Incomplete Information Games with Ambiguity Averse Players

We study incomplete information games involving players who perceive ambiguity about the types of others and may be ambiguity averse as modeled through smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji, 2005). Our focus is on multistage games with observed actions and on equilibrium concepts satisfying sequential optimality - each player's strategy must be optimal at each stage given the strategies of the other players and the player's conditional beliefs about types. We show that for the purpose of identifying strategy profiles that are part of a sequential optimum, it is without loss of generality to restrict attention to beliefs generated using a particular generalization of Bayesian updating. We propose and analyze two strengthenings of sequential optimality. Examples illustrate new strategic behavior that can arise under ambiguity aversion. Our concepts and framework are also suitable for examining the strategic use of ambiguity.