IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v2y2011i1p52-86d11354.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/2/1/52/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/2/1/52/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, April.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    3. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    4. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    5. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.
    6. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation for Research in Economics, Yale University.
    7. Moscati Ivan, 2009. "Interactive and common knowledge in the state-space model," CESMEP Working Papers 200903, University of Turin.
    8. Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    9. Cyril Hédoin, 2016. "Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals," Games, MDPI, vol. 7(4), pages 1-17, November.
    10. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
    11. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    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. Bonanno, Giacomo & Nehring, Klaus, 1998. "On the logic and role of Negative Introspection of Common Belief," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 17-36, January.
    14. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 24, University of California, Davis, Department of Economics.
    15. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    16. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    17. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    18. Áron Tóbiás, 2021. "Meet meets join: the interaction between pooled and common knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 989-1019, December.
    19. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    20. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:2:y:2011:i:1:p:52-86:d:11354. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.