Characterizing permissibility, proper rationalizability, and iterated admissibility by incomplete information

Shuige Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We characterize three interrelated solution concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model in a framework with incomplete information. Based on it, we give two groups of conditions; one characterizes permissibility and proper rationalizability, the other characterizes permissibility in an alternative way and iterated admissibility. In each group, the conditions for the latter are stronger than those for the former, which corresponds to the fact that proper rationalizability and iterated admissibility are incomparable but compatible refinements of permissibility within the complete information framework. The essential difference between the two groups is whether a full belief of rationality is needed.

Original languageEnglish
Pages (from-to)119-148
Number of pages30
JournalInternational Journal of Game Theory
Issue number1
Publication statusPublished - 2021 Mar


  • Epistemic game theory
  • Incomplete information
  • Iterated admissibility
  • Lexicographic belief
  • Permissibility
  • Proper rationalizability

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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