The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

Epistemic Game Theory: Complete Information

  • Adam Brandenburger
Living reference work entry


The epistemic programme can be viewed as a methodical construction of game theory from its most basic elements – rationality and irrationality, belief and knowledge about such matters, beliefs about beliefs, knowledge about knowledge, and so on. To date, the epistemic field has been mainly focused on game matrices and trees – that is, on the non-cooperative branch of game theory. It has been used to provide foundations for existing non-cooperative solution concepts, and also to uncover new solution concepts. The broader goal of the programme is to provide a method of analysing different sets of assumptions about games in a precise and uniform manner.


Admissibility Backward induction Common knowledge Conditional probability systems Correlation Epistemic game theory Epistemic game theory: complete information Finite games Invariance Iterated dominance Lexicographic probability systems Rational behaviour Rationalizability Strong dominance Type structures Uncertainty Weak dominance 

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  1. Asheim, G. 2001. Proper rationalizability in lexicographic beliefs. International Journal of Game Theory 30: 453–478.CrossRefGoogle Scholar
  2. Asheim, G., and A. Perea. 2005. Sequential and quasi-perfect rationalizability in extensive games. Games and Economic Behavior 53: 15–42.CrossRefGoogle Scholar
  3. Aumann, R. 1974. Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1: 67–96.CrossRefGoogle Scholar
  4. Aumann, R. 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55: 1–18.CrossRefGoogle Scholar
  5. Aumann, R. 1995. Backward induction and common knowledge of rationality. Games and Economic Behavior 8: 6–19.CrossRefGoogle Scholar
  6. Aumann, R. 1996. Reply to Binmore. Games and Economic Behavior 17: 138–146.CrossRefGoogle Scholar
  7. Aumann, R. 1998a. On the centipede game. Games and Economic Behavior 23: 97–105.CrossRefGoogle Scholar
  8. Aumann, R. 1998b. Common priors: A reply to Gul. Econometrica 66: 929–938.CrossRefGoogle Scholar
  9. Aumann, R., and A. Brandenburger. 1995. Epistemic conditions for Nash equilibrium. Econometrica 63: 1161–1180.CrossRefGoogle Scholar
  10. Balkenborg, D., and E. Winter. 1997. A necessary and sufficient epistemic condition for playing backward induction. Journal of Mathematical Economics 27: 325–345.CrossRefGoogle Scholar
  11. Basu, K. 1990. On the existence of a rationality definition for extensive games. International Journal of Game Theory 19: 33–44.CrossRefGoogle Scholar
  12. Battigalli, P. 1997. On rationalizability in extensive games. Journal of Economic Theory 74: 40–61.CrossRefGoogle Scholar
  13. Battigalli, P., and M. Siniscalchi. 1999. Hierarchies of conditional beliefs and interactive epistemology in dynamic games. Journal of Economic Theory 88: 188–230.CrossRefGoogle Scholar
  14. Battigalli, P., and M. Siniscalchi. 2002. Strong belief and forward-induction reasoning. Journal of Economic Theory 106: 356–391.CrossRefGoogle Scholar
  15. Ben Porath, E. 1997. Rationality, Nash equilibrium, and backward induction in perfect information games. Review of Economic Studies 64: 23–46.CrossRefGoogle Scholar
  16. Bernheim, D. 1984. Rationalizable strategic behavior. Econometrica 52: 1007–1028.CrossRefGoogle Scholar
  17. Bicchieri, C. 1988. Strategic behavior and counterfactuals. Synthese 76: 135–169.CrossRefGoogle Scholar
  18. Bicchieri, C. 1989. Self-refuting theories of strategic interaction: A paradox of common knowledge. Erkenntnis 30: 69–85.CrossRefGoogle Scholar
  19. Binmore, K. 1987. Modelling rational players I. Economics and Philosophy 3: 179–214.CrossRefGoogle Scholar
  20. Binmore, K. 1996. A note on backward induction. Games and Economic Behavior 17: 135–137.CrossRefGoogle Scholar
  21. Blume, L., A. Brandenburger, and E. Dekel. 1991a. Lexicographic probabilities and choice under uncertainty. Econometrica 59: 61–79.CrossRefGoogle Scholar
  22. Blume, L., A. Brandenburger, and E. Dekel. 1991b. Lexicographic probabilities and equilibrium refinements. Econometrica 59: 81–98.CrossRefGoogle Scholar
  23. Bonanno, G. 1991. The logic of rational play in games of perfect information. Economics and Philosophy 7: 37–65.CrossRefGoogle Scholar
  24. Bonanno, G., and K. Nehring. 1999. How to make sense of the common prior assumption under incomplete information. International Journal of Game Theory 28: 409–434.CrossRefGoogle Scholar
  25. Börgers, T. 1994. Weak dominance and approximate common knowledge. Journal of Economic Theory 64: 265–276.CrossRefGoogle Scholar
  26. Brandenburger, A. 1992. Lexicographic probabilities and iterated admissibility. In Economic analysis of markets and games, ed. P. Dasgupta, D. Gale, O. Hart, and E. Maskin. Cambridge, MA: MIT Press.Google Scholar
