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

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Johan Van Benthem & Eric Pacuit & Olivier Roy, 2011. "Toward a Theory of Play: A Logical Perspective on Games and Interaction," Games, MDPI, vol. 2(1), pages 1-35, February.
    • Handle: RePEc:gam:jgames:v:2:y:2011:i:1:p:52-86:d:11354
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    References listed on IDEAS

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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. 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(2), pages 175-210, October.
    3. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    4. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    5. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(2), pages 133-163, October.
    6. 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.
    7. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    9. van Benthem, Johan, 2001. "Games in Dynamic-Epistemic Logic," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 219-248, October.
    10. Bonanno, Giacomo, 2002. "Modal logic and game theory: two alternative approaches," Risk, Decision and Policy, Cambridge University Press, vol. 7(3), pages 309-324, December.
    11. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 465-492, April.
    12. Adam Brandenburger & Amanda Friedenberg, 2014. "Intrinsic Correlation in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 4, pages 59-111, World Scientific Publishing Co. Pte. Ltd..
    13. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    14. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
    15. 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.
    16. 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.
    17. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    18. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
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    Cited by:

    1. Chenwei Shi & Yiyang Wang, 2021. "Pareto Optimality, Functional Dependence and Collective Agency," Papers 2104.09112, arXiv.org.

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