Admissibility in Games

Adam Brandenburger, Amanda Friedenberg and H. Jerome Keisler

Chapter 7 in The Language of Game Theory:Putting Epistemics into the Mathematics of Games, 2014, pp 161-212 from World Scientific Publishing Co. Pte. Ltd.

Abstract: Suppose 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 mth-order assumption of rationality (RmAR) 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, RmAR is characterized by the set of strategies that survive m + 1 rounds of elimination of inadmissible strategies; (iii) under certain conditions, RCAR is impossible in a complete structure.

Keywords: Game Theory; Epistemic Game Theory; Foundations; Applied Mathematics; Social Neuroscience; Rationalizability; Nash Equilibrium; Probability; Uncertainty (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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Journal Article: Admissibility in Games (2008)
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