Essays on signaling and social networks [electronic resource]
Keywords: Economics

Over the last few decades some analytic tools intensely used by economics have produced 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 social 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 characteristics. Under this formulation different signals have inherent meanings, preceding any stable conventions that may be established. We use these prior meanings to propose an equilibrium selection criterion, which significantly refines the very large set of sequential equilibria in this class of games. 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 ostracism 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. 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 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.