The Role of Monotonicity in the Epistemic Analysis of Strategic Games

Details The Role of Monotonicity in the Epistemic Analysis of Strategic Games The Role of Monotonicity in the Epistemic Analysis of Strategic Games

2010-10-27

arxiv.org/abs/1010.5595v2

Games 2010, 1(4), 381-394; see http://www.mdpi.com/2073-4336/1/4/381/

Computer Science

Computer Science and Game Theory

20 pages

Scientific paper

10.3390/g1040381

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.

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