Reflexive games and non-Archimedean probabilities

In reflexive games we deal with an unlimited hierarchy of cognitive pictures. Aumann’s understanding of common knowledge satisfies the classical intuition that we can appeal only to inductive sets in our reasoning about these cognitive pictures involved in reflexive games. In this paper I propose to deny this intuition and appeal to non-Archimedean probabilities in defining cognitive pictures of our reflexion. This allows us to define reflexive games of finite or infinite levels.

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