Common assumption of rationality

Abstract

In this paper, we provide an epistemic characterization of iterated admissibility (IA), i.e., iterated elimination of weakly dominated strategies. We show that rationality and common assumption of rationality (RCAR) in complete lexicographic type structures implies IA, and that there exist such structures in which RCAR can be satisfied. Our result is unexpected in light of a negative result in Brandenburger, Friedenberg, and Keisler (2008) (BFK) that shows the impossibility of RCAR in complete continuous structures. We also show that every complete structure with RCAR has the same types and beliefs as some complete continuous structure. This enables us to reconcile and interpret the difference between our results and BFK’s. Finally, we extend BFK’s framework to obtain a single structure that contains a complete structure with an RCAR state for every game. This gives a game-independent epistemic condition for IA.Epistemic game theory; rationality; admissibility; iterated weak dominance; assumption; completeness; Borel Isomorphism Theorem; o-minimality