Common belief in approximate rationality

Angie Mounir*, Andrés Perea y Monsuwé, Elias Tsakas

*Corresponding author for this work

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This paper substitutes the standard rationality assumption with approximate rationality in normal form games. We assume that players believe that their opponents might be ε-rational, i.e. willing to settle for a suboptimal choice, and so give up an amount ε of expected utility, in response to the belief they hold. For every player i and every opponents’ degree of rationality ε, we require player i to attach at least probability Fi(ε) to his opponent being ε-rational, where the functions Fi are assumed to be common knowledge amongst the players. We refer to this event as belief in F -rationality. The notion of Common Belief in
F -Rationality (CBFR) is then introduced as an approximate rationality counterpart of the established Common Belief in Rationality. Finally, a corresponding recursive procedure is designed that characterizes those beliefs players can hold under CBFR.
Original languageEnglish
Pages (from-to)6-16
Number of pages11
JournalMathematical Social Sciences
Publication statusPublished - Jan 2018

JEL classifications

  • c72 - Noncooperative Games


  • epistemic game theory
  • approximate rationality

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