Mutual knowledge of rationality and correct beliefs in n-person games: An impossibility theorem
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There are two well-known sufficient conditions for Nash equilibrium: common knowledge of rationality, and common prior, which exogenously assumes a profile of beliefs that are correct. However, it is not known how players arrive at a common prior before playing the original game. In this note, I assume, in addition to (objective and subjective) rationality, that players' beliefs will be correct once the game is played, but a common prior is not assumed. I study whether and under what conditions players endogenously arrive at a common prior. The main finding is an impossibility theorem, which states that mutual knowledge of rationality and mutual knowledge of correct beliefs are not in general logically consistent in n-person games. However, the two assumptions are consistent in two-player zero-sum games.
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