The Role of Monotonicity in the Epistemic Analysis of Strategic Games

Krzysztof R. Apt and Jonathan A. Zvesper
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Krzysztof R. Apt: Centrum for Mathematics and Computer Science (CWI), University of Amsterdam, Science Park 123, 1098 XG Amsterdam, The Netherlands
Jonathan A. Zvesper: Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK

Games, 2010, vol. 1, issue 4, 1-14

Abstract: It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski’s Fixpoint Theorem.

Keywords: true common beliefs; arbitrary games; monotonicity; Tarski’s Fixpoint Theorem (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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