ESSAYS ON GAME THEORY

Abstract

Strategic interactions are common phenomena in economics. This thesis considers such interactions in the environment of many players or asymmetric private information, which boils down to the study of equilibria in games with a continuum of players or games with incomplete information. Specifically, the focus is on three classes of games: large games with infinitely many actions, Bayesian games with interdependent payoffs and correlated types, and large stochastic games. The content is thus divided into three separated chapters. In Chapter 2, we formulate the notion of perfect equilibria in large games with infinitely many actions, and provide a complete characterization of the existence of perfect equilibria. The property of limit admissibility as well as robustness is further discussed. In Chapter 3, we study pure-strategy Bayesian Nash equilibria in games with incomplete information, interdependent payoffs and correlated types. We identify a necessary and sufficient condition for such existence, followed by a related purification result. In Chapter 4, we establish the existence of behavioral-strategy stationary Markov perfect equilibria in every large stochastic game, and provide a necessary and sufficient condition for the existence of pure-strategy stationary Markov perfect equilibria in this setting. We further present a purification result as well as the closed-graph property for such equilibria.