essays on communication, coordination, and correlation

Open Access
Author:
Chen, Chun-ting
Graduate Program:
Economics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 05, 2015
Committee Members:
  • Kalyan Chatterjee, Dissertation Advisor
  • Kalyan Chatterjee, Committee Chair
  • Edward James Green, Committee Member
  • James Schuyler Jordan, Committee Member
  • Sona Nadenichek Golder, Committee Member
Keywords:
  • repeated game
  • coordination
  • correlated equilibrium
  • pre-play communication
  • social networks
Abstract:
Each of the two chapters in this dissertation is based on a game theory paper. Although the topic of each chapter is different, they are linked by the question: How do players coordinate their actions through communication? Each chapter develops a communication schema, depicts equilibrium strategies, and responds to this inquiry. In the first chapter, I study a collective action problem in a setting of discounted repeated coordination games in which players know their neighbors' inclination to participate as well as monitor their neighbors' past actions. I define strong connectedness to characterize those states in which, for every two players who incline to participate, there is a path consisting of players with the same inclination to connect them. Given that the networks are fixed, finite, connected, commonly known, undirected and without cycles, I show that if the priors have full support on the strong connectedness states, there is a weak sequential equilibrium in which the ex-post efficient outcome repeats after a finite time $T$ in the path when discount factor is sufficiently high. This equilibrium is constructive and does not depend on public or private signals other than players' actions. In the second chapter, I consider the three-player complete information games augmented with pre-play communication. Players can privately communicate with others, but not through a mediator. I implement correlated equilibria by letting players be able to authenticate their messages and forward the authenticated messages during communication. Authenticated messages, such as letters with signatures, cannot be duplicated but can be sent or received by players. With authenticated messages, I show that, if a game $G$ has a worst Nash equilibrium $\alpha$, then any correlated equilibrium distribution in $G$, which has rational components and gives each player higher payoff than what $\alpha$ does, can be implemented by a pre-play communication. The proposed communication protocol does not publicly expose players' messages in any stage during communication.