Rational behavior under correlated uncertainty

Mira Frick*, Assaf Romm

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In complete information games, Dekel and Fudenberg (1990) and Börgers (1994) have proposed the solution concept SW (one round of elimination of weakly dominated strategies followed by iterated elimination of strongly dominated strategies), motivating it by a characterization in terms of "approximate common certainty" of admissibility. We examine the validity of this characterization of SW in an incomplete information setting. We argue that in Bayesian games with a nontrivial state space, the characterization is very sensitive to the way in which uncertainty in the form of approximate common certainty of admissibility is taken to interact with the uncertainty already captured by players' beliefs about the states of nature: We show that SW corresponds to approximate common certainty of admissibility when this is not allowed to coincide with any changes to players' beliefs about states. If approximate common certainty of admissibility is accompanied by vanishingly small perturbations to beliefs, then SW is a (generally strict) subset of the predicted behavior, which we characterize in terms of a generalization of Hu's (2007) perfect p-rationalizable set.

Original languageAmerican English
Pages (from-to)56-71
Number of pages16
JournalJournal of Economic Theory
Volume160
DOIs
StatePublished - 1 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

  • Admissibility
  • Approximate common certainty
  • Common p-belief
  • Incomplete information
  • Rationality
  • Robustness

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