Essays in Game Theory and Political Economy

Open Access
Author:
Krishna, R. Vijay
Graduate Program:
Economics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 24, 2004
Committee Members:
  • Kalyan Chatterjee, Committee Chair
  • J Tomas Sjostrom, Committee Chair
  • James Schuyler Jordan, Committee Member
  • Anthony Mark Kwasnica, Committee Member
Keywords:
  • Communication in games
  • Political Economy
  • Game Theory
  • cheap talk
Abstract:
Game Theory plays a fundamental role in the social sciences. In this dissertation, we present three essays---the first two dealing with the pure theory of games and the third with an application of game theory to political economy. In the first essay, we consider the effect of unbounded communication between agents. Aumann and Hart (Econometrica, Nov. 2003) have shown that in games of one-sided incomplete information, the set of equilibrium outcomes achievable can be expanded considerably if the players are allowed to communicate without exogenous time limits. Their research provokes (at least) three questions. The first is with regards to the structure of equilibrium payoffs when the player can communicate for large but finitely many periods. Is it true that the set of equilibrium payoffs stabilises (i.e. remains unchanged) if there are sufficiently many rounds of communication? The second is if the set of equilibria from communication which is unbounded but finite with probability one is the same as equilibria from communication which is just unbounded. The third question is whether any of these sets of equilibria are ``simple' and if so, is there an algorithm to compute them. We show that in the context of finite Sender-Receiver games, the answer to all three is yes if the game satisfies a certain geometric condition. We then relate this condition to some geometric facts about the notion of bi-convexity and argue that if any of the questions has a negative answer then all three of the questions are likely to have a negative answer. In the second essay, we study the effect of communication in two-person games of incomplete information. We show that any rational mediated communication mechanism outcome satisfying a Nash domination condition can be implemented as the perfect Bayesian equilibrium of an extended communication game built from the original game and ends in finite time with probability 1. In the third paper, we study a model of spatial voting where players have objectives different from the traditional Hotelling-Downs model. The players are rank maximisers and enter sequentially with a given order of entry and where k winners get a payoff v. If the players make their decisions and enter simultaneously, the resulting Nash equilibrium (with k winners) is the Greenberg-Shepsle k-equilibrium, which does not exist for all distributions of voters. We partition the set of distributions into 3 cells. The first of these cells consists of regular distributions, wherein the set of SPE is isomorphic to the set Greenberg-Shepsle equilibria in the sense that every SPE generates an outcome which is a k-equilibrium and every k-equilibrium is the outcome of an SPE. The second type of distributions are called semi-clustered distributions. These have Greenberg-Shepsle k-equilibria but also have SPE that generate outcomes which are not k-equilibria. The remaining distributions are called clustered distributions. These distributions do not have k-equilibria. Nonetheless, they always have SPE with k entrants. We also give conditions to determine if a distribution has a k-equilibrium or not.