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Keywords = Tarski’s Fixpoint Theorem

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15 pages, 224 KiB  
Article
The Role of Monotonicity in the Epistemic Analysis of Strategic Games
by Krzysztof R. Apt and Jonathan A. Zvesper
Games 2010, 1(4), 381-394; https://doi.org/10.3390/g1040381 - 8 Oct 2010
Cited by 11 | Viewed by 6770
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Epistemic Game Theory and Modal Logic)
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