Incomplete Information Games with Smooth Ambiguity Preferences

Abstract: We propose equilibrium notions for incomplete information games involving players who perceive ambiguity about the types of others. Players have smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji, 2005) and may be ambiguity averse. In the smooth ambiguity model it is possible to hold the agents’ information fixed while varying the agent’s ambiguity attitude from aversion to neutrality (i.e., expected utility). This facilitates a natural way to understand the effect of introducing ambiguity attitude into a strategic environment. Our focus is on extensive form games, specifically multi-stage games with observed actions, and on equilibrium concepts satisfying perfection (sequential optimality). We propose the notions of Perfect Equilibrium with Ambiguity (PEA) and Sequential Equilibrium with Ambiguity (SEA) for such games, investigate their properties and provide several examples applying them.