Common belief in approximate rationality

Angie Mounir, Andrés Perea and Elias Tsakas

Mathematical Social Sciences, 2018, vol. 91, issue C, 6-16

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:91:y:2018:i:c:p:6-16

DOI: 10.1016/j.mathsocsci.2017.10.001

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