In a game with uncertainty as defined by Harsanyi, under a common prior assumption, Nash Equilibrium of fully rational and sophisticated players is characterized as common knowledge of rationalizability and consistency in the sense of rational expectations. This is then extended as a definition to the case of heterogeneous priors. It is shown that the resulting equilibrium behavior may be different from Nash equilibrium behavior under any common prior. Equilibrium behavior may require players to make infinite regress of assessments, which is different than if they were to make assessments only up to some finite order.

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