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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)

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, 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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    References listed on IDEAS

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    1. Johan Van Benthem, 2007. "Rational Dynamics And Epistemic Logic In Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 13-45.
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    Citations

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    Cited by:

    1. Bonanno, Giacomo & Tsakas, Elias, 2018. "Common belief of weak-dominance rationality in strategic-form games: A qualitative analysis," Games and Economic Behavior, Elsevier, vol. 112(C), pages 231-241.
    2. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economics Research Papers 2014-032, Friedrich-Schiller-University Jena.
    3. Jaeok Park & Doo Hyung Yun, 2023. "Possibilistic beliefs in strategic games," Theory and Decision, Springer, vol. 95(2), pages 205-228, August.
    4. Michael Trost, 2012. "An Epistemic Rationale for Order-Independence," Jena Economics Research Papers 2012-010, Friedrich-Schiller-University Jena.
    5. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    6. Trost, Michael, 2019. "On the equivalence between iterated application of choice rules and common belief of applying these rules," Games and Economic Behavior, Elsevier, vol. 116(C), pages 1-37.

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