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The Role of Monotonicity in the Epistemic Analysis of Strategic Games

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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)

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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.

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    Bibliographic Info

    Article provided by MDPI, Open Access Journal in its journal Games.

    Volume (Year): 1 (2010)
    Issue (Month): 4 (October)
    Pages: 381-394

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    Handle: RePEc:gam:jgames:v:1:y:2010:i:4:p:381-394:d:9784

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    Web page: http://www.mdpi.com/

    Related research

    Keywords: true common beliefs; arbitrary games; monotonicity; Tarski’s Fixpoint Theorem;

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    Cited by:
    1. Michael Trost, 2012. "An Epistemic Rationale for Order-Independence," Jena Economic Research Papers 2012-010, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.

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