Equilibrium Departures From Common Knowledge in Games With Non-Additive Expected Utility.

In a game where the players have non-additive beliefs, we explore the beliefs implicit in the equilibrium behaviour of the players. Under one interpretation, we can show that there are well-defined departures from common knowledge of the game among the players. Our argument revolves around a representation theorem which relates equilibrium under under non-additive beliefs to equilibrium actions of a set of types in a Bayesian game with a common prior. Among these types, the game is common p-belief, where the 'p' depends on the degree of uncertainty aversion. Only when the beliefs are additive is p=1.