Compromise, Don't Optimize: Generalizing Perfect Bayesian Equilibrium to Allow for Ambiguity

We introduce a solution concept for extensive-form games of incomplete information in which players need not assign likelihoods to what they do not know about the game. This is embedded in a model in which players can hold multiple priors. Players make choices by looking for compromises that yield a good performance under each of their updated priors. Our solution concept is called perfect compromise equilibrium. It generalizes perfect Bayesian equilibrium. We show how it deals with ambiguity in Cournot and Bertrand markets, public good provision, Spence's job market signaling, bilateral trade with common value, and forecasting.