Admissibility and Event-Rationality

40 Pages Posted: 7 Jun 2010 Last revised: 18 Apr 2018

See all articles by Paulo Barelli

Paulo Barelli

University of Rochester - Department of Economics

Spyros Galanis

City, University of London

Date Written: September 20, 2012

Abstract

Brandenburger et al. (2008) establish epistemic foundations for admissibility, or the avoidance of weakly dominated strategies, by using lexicographic type structures and the notion of rationality and common assumption of rationality (RCAR). Their negative result that RCAR is empty whenever the type structure is complete and continuous suggests that iterated admissibility (IA) requires players to have prior knowledge about each other, and therefore is a strong solution concept, not at the same level as iterated elimination of strongly dominated strategies (IEDS). We follow an alternative approach, using standard type structures and the notion of event-rationality. We characterize the set of strategies that are generated under event-rationality and common belief of event-rationality (RCBER) and show that, in a complete structure, it consists of the strategies that are admissible and survive iterated elimination of dominated strategies (Dekel and Fudenberg (1990)). By requiring that agents believe that themselves are E-rational at each level of mutual belief we construct and characterize RCBeER and show that in a complete structure it generates the IA strategies. Contrary to the negative result in Brandenburger et al. (2008), we show that RCBER and RCBeER are nonempty in complete, continuous and compact type structures, therefore providing an epistemic criterion for IA.

Keywords: epistemic game theory, admissibility, iterated weak dominance, common knowledge, rationality, completeness

JEL Classification: C72

Suggested Citation

Barelli, Paulo and Galanis, Spyros, Admissibility and Event-Rationality (September 20, 2012). Games and Economic Behavior, Vol. 77, 2013. Available at SSRN: https://ssrn.com/abstract=1621795 or http://dx.doi.org/10.2139/ssrn.1621795

Paulo Barelli

University of Rochester - Department of Economics ( email )

Harkness Hall
Rochester, NY 14627
United States
(585) 275-8075 (Phone)

Spyros Galanis (Contact Author)

City, University of London ( email )

Northampton Square
London, EC1V 0HB
United Kingdom

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