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Logic and Game Theory

Author

Listed:
  • Giacomo Bonanno
  • Cédric Dégremont

    (Department of Economics, University of California Davis)

Abstract
Johan van Benthem has highlighted in his work that many questions arising in the analysis of strategic interaction call for logical and computational analysis. These questions lead to both formal and conceptually illuminating answers, in that they contribute to clarifying some of the underlying assumptions behind certain aspects of game-theoretical reasoning. We focus on the insights of a part of the literature at the interface of game theory and mathematical logic that gravitates around van Benthem's work. We discuss the formal questions raised by the perspective consisting in taking games as models for formal languages, in particular modal languages, and how eliminative reasoning processes and solution algorithms can be analyzed logically as epistemic dynamics and discuss the role played by beliefs in game-theoretical analysis and how they should be modeled from a logical point of view. We give many pointers to the literature throughout the paper.

Suggested Citation

  • Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 24, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:24
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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. Bonanno, Giacomo, 1992. "Players' information in extensive games," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 35-48, August.
    3. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    4. Bonanno, G, 1992. "Set-Theoretic Equivalence of Extensive-Form Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 429-447.
    5. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Synchronic information, knowledge and common knowledge in extensive games," Research in Economics, Elsevier, vol. 53(1), pages 77-99, March.
    6. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    7. Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
    8. 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.
    9. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    10. Giacomo Bonanno, 2007. "A Syntactic Approach to Rationality in Games," Working Papers 247, University of California, Davis, Department of Economics.
    11. Giacomo Bonanno, 2007. "A Syntactic Approach to Rationality in Games," Working Papers 71, University of California, Davis, Department of Economics.
    12. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    13. van Benthem, Johan, 2001. "Games in Dynamic-Epistemic Logic," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 219-248, October.
    14. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    15. Quesada, Antonio, 2001. "On expressing maximum information in extensive games," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 161-167, September.
    16. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
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    More about this item

    Keywords

    Game theory; Modal logic; Formal languages; Beliefs; Epistemic dynamics;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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