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Payoff Information and Self-Confirming Equilibrium

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  • Eddie Dekel
  • Drew Fudenberg
  • David K. Levine

Abstract

In a self-confirming equilibrium, each player correctly forecasts the actions that opponents will take along the equilibrium path, but may be mistaken about the way that opponents would respond to deviations. Intuitively, this equilibrium concept models the possible steady states of a learning process in which, each time the game is played, players observe only the actions played by their opponents (as opposed to the complete specification of the opponents' strategies) so that they need never receive evidence that their forecasts of off-path play are incorrect. 3 Because self- confirming equilibrium (henceforth "SCE") allows beliefs about off-path play to be completely arbitrary, it (like Nash equilibrium) corresponds to a situation in which players have no prior information about the payoff fimctions of their opponents.4 This may be a good approximation of some real-world situations; it is also the obvious way to model play in game theory experiments in which subjects are given no itiormation about opponents' payoffs. In other cases, both in the real world and in the laboratory, it seems plausible that players do have some prior information about their opponents' payoffs. The goal of this paper is to develop a more restrictive version of SCE that incorporates the effects of such prior information. In carrying out this program, a key issue is what sort of prior itiormation about payoffs should be considered. It is well known that predictions based on common certainty of payoffs are not robust to even a small amount of uncertainty. Following Fudenberg, Kreps and Levine (1987), we are interested in the strongest possible assumption that is robust to payoff uncertainty. Past work suggests that this assumption should be that payoffs are almost common certainty in the sense of Monderer and Samet (1989).5 Therefore we start by developing a preliminary concept -- rationalizability at reachable nodes -- that is robust and incorporates almost common certainty of th

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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 172.

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Date of creation: 24 Jan 1999
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Handle: RePEc:cla:levarc:172

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  1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  2. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  3. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
  4. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  5. Drew Fudenberg & David Kreps & David K. Levine, 1988. "On the Robustness of Equilibrium Refinements," Levine's Working Paper Archive 227, David K. Levine.
  6. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  7. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
  8. Basu, Kaushik, 1988. "Strategic irrationality in extensive games," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 247-260, June.
  9. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
  10. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
  11. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  12. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  13. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  14. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  15. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  16. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 23-46, January.
  17. Lawrence E. Blume & William R. Zame, 1993. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Game Theory and Information 9309001, EconWPA.
  18. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  19. Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of Solution Concepts of Games," Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  20. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
  21. D. Fudenberg & D. M. Kreps, 2010. "Learning in Extensive Games, I: Self-Confirming Equilibrium," Levine's Working Paper Archive 382, David K. Levine.
  22. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
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