Dynamic Models of Rational Deliberation in Games

  • Eric PacuitEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8972)


There is a growing body of literature that analyzes games in terms of the “process of deliberation” that leads the players to select their component of a rational outcome. Although the details of the various models of deliberation in games are different, they share a common line of thought: The rational outcomes of a game are arrived at through a process in which each player settles on an optimal choice given her evolving beliefs about her own choices and the choices of her opponents. The goal is to describe deliberation in terms of a sequence of belief changes about what the players are doing or what their opponents may be thinking. The central question is: What are the update mechanisms that match different game-theoretic analyses? The general conclusion is that the rational outcomes of a game depend not only on the structure of the game, but also on the players’ initial beliefs, which dynamical rule is being used by the players to update their inclinations (in general, different players may be using different rules), and what exactly is commonly known about the process of deliberation.


Epistemic game theory Dynamic epistemic logic Belief revision 


  1. 1.
    Alexander, J.M.: Local interactions and the dynamics of rational deliberation. Philos. Stud. 147(1), 103–121 (2010)CrossRefGoogle Scholar
  2. 2.
    Apt, K.R.: A primer on strategic games. In: Apt, K.R., Grädel, E. (eds.) Lectures in Game Theory for Computer Scientists, pp. 1–33. Cambridge University Press, Cambridge (2011)CrossRefGoogle Scholar
  3. 3.
    Apt, K.R., Zvesper, J.A.: Public announcements in strategic games with arbitrary strategy sets. In: Proceedings of LOFT 2010 (2010)Google Scholar
  4. 4.
    Apt, K.R., Zvesper, J.A.: Public announcements in strategic games with arbitrary strategy sets. CoRR (2010).
  5. 5.
    Asheim, G., Dufwenberg, M.: Admissibility and common belief. Games Econ. Behav. 42, 208–234 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Aumann, R.: Agreeing to disagree. Ann. Stat. 4, 1236–1239 (1976)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Aumann, R.: Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55(1), 1–18 (1987)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Aumann, R.: Backward induction and common knowledge of rationality. Game Econ. Behav. 8, 6–19 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Aumann, R.: On the centipede game. Game Econ. Behav. 23, 97–105 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Aumann, R., Brandenburger, A.: Epistemic conditions for Nash equilibrium. Econometrica 63, 1161–1180 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., De Lima, T.: ‘Knowable’ as ‘known after an announcement’. Rev. Symb. Log. 1(3), 305–334 (2008)zbMATHCrossRefGoogle Scholar
  12. 12.
    Baltag, A., Gierasimczuk, N., Smets, S.: Belief revision as a truth-tracking process. In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, TARK XIII, pp. 187–190, ACM (2011)Google Scholar
  13. 13.
    Baltag, A., Smets, S.: ESSLLI 2009 course: dynamic logics for interactive belief revision (2009). Slides available online at
  14. 14.
    Baltag, A., Smets, S.: Group belief dynamics under iterated revision: Fixed points and cycles of joint upgrades. In: Proceedings of Theoretical Aspects of Rationality and Knowledge (2009)Google Scholar
  15. 15.
    Baltag, A., Smets, S., Zvesper, J.A.: Keep ‘hoping’ for rationality: A solution to the backwards induction paradox. Synthese 169, 301–333 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Battigalli, P., Siniscalchi, M.: Strong belief and forward induction reasoning. J. Econ. Theor. 105, 356–391 (2002)MathSciNetCrossRefGoogle Scholar
  17. 17.
    van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Log. 14(2), 129–155 (2004)Google Scholar
  18. 18.
    van Benthem, J.: Rational dynamics and epistemic logic in games. Int. Game Theor. Rev. 9(1), 13–45 (2007)zbMATHCrossRefGoogle Scholar
  19. 19.
    van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)zbMATHCrossRefGoogle Scholar
  20. 20.
    van Benthem, J., Gheerbrant, A.: Game solution, epistemic dynamics and fixed-point logics. Fundam. Inform. 100, 1–23 (2010)Google Scholar
  21. 21.
