Incomplete Information Games with Ambiguity Averse Players

We study incomplete information games with ambiguity averse players. Our focus is on equilibrium concepts satisfying sequential optimality -- each player's strategy is optimal at each information set given opponents' strategies. We show sequential optimality, which does not make any explicit assumption on updating, is equivalent to sequential optimality with respect to beliefs updated using a particular generalization of Bayesian updating. Ambiguity aversion expands the set of equilibria compatible with players sharing common ambiguous beliefs. We connect ambiguity aversion with belief robustness. Examples illustrate new strategic behavior, including strategic use of ambiguity, under ambiguity aversion.