooperation from that perspective. Ours is one of the first efforts to understand the network restrictions that emerge purely from the credibility of ostracism, carefully considering the implications that the dissolution of any given relationship may have over the sustainability of other relations in the community. More concretely we study a model of favor exchange in small communities in which each period an opportunity for a socially efficient exchange of a favor arises among a pair of agents randomly chosen among all those that are linked in the network of relationships that is in place. Agents have complete and perfect information, and we work under the crucial assumption that once a link is deleted it cannot be resusci- tated. We define renegotiation-proof networks as networks in which every agent can be compelled not to misbehave along any of his links by the fear of nonnegotiable automatic prosocial retaliation from the offended party plus a credible threat by all or part of his other neighbors to permanently ostracize him. A threat is credible if the link deletions that it entails lead to a network which is itself renegotiation-proof, and importantly, does not expect the community to be able to commit not to forgive itself, and instead implement some other intermediate renegotiation-proof network vi involving the deletion of a strict subset of the links that the full punishment con- templates. We provide a full characterization of the collection of renegotiation-proof networks assuming homogeneous agents and relationships. One issue with renegotia- tion proofness is that while the threats upon which the networks stand are credible in the very strong sense just discussed, they may require the deletion of links that do not involve the offending party, and thus be very costly to parties completely unrelated to the behavior being penalized. This observation leads us to consider robust networks, a subclass of renegotiation proof networks that can be supported by punishments that only contemplate the disappearance of relationships involving the offending agent and leading to networks within this same subclass. We fully characterize the collection of robust networks assuming homogeneity and a variety of forms of heterogeneity. In particular we show that a property of all renegotiation proof networks in which no relationship is self-sustainable is that relationships must be supported, that is, all pairs of linked agents (friends) must have at least one friend in common. One implication of this property which illustrates well its reach is that it rules out social structures which include relationship that are not self sustaining, and which bridge otherwise disjoint clans (i.e. structures which can do no better than rely on social norms which depend upon Capulets reproaching Capulets and Montagues reproaching Montagues). The paper ends by exploring the occurrence of support in the networks corresponding to a large variety of relationships in 75 Indian Villages. We simultaneously explore the occurrence of clustering which is the much stronger network structure most commonly associated to cooperation by the prior literature. Our main finding is that while support tends to be very high in networks that can be classified as reflecting favor exchange among a variety of other social networks, clustering tends to be indiscriminately low in all the different networks. In Chapter 3 I study the sets of Pure Strategy Nash equilibria of a variety of binary games of social influence under complete information. In a game of social influence agents simultaneously choose one of two possible strategies(to be inactive or be active), and the optimal choice depends on the strategies of the agents in their social environment. Different social environments and assumptions on the way in which they influence the behavior of the agents lead to different classes of games of vii varying degrees of tractability. In any such game an equilibrium can be described by the set of agents that are active, and the full set of equilibria can be thus represented as a collection of subsets of the set of agents. I build the analysis of each of the classes of games that I consider around the question: What collections of sets are expressible as the set of equilibria of some game in the class? I am able to provide precise answers to these questions in some of the classes studied, and in other cases just some pointers. The paper begins by studying general games of social influence displaying strategic complements and then focuses on various subclasses that arise from imposing restrictions on the best response behavior of the agents stemming from social structure: Simple games in which each agent is influenced by only one core group of other agents. Nested games in which each agent can only be influenced by agents who are in turn influenced by other agents that influence him. Hierarchical games in which the agents can be embedded in a hierarchy that respects the influence structure. Clan-like games, which are simple games with the additional property that the influence is always mutual. And finally Games of thresholds, in which the way in which agents influence each other can be represented by a network.
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