    van Benthem, J., Pacuit, E., Roy, O.: Towards a theory of play: A logical perspective on games and interaction. Games 2(1), 52–86 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Bernheim, B.D.: Rationalizable strategic behavior. Econometrica 52(4), 1007–1028 (1984)zbMATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Board, O.: Dynamic interactive epistemology. Games Econ. Behav. 49, 49–80 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Bonanno, G.: Reasoning about strategies and rational play in dynamic games. In: van Benthem, J., Ghosh, S., Verbrugge, R. (eds.) Models of Strategic Reasoning. LNCS, vol. 8972, pp. 34–62. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  25. 25.
    Boutilier, C.: Conditional logics for default reasoning and belief revision. Ph.D. thesis, University of Toronto (1992)Google Scholar
  26. 26.
    Brandenburger, A.: The power of paradox: some recent developments in interactive epistemology. Int. J. Game Theor. 35, 465–492 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    Brandenburger, A., Friedenberg, A., Keisler, H.J.: Admissibility in games. Econometrica 76(2), 307–352 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    Chwe, M.S.-Y.: Rational Ritual. Princeton University Press, Princeton (2001)Google Scholar
  29. 29.
    Colman, A.: Cooperation, psychological game theory, and limitations of rationality in social interactions. Behav. Brain Sci. 26, 139–198 (2003)Google Scholar
  30. 30.
    Colman, A.: Depth of strategic reasoning in games. TRENDS Cogn. Sci. 7(1), 2–4 (2003)CrossRefGoogle Scholar
  31. 31.
    Cubitt, R.P., Sugden, R.: Common knowledge, salience and convention: A reconstruction of David Lewis’ game theory. Econ. Philos. 19(2), 175–210 (2003)CrossRefGoogle Scholar
  32. 32.
    Cubitt, R.P., Sugden, R.: The reasoning-based expected utility procedure. Games Econ. Behav. 71(2), 328–338 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  33. 33.
    Cubitt, R.P., Sugden, R.: Common reasoning in games: A Lewisian analysis of common knowledge of rationality. Econ. Philos. 30(03), 285–329 (2014)CrossRefGoogle Scholar
  34. 34.
    van Ditmarsch, H., van Eijck, J., Verbrugge, R.: Common knowledge and common belief. In: van Eijck, J., Verbrugge, R. (eds.) Discourses on Social Software, pp. 99–122. Amsterdam University Press, Amsterdam (2009)Google Scholar
  35. 35.
    Douven, I.: Decision theory and the rationality of further deliberation. Econ. Philos. 18(2), 303–328 (2002)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. The MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  37. 37.
    Gerbrandy, J.: Bisimulations on planet Kripke. Ph.D. thesis, University of Amsterdam (1999)Google Scholar
  38. 38.
    Gierasimczuk, N.: Knowing one’s limits: Logical analysis of inductive inference. Ph.D. thesis, Institute for Logic, Language and Information, University of Amsterdam (2011)Google Scholar
  39. 39.
    Halpern, J.: Substantive rationality and backward induction. Games Econ. Behav. 37(2), 425–435 (2001)zbMATHCrossRefGoogle Scholar
  40. 40.
    Halpern, J., Moses, Y.: Knowledge and common knowledge in a distributed environment. J. ACM 37(3), 549–587 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  41. 41.
    Halpern, J., Pass, R.: A logical characterization of iterated admissibility. In: Heifetz, A. (ed.) Proceedings of the Twelfth Conference on Theoretical Aspects of Rationality and Knoweldge, pp. 146–155 (2009)Google Scholar
  42. 42.
    Harsanyi, J.: The tracing procedure: a Bayesian approach to defining a solution for \(n\)-person noncooperative games. Int. J. Game Theor. 4, 61–94 (1975)zbMATHMathSciNetCrossRefGoogle Scholar
  43. 43.
    Harsanyi, J., Selten, R.: A General Theory of Equilibrium Selection in Games. The MIT Press, Cambridge (1988)zbMATHGoogle Scholar
  44. 44.
    Hedden, T., Zhang, J.: What do you think I think you think? strategic reasoning in matrix games. Cognition 85, 1–36 (2002)CrossRefGoogle Scholar
  45. 45.
    Jeffrey, R.: Review of the dynamics of rational deliberation by Brian Skyrms. Philos. Phenomenol. Res. 52(3), 734–737 (1992)CrossRefGoogle Scholar
  46. 46.
    Kadane, J.B., Larkey, P.D.: Subjective probability and the theory of games. Manag. Sci. 28(2), 113–120 (1982)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Kets, W.: Bounded reasoning and higher-order uncertainty. Working paper (2010)Google Scholar
  48. 48.
    Lamarre, P., Shoham, Y.: Knowledge, certainty, belief and conditionalisation. In: Proceedings of the International Conference on Knowledge Representation and Reasoning, pp. 415–424 (1994)Google Scholar
  49. 49.
    Leitgeb, H.: Beliefs in conditionals vs. conditional beliefs. Topoi 26(1), 115–132 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  50. 50.
    Levi, I.: Feasibility. In: Bicchieri, C., Chiara, L.D. (eds.) Knowledge, Belief and Strategic Interaction, pp. 1–20. Cambridge University Press, Cambridge (1992)CrossRefGoogle Scholar
  51. 51.
