The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call...

We define and characterize a notion of correlated equilibrium for games with incomplete information, which we call Bayes correlated equilibrium: The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals...

We propose an incomplete information analogue of rationalizability. An action is said to be belief-free rationalizable if it survives the following iterated deletion process. At each stage, we delete actions for a type of a player that are not a best response to some conjecture that puts weight...

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is equivalent to the set of a version of incomplete information correlated equilibrium which we dub Bayes...

We study the classic sequential screening problem under ex-post participation constraints. Thus the seller is required to satisfy buyers' ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently cannot use up-front fees and...

Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion...

We study the classic sequential screening problem under ex-post participation constraints. Thus the seller is required to satisfy buyers' ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently cannot use up-front fees and...

We study a linear interaction model with asymmetric information. We first characterize the linear Bayes Nash equilibrium for a class of one dimensional signals. It is then shown that this class of one dimensional signals provide a comprehensive description of the first and second moments of the...

We study the classic sequential screening problem in the presence of buyers' ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently do not use up-front fees and instead use transaction-contingent fees. We establish conditions...

We analyze the canonical nonlinear pricing model with limited information. A seller offers a menu with a finite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal finite menu for...