On Hurwicz–Nash equilibria of non-Bayesian games under incomplete information

We consider finite-player simultaneous-play games of private information in which a player has no prior belief concerning the information under which the other players take their decisions, and which he therefore cannot discern. This dissonance leads us to develop the notion of Hurwicz–Nash equilibria of non-Bayesian games, and to present a theorem on the existence of such an equilibrium in a finite-action setting. Our pure-strategy equilibrium is based on non-expected utility under ambiguity as developed in Gul and Pesendorfer (2015). We do not assume a linear structure on the individual action sets, but do assume private information to be “diffused” and “dispersed.” The proof involves a multi-valued extension of an individual's prior to the join of the finest σ-algebra F of the information of the other players, and hinges on an absolute-continuity assumption on an individual's belief with respect to the extended beliefs on F.