Econometrica: Mar 2008, Volume 76, Issue 2
Admissibility in Games
Adam Brandenburger, Amanda Friedenberg, H. Jerome KeislerSuppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement—that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide an epistemic framework in which to address this question. Specifically, we formulate conditions of rationality and th‐order assumption of rationality (RAR) and rationality and common assumption of rationality (RCAR). We show that (i) RCAR is characterized by a solution concept we call a “self‐admissible set”; (ii) in a “complete” type structure, RAR is characterized by the set of strategies that survive +1 rounds of elimination of inadmissible strategies; (iii) under certain conditions, RCAR is impossible in a complete structure.
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