Robust Bilateral Trade and an Essay on Awareness as an Equilibrium Notion

The aim of this thesis is to analyze various effects of informational constraints. In chapters 1 and 2 we consider a robust model of bilateral trade where traders have private reservation values and utility functions are common knowledge. In chapter 1 we study direct-revelation mechanisms. Under incentive and participation constraints, we define the notion of ex-post constrained efficiency, which does not depend on the distribution of types. Given ex-post incentive and participation constraints, a sufficient condition for constrained efficiency is simplicity: the outcome is a lottery between trade at one type-contingent price and no trade. For constant-relative-risk-aversion environments, we characterize simple mechanisms. Under risk neutrality they are equivalent to probability distributions over posted prices. Generically, simple mechanisms converge to full efficiency as agents' risk aversion goes to infinity. Under risk neutrality, ex-ante optimal mechanisms are deterministic, and under risk aversion, they are not. In chapter 2 we address indirect implementation. We define Mediated Bargaining Game - a continuous-time double auction with a hidden order book. It is the optimal bargaining game in the sense that its ex-post Nash equilibria in weakly undominated strategies constitute the Pareto-optimal frontier of the set of all ex-post Nash equilibria of all bargaining games. In Mediated Bargaining Game, type-monotone Bayesian equilibria coincide with ex-post Nash equilibria. The inefficiency due to incomplete information is manifested through delay. In contrast with the direct revelation mechanisms, in Mediated Bargaining Game the mechanism designer does not need to know the agents' risk attitudes. Informational constraints may also be a result of agents' subjective knowledge of the economic situation. In chapter 3 we study normal-form games, where each player may be aware of a subset of the set of possible actions, and has a set of possible awareness architectures. Awareness architecture is given by agents' perceptions, and an infinite regress of conjectures about others. Awareness equilibrium is a steady state where neither actions nor awareness architectures can change. We provide conditions under which awareness equilibria exists and study a parametrization of the set of possible awareness architectures.