THREE ESSAYS ON GAME THEORY

Abstract

This thesis consists of three essays on game theory. In the first essay, we study various forms of iterated elimination processes in arbitrary strategic games. We show a general existence result and offer a sufficient condition for the uniqueness (or order independence) of iterated elimination procedure. Our result is applicable to any form of iterated elimination processes, including iterated dominance and rationalizability. In the second essay, we study Pearce’s (1984) extensive form rationalizability, as a special kind of iterated elimination procedure, under general preferences. We conclude that in generic perfect information games, regardless of preference models, backward induction outcome is the unique rationalizable outcome. In the last essay, we present a unified framework for analyzing different kinds of rational strategic behavior in extensive games. We deliver a fundamental generic equivalence between sequential and perfect rational behavior. Our result is applicable to various solution concepts including equilibrium, rationalizability and iterated dominance.