A Dynamic Analysis of Interactive Rationality

  • Eric PacuitEmail author
  • Olivier Roy
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 38)


Epistemic game theory has shown the importance of informational contexts to understand strategic interaction. We propose a general framework to analyze how such contexts may arise. The idea is to view informational contexts as the fixed points of iterated, rational responses to incoming information about the agents’ possible choices. We discuss conditions under which such fixed points may exist. In the process, we generalize existing rules for information updates used in the dynamic epistemic logic literature. We then apply this framework to weak dominance. Our analysis provides a new perspective on a well known problem with the epistemic characterization of iterated removal of weakly dominated strategies.


Game theory Dynamic epistemic logic Rationality Update Fixed points Admissibility 


  1. Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50, 510–530 (1985)CrossRefGoogle Scholar
  2. Anglberger, A.J.J., Gratzl, N., Roy, O.: Obligation, free choice and the logic of weakest permission. Rev. Symb. Log. 8(4), 807–827 (2015)CrossRefGoogle Scholar
  3. Apt, K., Zvesper, J.: Public announcements in strategic games with arbitrary strategy sets. In: Proceedings of LOFT 2010, Toulouse, France (2010a)Google Scholar
  4. Apt, K., Zvesper, J.: The role of monotonicity in the epistemic analysis of strategic games. Games 1(4), 381–394 (2010b)Google Scholar
  5. Arntzenius, F.: No regrest, or: edith piaf revamps decision theory. Erkenntnis 68, 277–297 (2008)CrossRefGoogle Scholar
  6. 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, Stanford (2009)CrossRefGoogle Scholar
  7. Baltag, A., Smets, S., Zvesper, J.: Keep ‘hoping’ for rationality: a solution to the backwards induction paradox. Synthese 169, 301–333 (2009)CrossRefGoogle Scholar
  8. Board, O.: Dynamic interactive epistemology. Games Econ. Behav. 49, 49–80 (2004)CrossRefGoogle Scholar
  9. Boutilier, C.: Conditional logics for default reasoning and belief revision. PhD thesis, University of Toronto (1992)Google Scholar
  10. Brandenburger, A., Friedenberg, A., Keisler, H.J.: Admissibility in games. Econometrica 76, 307–352 (2008)CrossRefGoogle Scholar
  11. Cubitt, R., Sugden, R.: Common knowledge, salience and convention: a reconstruction of David Lewis’ game theory. Econ. Philos. 19(2), 175–210 (2003)CrossRefGoogle Scholar
  12. Cubitt, R., Sugden, R.: The reasoning-based expected utility procedure. Games Econ. Behav. 71(2), 328–338 (2011)CrossRefGoogle Scholar
  13. Cubitt, R., Sugden, R.: Common reasoning in games: a Lewisian analysis of common knowledge of rationality. Econ. Philos. 30(3), 285–329 (2014)CrossRefGoogle Scholar
  14. Dekel, E., Siniscalchi, M.: Epistemic game theory. In: Peyton Young, H., Shmuel, Z. (eds.) Handbook of Game Theory with Economic Applications, vol. 4, pp. 619–702. Elsevier, Amsterdam (2015)Google Scholar
  15. Gerbrandy, J.: Bisimulations on planet Kripke. PhD thesis, University of Amsterdam (1999)Google Scholar
  16. 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, Stanford, pp. 146–155 (2009)Google Scholar
  17. Harsanyi, J.: The tracing procedure: a Bayesian approach to defining a solution for n-person noncooperative games. Int. J. Game Theory 4, 61–94 (1975)CrossRefGoogle Scholar
  18. Holliday, W.: Trust and the dynamics of testimony. In: Logic and interaction rationality: Seminar’s yearbook 2009, pp. 147–178. ILLC technical reports (2009)Google Scholar