    Lewis, D.K.: Counterfactuals. Harvard University Press, Cambridge (1973)Google Scholar
  52. 52.
    Leyton-Brown, K., Shoham, Y.: Essentials of Game Theory: A Concise Multidisciplinary Introduction. Morgan & Claypool Publishers, San Rafael (2008)Google Scholar
  53. 53.
    Meijering, B., van Rijn, H., Taatgen, N., Verbrugge, R.: I do know what you think I think: Second-order social reasoning is not that difficult. In: Proceedings of the 33rd Annual Meeting of the Cognitive Science Society, pp. 1423–1428 (2010)Google Scholar
  54. 54.
    Meijering, B., van Rijn, H., Taatgen, N., Verbrugge, R.: What eye movements can tell about theory of mind in a strategic game. PLoS ONE 7(9), e45961 (2012)CrossRefGoogle Scholar
  55. 55.
    Monderer, D., Samet, D.: Approximating common knowledge with common beliefs. Games Econ. Behav. 1, 170–190 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  56. 56.
    Morgenbesser, S., Ullmann-Margalit, E.: Picking and choosing. Soc. Res. 44(4), 757–785 (1977)Google Scholar
  57. 57.
    Pacuit, E.: Dynamic epistemic logic I: Modeling knowledge and beliefs. Philos. Compass 8(9), 798–814 (2013)CrossRefGoogle Scholar
  58. 58.
    Pacuit, E.: Dynamic epistemic logic II: Logics of information change. Philos. Compass 8(9), 815–833 (2013)CrossRefGoogle Scholar
  59. 59.
    Pacuit, E., Roy, O.: A dynamic analysis of interactive rationality. In: Ju, S., Lang, J., van Ditmarsch, H. (eds.) LORI 2011. LNCS, vol. 6953, pp. 244–257. Springer, Heidelberg (2011)Google Scholar
  60. 60.
    Pearce, D.G.: Rationalizable strategic behavior and the problem of perfection. Econometrica 52(4), 1029–1050 (1984)zbMATHMathSciNetCrossRefGoogle Scholar
  61. 61.
    Perea, A.: Epistemic foundations for backward induction: An overview. In: van Benthem, J., Gabbay, D., Löwe, B. (eds.) Proceedings of the 7th Augustus de Morgan Workshop, pp. 159–193. Texts in Logic and Games, Amsterdam University Press (2007)Google Scholar
  62. 62.
    Perea, A.: A one-person doxastic characterization of Nash strategies. Synthese 158, 251–271 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  63. 63.
    Perea, A.: Epistemic Game Theory: Reasoning and Choice. Cambridge University Press, Cambridge (2012)CrossRefGoogle Scholar
  64. 64.
    Perea, A.: Finite reasoning procedures for dynamic games. In: van Benthem, J., Ghosh, S., Verbrugge, R. (eds.) Models of Strategic Reasoning. LNCS, vol. 8972, pp. 63–90. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  65. 65.
    Plaza, J.: Logics of public communications. In: Emrich, M.L., Pfeifer, M.S., Hadzikadic, M., Ras, Z.W. (eds.) Proceedings, 4th International Symposium on Methodologies for Intelligent Systems, pp. 201–216 (republished as [66]) (1989)Google Scholar
  66. 66.
    Plaza, J.: Logics of public communications. Synthese 158(2), 165–179 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  67. 67.
    Rabinowicz, W.: Does practical deliberation crowd out self-prediction? Erkenntnis 57, 91–122 (2002)CrossRefGoogle Scholar
  68. 68.
    Risse, M.: What is rational about Nash equilibrium? Synthese 124(3), 361–384 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  69. 69.
    Rubinstein, A.: Comments on the interpretation of game theory. Econometrica 59(4), 909–924 (1991)CrossRefGoogle Scholar
  70. 70.
    Samuelson, L.: Dominated strategies and common knowledge. Games Econ. Behav. 4, 284–313 (1992)zbMATHMathSciNetCrossRefGoogle Scholar
  71. 71.
    Selten, R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theor. 4(1), 25–55 (1975)zbMATHMathSciNetCrossRefGoogle Scholar
  72. 72.
    Skyrms, B.: The Dynamics of Rational Deliberation. Harvard University Press, Cambridge (1990)zbMATHGoogle Scholar
  73. 73.
    Stahl, D.O., Wilson, P.W.: On players’ models of other players: theory and experimental evidence. Games Econ. Behav. 10, 218–254 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  74. 74.
    Stalnaker, R.: Knowledge, belief, and counterfactual reasoning in games. Econ. Philos. 12, 133–163 (1996)CrossRefGoogle Scholar
  75. 75.
    Stalnaker, R.: Belief revision in games: Forward and backward induction. Math. Soc. Sci. 36, 31–56 (1998)zbMATHMathSciNetCrossRefGoogle Scholar
  76. 76.
    Vanderschraaf, P., Sillari, G.: Common knowledge. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Spring 2009 edition (2009)Google Scholar
  77. 77.
    Verbrugge, R.: Logic and social cognition: the facts matter, and so do computational models. J. Philos. Log. 38(6), 649–680 (2009)zbMATHMathSciNetCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MarylandCollege ParkUSA

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