Discussion Paper 0915, "Admissibility and Event-Rationality", by Paulo Barelli & Spyros Galanis
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: D80, D82, C72