Admissibility and event-rationality

Brandenburger et al. (2008) establish epistemic foundations for rationality and common assumption of rationality (RCAR), where rationality includes admissibility, using lexicographic type structures. 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 show that IA can be generated in a complete and continuous type structure. A strategy is event-rational if it is a best response to a conjecture, as usual, and in addition it passes a “tie-breaking” test based on a set E of strategies of the other player. Event-rationality and common belief in event-rationality (RCBER) is characterized by a solution concept we call hypo-admissible sets and, in a complete structure, generates the strategies that are admissible and survive the iterated elimination of strongly dominated strategies (Dekel and Fudenberg (1990)). Extending event-rationality by adding what a player is certain about the other’s strategies as a tie-breaking set to each round of mutual belief we get common belief of extended event-rationality (RCBeER), which generates a more restrictive solution concept than the SAS (Brandenburger et al. (2008)) and in a complete structure produces 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.