  19. Lamarre, P., Shoham, Y.: Knowledge, certainty, belief and conditionalisation. In: Proceedings of the International Conference on Knoweldge Representation and Reasoning, pp. 415–424 (1994)Google Scholar
  20. Levi, I.: Rationality, prediction, and autonomous choice. Can. J. Philos. 23(1), 339–363 (1993)Google Scholar
  21. Lewis, D.: Convention. Harvard University Press, Cambridge (1969)Google Scholar
  22. Lewis, D.: Counterfactuals. Blackwell, Oxford (1973)Google Scholar
  23. Leyton-Brown, K., Shoham, Y.: Essentials of Game Theory: A Concise Multidisciplinary Introduction. Morgan & Claypool, San Rafael (2008)Google Scholar
  24. Pacuit, E.: Dynamic epistemic logic II: logics of informaiton change. Philos. Compass 8(9), 815–833 (2013)CrossRefGoogle Scholar
  25. Pacuit, E.: Dynamic models of rational deliberation in games. In: van Benthem, J., Ghosh, S., Verbrugge, R. (eds.) Models of Strategic Reasoning: Logics, Games and Communities. Springer (2015)Google Scholar
  26. Pacuit, E., Roy, O.: Epistemic foundations of game theory. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2015)Google Scholar
  27. Perea, A.: Epistemic Game Theory: Reasoning and Choice. Cambridge University Press, New York (2012)CrossRefGoogle Scholar
  28. Peterson, M.: An Introduction to Decision Theory. Cambridge University Press, Cambridge/New York (2009)CrossRefGoogle Scholar
  29. 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 (1989)Google Scholar
  30. Rabinowicz, W.: Tortous labyrinth: noncooperative normal-form games between hyperrational players. In: Bicchieri, C., Chiara, M.L.D. (eds.) Knowledge, Belief and Strategic Interaction. Cambridge University Press, Cambridge/New York, pp. 107–125 (1992)Google Scholar
  31. Rabinowicz, W.: Does practical deliberation crowd out self-prediction. Erkenntnis 57, 91–122 (2002)CrossRefGoogle Scholar
  32. Rott, H.: Shifting priorities: simple representations for 27 itereated theory change operators. In: Lagerlund, H., Lindström, S., Sliwinski, R. (eds.) Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg. Uppsala Philosophical Studies, vol. 53, pp. 359–384 (2006)Google Scholar
  33. Roy, O., Anglberger, A.J.J., Gratzl, N.: The logic of best action from a deontic perspective. In: Baltag, A., Smets, S. (eds.) Johan FAK van Benthem on Logical and Informational Dynamics. Springer (2014)Google Scholar
  34. Samuelson, L.: Dominated strategies and common knowledge. Game Econ. Behav. 4, 284–313 (1992)CrossRefGoogle Scholar
  35. Schick, F.: Self-knowledge, uncertainty and choice. Br. J. Philos. Sci. 30(3), 235–252 (1979)CrossRefGoogle Scholar
  36. Skyrms, B.: The Dynamics of Rational Deliberation. Harvard University Press, Cambridge (1990)Google Scholar
  37. Ullmann-Margalit, E., Morgenbesser, S.: Picking and choosing. Soc. Res. 44, 757–785 (1977)Google Scholar
  38. van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-class. Log. 14(2), 129–155 (2004)Google Scholar
  39. van Benthem, J.: Rational dynamics and epistemic logic in games. Int. Game Theory Rev. 9(1), 13–45 (2007)CrossRefGoogle Scholar
  40. van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press (2010)Google Scholar
  41. van Benthem, J.: Logic in Games. MIT, Cambridge/London (2014)Google Scholar
  42. van Benthem, J., Gheerbrant, A.: Game solution, epistemic dynamics and fixed-point logics. Fund. Inf. 100, 1–23 (2010)Google Scholar
  43. 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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MarylandCollege ParkUSA
  2. 2.Institut für PhilosophieUniversität BayreuthBayreuthGermany

Personalised recommendations