IDEAS home Printed from https://ideas.repec.org/p/not/notcdx/2011-01.html
   My bibliography  Save this paper

Common reasoning in games: a Lewisian analysis of common knowledge of rationality

Author

Listed:
  • Robin Cubitt

    (School of Economics, University of Nottingham)

  • Robert Sugden

    (School of Economics, University of East Anglia)

Abstract

The game-theoretic assumption of ‘common knowledge of rationality’ leads to paradoxes when rationality is represented in a Bayesian framework as cautious expected utility maximisation with independent beliefs (ICEU). We diagnose and resolve these paradoxes by presenting a new class of formal models of players’ reasoning, inspired by David Lewis’s account of common knowledge, in which the analogue of common knowledge is derivability in common reason. We show that such models can consistently incorporate any of a wide range of standards of decision-theoretic practical rationality. We investigate the implications arising when the standard of decision-theoretic rationality so assumed is ICEU.

Suggested Citation

  • Robin Cubitt & Robert Sugden, 2011. "Common reasoning in games: a Lewisian analysis of common knowledge of rationality," Discussion Papers 2011-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    • Handle: RePEc:not:notcdx:2011-01
    as

    Download full text from publisher

    File URL: https://www.nottingham.ac.uk/cedex/documents/papers/2011-01.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    2. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    3. 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.
    4. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(1), pages 9-55, April.
    5. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    6. Cubitt, Robin P. & Sugden, Robert, 2011. "The reasoning-based expected utility procedure," Games and Economic Behavior, Elsevier, vol. 71(2), pages 328-338, March.
    7. 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.
    8. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
    9. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    10. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    11. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
    12. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    13. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    14. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    15. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    16. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
    17. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
    18. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 13-25.
    19. Cubitt, Robin P & Sugden, Robert, 1994. "Rationally Justifiable Play and the Theory of Non-cooperative Games," Economic Journal, Royal Economic Society, vol. 104(425), pages 798-803, July.
    20. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    21. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    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. repec:cup:judgdm:v:13:y:2018:i:1:p:137-149 is not listed on IDEAS
    2. Michiru Nagatsu & Karen Larsen & Mia Karabegovic & Marcell Székely & Dan Mønster & John Michael, 2018. "Making good cider out of bad apples --- Signaling expectations boosts cooperation among would-be free riders," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(1), pages 137-149, January.
    3. Cyril Hédoin, 2016. "Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals," Games, MDPI, vol. 7(4), pages 1-17, November.
    4. Ashton T. Sperry-Taylor, 2017. "Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies," Games, MDPI, vol. 8(1), pages 1-13, January.

    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. Cubitt, Robin P. & Sugden, Robert, 2014. "Common Reasoning In Games: A Lewisian Analysis Of Common Knowledge Of Rationality," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 285-329, November.
    2. 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.
    3. Robin P. Cubitt & Robert Sugden, 2008. "Common reasoning in games," Discussion Papers 2008-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    4. Robin P. Cubitt & Robert Sugden, 2008. "Common reasoning in games," Discussion Papers 2008-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    5. 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.
    6. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. 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.
    8. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    9. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    10. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    11. 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.
    12. Moscati Ivan, 2009. "Interactive and common knowledge in the state-space model," CESMEP Working Papers 200903, University of Turin.
    13. Christian Bach & Jérémie Cabessa, 2012. "Common knowledge and limit knowledge," Theory and Decision, Springer, vol. 73(3), pages 423-440, September.
    14. Zambrano, Eduardo, 2008. "Epistemic conditions for rationalizability," Games and Economic Behavior, Elsevier, vol. 63(1), pages 395-405, May.
    15. Søvik, Ylva, 2009. "Strength of dominance and depths of reasoning--An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 196-205, May.
    16. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    17. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    18. Colin Camerer & Teck-Hua Ho & Juin Kuan Chong, 2003. "A cognitive hierarchy theory of one-shot games: Some preliminary results," Levine's Bibliography 506439000000000495, UCLA Department of Economics.
    19. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    20. Licun Xue, "undated". "A Notion of Consistent Rationalizability - Between Weak and Pearce's Extensive Form Rationalizability," Economics Working Papers 2000-4, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Common reasoning; common knowledge; common knowledge of rationality; David Lewis; Bayesian models of games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    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:not:notcdx:2011-01. 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: Jose V Guinot Saporta (email available below). General contact details of provider: https://edirc.repec.org/data/cdnotuk.html .

    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.