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Theory and Decision

, Volume 73, Issue 3, pp 423–440 | Cite as

Common knowledge and limit knowledge

  • Christian W. Bach
  • Jérémie Cabessa
Article

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.

Keywords

Aumann structures Common knowledge Epistemic game theory Interactive epistemology Limit knowledge 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of Quantitative EconomicsMaastricht UniversityMaastrichtThe Netherlands
  2. 2.Department of Computer ScienceUniversity of Massachusetts AmherstAmherstUSA

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