On p-rationalizability and approximate common certainty of rationality

This paper shows that common p-belief of rationality implies p-rationalizability for games with compact strategy sets. We also establish the Bayesian foundation for the perfect p-rationalizability for finite games. The p-rationalizability is then used to analyze the robustness of rationalizable sets. For any game with compact strategy sets, we show that the rationalizable set is robust, i.e., the strategies characterized by common p-belief of rationality are close to the rationalizable set when p → 1.