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Games 2010, 1(4), 381-394; doi:10.3390/g1040381
Article

The Role of Monotonicity in the Epistemic Analysis of Strategic Games

1,*  and 2
Received: 23 July 2010 / Revised: 18 September 2010 / Accepted: 19 September 2010 / Published: 8 October 2010
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
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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 true common beliefs; arbitrary games; monotonicity; Tarski’s Fixpoint Theorem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Apt, K.R.; Zvesper, J.A. The Role of Monotonicity in the Epistemic Analysis of Strategic Games. Games 2010, 1, 381-394.

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