Self-Admissible Sets

Best-response sets (Pearce [1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger, Friedenberg, and Keisler [2008]) characterizes “rationality and common assumption of rationality.” We analyze the behavior of SAS's in some games of interest — Centipede, the Finitely Repeated Prisoner's Dilemma, and Chain Store. We then establish some general properties of SAS's, including a characterization in perfect-information games.