Three Essays on Microeconomic Theory

Abstract

This thesis considers three issues in microeconomic theory - two-sided matching, strategic voting, and revealed preferences. In the first chapter I discuss the strategic manipulation of stable matching mechanisms commonly used in two-sided matching markets. Stable matching mechanisms are very successful in practice, despite theoretical concerns that they are manipulable by participants. The key finding is that most agents in large markets are close to being indifferent among partners in all stable matchings. It is known that the utility gain by manipulating a stable matching mechanism is bounded by the difference between utilities from the best and the worst stable matching partners. Thus, the main finding implies that the proportion of agents who may obtain a significant utility gain from manipulation vanishes in large markets. This result reconciles the success of stable mechanisms in practice with the theoretical concerns about strategic manipulation. Methodologically, I introduce techniques from the theory of random bipartite graphs for the analysis of large matching markets. In the second chapter I study the criminal court process, focusing on plea bargaining. Plea bargains screen the types of defendants, guilty or innocent, who go to jury trial, which affects the jurors' voting decision and, in turn, the performance of the entire criminal court. The equilibrium jurors' voting behavior in the case of plea bargaining resembles the equilibrium behavior in the classical jury model in the absence of plea bargaining. By optimizing a plea bargain offer, a prosecutor, however, may induce jurors to act as if they echo the prosecutor's preferences against convicting innocent defendants and acquitting guilty defendants. With reference to Feddersen and Pesendorfer (1998), I study different voting rules in the trial stage and their consequences in the entire court process. Compared to general super-majority rules, we find that a court using the unanimity rule delivers more expected punishment to innocent defendants and less punishment to guilty defendants. In the third chapter I study collective choices from the revealed preference theory viewpoint. For every product set of individual actions, joint choices are called Nash-rationalizable if there exists a preference relation for each player such that the selected joint actions are Nash equilibria of the corresponding game. I characterize Nash-rationalizable joint choice behavior by zero-sum games, or games of conflicting interests. If the joint choice behavior forms a product subset, the behavior is called interchangeable. I prove that interchangeability is the only additional empirical condition which distinguishes zero-sum games from general noncooperative games.