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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. This is embedded in a model in which players can hold a set of beliefs. Players make choices by looking for compromises that yield a good performance under each of their beliefs. Our solution concept is called perfect compromise equilibrium. It generalizes perfect Bayesian equilibrium. We show how it deals with uncertainty without using probabilities in Cournot and Bertrand markets, Spence’s job market signaling, as well as in bilateral trade with common value.
