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Toward a Theory of Play: A Logical Perspective on Games and Interaction

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  • Johan Van Benthem

    ()
    (ILLC, University of Amsterdam, 1090 GE Amsterdam, The Netherlands
    Department of Philosophy, Stanford University, Stanford, CA 94305, USA)

  • Eric Pacuit

    (TiLPS, Tilburg University, Warandelaan 2, 5037 AB Tilburg, The Netherlands)

  • Olivier Roy

    (Faculty of Philosophy, University of Groningen, 9700 AB Groningen, The Netherlands
    Current address: Ludwig-Maximilians-Universität München, Munich Center for Mathematical Philosophy, Ludwigstrasse 31, 80539 Munich, Germany.)

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    Abstract

    Logic and game theory have had a few decades of contacts by now, with the classical results of epistemic game theory as major high-lights. In this paper, we emphasize a recent new perspective toward “logical dynamics”, designing logical systems that focus on the actions that change information, preference, and other driving forces of agency. We show how this dynamic turn works out for games, drawing on some recent advances in the literature. Our key examples are the long-term dynamics of information exchange, as well as the much-discussed issue of extensive game rationality. Our paper also proposes a new broader interpretation of what is happening here. The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, and we are witnessing the birth of something new which is not just logic, nor just game theory, but rather a Theory of Play.

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    Bibliographic Info

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

    Volume (Year): 2 (2011)
    Issue (Month): 1 (February)
    Pages: 52-86

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    Handle: RePEc:gam:jgames:v:2:y:2011:i:1:p:52-86:d:11354

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    Related research

    Keywords: dynamic epistemic logic; games; interaction;

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    1. Oliver Board, 2002. "Dynamic Interactive Epistemology," Economics Series Working Papers 125, University of Oxford, Department of Economics.
    2. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    3. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
    4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    5. Cubitt, Robin P. & Sugden, Robert, 2003. "Common Knowledge, Salience And Convention: A Reconstruction Of David Lewis' Game Theory," Economics and Philosophy, Cambridge University Press, vol. 19(02), pages 175-210, October.
    6. Bonanno, Giacomo, 2002. "Modal logic and game theory: two alternative approaches," Risk, Decision and Policy, Cambridge University Press, vol. 7(03), pages 309-324, December.
    7. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
    8. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, December.
    9. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
    10. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    11. van Benthem, Johan, 2001. "Games in Dynamic-Epistemic Logic," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 219-48, October.
    12. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    13. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    14. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    15. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, vol. 35(4), pages 465-492, April.
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