Essays in economic theory

Abstract

This dissertation contributes to economic theory on economies and games with discontinuous payoffs and ambiguity. In Chapter 1, we consider economic environments with complete information, where agents' payoffs may exhibit discontinuities. To handle this difficulty, we propose the condition of “continuous inclusion property", and prove the existence of equilibria in a very general framework. Chapter 2 addresses the issues on the existence of pure and behavioral strategy equilibria in games with incomplete information and discontinuous payoffs. We provide several examples to show that a Bayesian equilibrium may not exist and previous results are not directly applicable. We introduce some general conditions to retain the existence of both pure strategy and behavioral strategy Bayesian equilibria, and apply our results to analyze all-pay auctions with general tie-breaking rules. Chapter 3 studies a general equilibrium model with incomplete information and ambiguity aversion. We assume that agents adopt the maximin preferences, and show the existence of maximin expectations equilibrium and maximin core. Importantly, we prove that the desirable incentive compatibility property can be guaranteed for efficient allocations, which typically fails in the conventional approach.