  27. Brandenburger, A. 2007. The power of paradox: Some recent results in interactive epistemology. International Journal of Game Theory 35: 465–492.CrossRefGoogle Scholar
  28. Brandenburger, A., and E. Dekel. 1987. Rationalizability and correlated equilibria. Econometrica 55: 1391–1402.CrossRefGoogle Scholar
  29. Brandenburger, A., Friedenberg, A. and Keisler, H.J. 2006. Admissibility in games. Unpublished, Stern School of Business, New York University.Google Scholar
  30. Dalkey, N. 1953. Equivalence of information patterns and essentially determinate games. In Contributions to the theory of games, ed. H. Kuhn and A. Tucker, Vol. 2. Princeton: Princeton University Press.Google Scholar
  31. Dekel, E., and D. Fudenberg. 1990. Rational behavior with payoff uncertainty. Journal of Economic Theory 52: 243–267.CrossRefGoogle Scholar
  32. Ewerhart, C. 2002. Ex-ante justifiable behavior, common knowledge, and iterated admissibility. Unpublished, Department of Economics, University of Bonn.Google Scholar
  33. Feinberg, Y. 2000. Characterizing common priors in terms of posteriors. Journal of Economic Theory 91: 127–179.CrossRefGoogle Scholar
  34. Friedenberg, A. 2002. When common belief is correct belief. Unpublished, Olin School of Business, Washington University.Google Scholar
  35. Gale, D. 1953. A theory of n-person games with perfect information. Proceedings of the National Academy of Sciences 39: 496–501.CrossRefGoogle Scholar
  36. Gul, F. 1998. A comment on Aumann’s Bayesian view. Econometrica 66: 923–927.CrossRefGoogle Scholar
  37. Halpern, J. 1999. Hypothetical knowledge and counterfactual reasoning. International Journal of Game Theory 28: 315–330.CrossRefGoogle Scholar
  38. Halpern, J. 2001. Substantive rationality and backward induction. Games and Economic Behavior 37: 425–435.CrossRefGoogle Scholar
  39. Halpern, J. 2002. Characterizing the common prior assumption. Journal of Economic Theory 106: 316–355.CrossRefGoogle Scholar
  40. Harsanyi, J. 1967–8. Games with incomplete information played by ‘Bayesian’ players, I–III. Management Science 14: 159–182, 320–334, 486–502.Google Scholar
  41. Harsanyi, J. 1973. Games with randomly disturbed payoffs: A new rationale for mixed strategy equilibrium points. International Journal of Game Theory 2: 1–23.CrossRefGoogle Scholar
  42. Kohlberg, E., and J.-F. Mertens. 1986. On the strategic stability of equilibria. Econometrica 54: 1003–1037.CrossRefGoogle Scholar
  43. Marx, L., and J. Swinkels. 1997. Order independence for iterated weak dominance. Games and Economic Behavior 18: 219–245.CrossRefGoogle Scholar
  44. Mertens, J.-F. 1989. Stable equilibria – A reformulation. Mathematics of Operations Research 14: 575–625.CrossRefGoogle Scholar
  45. Morris, S. 1994. Trade with heterogeneous prior beliefs and asymmetric information. Econometrica 62: 1327–1347.CrossRefGoogle Scholar
  46. Myerson, R. 1978. Refinements of the Nash equilibrium concept. International Journal of Game Theory 1: 73–80.CrossRefGoogle Scholar
  47. Myerson, R. 1991. Game theory. Cambridge, MA: Harvard University Press.Google Scholar
  48. Pearce, D. 1984. Rational strategic behavior and the problem of perfection. Econometrica 52: 1029–1050.CrossRefGoogle Scholar
  49. Reny, P. 1992. Rationality in extensive form games. Journal of Economic Perspectives 6(4): 103–118.CrossRefGoogle Scholar
  50. Rényi, A. 1955. On a new axiomatic theory of probability. Acta Mathematica Academiae Scientiarum Hungaricae 6: 285–335.CrossRefGoogle Scholar
  51. Rosenthal, R. 1981. Games of perfect information, predatory pricing and the chain-store paradox. Journal of Economic Theory 25: 92–100.CrossRefGoogle Scholar
  52. Samet, D. 1996. Hypothetical knowledge and games with perfect information. Games and Economic Behavior 17: 230–251.CrossRefGoogle Scholar
  53. Samet, D. 1998a. Common priors and the separation of convex sets. Games and Economic Behavior 24: 172–174.CrossRefGoogle Scholar
  54. Samet, D. 1998b. Iterated expectations and common priors. Games and Economic Behavior 24: 131–141.CrossRefGoogle Scholar
  55. Samuelson, L. 1992. Dominated strategies and common knowledge. Games and Economic Behavior 4: 284–313.CrossRefGoogle Scholar
  56. Stahl, D. 1995. Lexicographic rationalizability and iterated admissibility. Economic Letters 47: 155–159.CrossRefGoogle Scholar
  57. Stalnaker, R. 1996. Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy 12: 133–163.CrossRefGoogle Scholar
  58. Stalnaker, R. 1998. Belief revision in games: Forward and backward induction. Mathematical Social Sciences 36: 31–56.CrossRefGoogle Scholar
  59. Tan, T., and S. Werlang. 1988. The Bayesian foundations of solution concepts of games. Journal of Economic Theory 45: 370–391.CrossRefGoogle Scholar
  60. Thompson, F. 1952. Equivalence of games in extensive form. Research Memorandum RM-759. The RAND Corporation.Google Scholar

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Authors and Affiliations

  • Adam Brandenburger
    • 1
  1. 1.