| This thesis is a collection of three essays on equilibrium, iterated admissibility, and rationalizability.;In Chapter 1, we examine the epistemic foundation of iterated admissibility. Brandenburger, Friedenberg, and Keisler (2008 Econometrica 76, 307--352) propose the notion of rationality and common assumption of rationality (RCAR) to characterize iterated admissibility (IA). They show that when players are not indifferent, RCAR is empty in a complete and continuous type structure. We propose a notion of weak assumption as an extension of knowledge. We show that rationality and common weak assumption of rationality (RCWAR) is nonempty in a complete, continuous and compact type structure. Moreover, the outcome of RCWAR is IA.;In Chapter 2, we propose a new notion of equilibrium in a finite normal form game where players are able to communicate by using correlated strategies and do not share a common prior belief. Subjective coalitional equilibrium is a refinement of Brandenburger and Dekel's (1987, Econometrica 55, 1391--1402) a posteriori equilibrium. We prove that every finite normal form game has a subjective coalitional equilibrium. We show that Luo and Yang's (2009, JET 144, 248--263) coalitional rationalizable set is outcome equivalent to a subjective coalitional equilibrium. Moreover, under the assumption of independent common priors, subjective coalitional equilibria are ex ante identical to the intersection of the set of Nash equilibria and coalitional rationalizable sets.;Chapter 3 is based on a joint work with Xiao Luo entitiled "Epistemic Foundation of Bayesian Coalitional Rationalizability." In Chapter 3, we establish epistemic foundations for the notion of Bayesian coalitional rationalizability (Bayesian c-Rationalizability) proposed by Luo and Yang (2009, JET 144, 248--263). In the standard semantic framework, we formulate a coalitional version of rationality (c-rationality) and offer an epistemic characterization of Bayesian c-rationalizability by common knowledge of c-rationality. |
