Common knowledge and limit knowledge

C.W. Bach, J. Cabessa

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)423-440
Number of pages18
JournalTheory and Decision
Volume73
Issue number3
DOIs
Publication statusPublished - Sep 2012

Keywords

  • Aumann structures
  • Common knowledge
  • Epistemic game theory
  • Interactive epistemology
  • Limit knowledge
  • RATIONALIZABLE STRATEGIC BEHAVIOR
  • EQUILIBRIUM
  • DOMINANCE

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