Abstract
We study the relationship between common knowledge and the sequence of iterated mutual knowledge from a topological point of view. It is shown that common knowledge is not equivalent to the limit of the sequence of iterated mutual knowledge. On that account the new epistemic operator limit knowledge is introduced and analyzed in the context of games. Indeed, an example is constructed where the behavioral implications of limit knowledge of rationality strictly refine those of common knowledge of rationality. More generally, it is then shown that limit knowledge of rationality is capable of characterizing any solution concept for some appropriate epistemic-topological conditions. Finally, some perspectives of a topologically enriched epistemic framework for games are discussed.
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An extended abstract of a preliminary version of this paper appears under the title “Limit Knowledge of Rationality” in Aviad Heifetz (ed.), Theoretical Aspects of Rationality and Knowledge: Proceedings of the Twelfth Conference (TARK 2009), 34–40, ACM.
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Bach, C.W., Cabessa, J. Common knowledge and limit knowledge. Theory Decis 73, 423–440 (2012). https://doi.org/10.1007/s11238-011-9257-4
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DOI: https://doi.org/10.1007/s11238-011-9257-4