This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogenous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior puts high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is consists of the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria. Journal of Economic Literature Classification Numbers: C72, D82.

Key Words: incomplete information; robustness; common prior assumption; higher order belief.

Journal of Economic Theory 145 (2010), 752-784. PDF file
First draft: December 31, 2005; this version: March 25, 2009. PDF file

Former title: Strategic Implications of (Non-)Common Priors II: Robustness of Equilibria