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The Role of Monotonicity in the Epistemic Analysis of Strategic Games

Author

Listed:
  • 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)

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.

Suggested Citation

  • Krzysztof R. Apt & Jonathan A. Zvesper, 2010. "The Role of Monotonicity in the Epistemic Analysis of Strategic Games," Games, MDPI, Open Access Journal, vol. 1(4), pages 1-14, October.
  • Handle: RePEc:gam:jgames:v:1:y:2010:i:4:p:381-394:d:9784
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    Citations

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    Cited by:

    1. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economic Research Papers 2014-032, Friedrich-Schiller-University Jena.
    2. Michael Trost, 2012. "An Epistemic Rationale for Order-Independence," Jena Economic Research Papers 2012-010, Friedrich-Schiller-University Jena.

    More about this item

    Keywords

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

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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