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A Modal Logic of Epistemic Games

Author

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  • Emiliano Lorini

    (IRIT-CNRS, Université de Toulouse, 118 route de Narbonne, 31062 Toulouse, France)

  • François Schwarzentruber

    (IRIT-CNRS, Université de Toulouse, 118 route de Narbonne, 31062 Toulouse, France)

Abstract

We propose some variants of a multi-modal of joint action, preference and knowledge that support reasoning about epistemic games in strategic form. The first part of the paper deals with games with complete information. We first provide syntactic proofs of some well-known theorems in the area of interactive epistemology that specify some sufficient epistemic conditions of equilibrium notions such as Nash equilibrium and Iterated Deletion of Strictly Dominated Strategies (IDSDS). Then, we present a variant of the logic extended with dynamic operators of Dynamic Epistemic Logic (DEL). We show that it allows to express the notion IDSDS in a more compact way. The second part of the paper deals with games with weaker forms of complete information. We first discuss several assumptions on different aspects of perfect information about the game structure (e.g., the assumption that a player has perfect knowledge about the players’ strategy sets or about the preference orderings over strategy profiles), and show that every assumption is expressed by a corresponding logical axiom of our logic. Then we provide a proof of Harsanyi’s claim that all uncertainty about the structure of a game can be reduced to uncertainty about payoffs. Sound and complete axiomatizations of the logics are given, as well as some complexity results for the satisfiability problem.

Suggested Citation

  • Emiliano Lorini & François Schwarzentruber, 2010. "A Modal Logic of Epistemic Games," Games, MDPI, vol. 1(4), pages 1-49, November.
    • Handle: RePEc:gam:jgames:v:1:y:2010:i:4:p:478-526:d:10053
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    References listed on IDEAS

    as
    1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    2. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    3. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    4. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Adam Brandenburger, 1992. "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 83-101, Fall.
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    Cited by:

    1. Michele Crescenzi, 2022. "Coordination through ambiguous language," Papers 2211.03426, arXiv.org.

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