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The Role of Monotonicity in the Epistemic Analysis of Strategic Games
Centrum for Mathematics and Computer Science (CWI), University of Amsterdam, Science Park 123, 1098 XG Amsterdam, The Netherlands
Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
* Author to whom correspondence should be addressed.
Received: 23 July 2010; in revised form: 18 September 2010 / Accepted: 19 September 2010 / Published: 8 October 2010
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
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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.
Apt KR, Zvesper JA. The Role of Monotonicity in the Epistemic Analysis of Strategic Games. Games. 2010; 1(4):381-394.
Apt, Krzysztof R.; Zvesper, Jonathan A. 2010. "The Role of Monotonicity in the Epistemic Analysis of Strategic Games." Games 1, no. 4: 381-394.