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Payoff Information and Self-Confirming Equilibrium

  • Eddie Dekel
  • Drew Fudenberg
  • David K. Levine

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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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 040.

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Handle: RePEc:els:esrcls:040
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  1. 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.
  2. Basu, Kaushik, 1988. "Strategic irrationality in extensive games," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 247-260, June.
  3. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  4. D. Fudenberg & D. M. Kreps, 2010. "Learning in Extensive Games, I: Self-Confirming Equilibrium," Levine's Working Paper Archive 382, David K. Levine.
  5. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
  6. 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.
  7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  8. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
  10. Drew Fudenberg & David M. Kreps & David K. Levine, 1986. "On the Robustness of Equilibrium Refinements," UCLA Economics Working Papers 398, UCLA Department of Economics.
  11. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  12. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
  13. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  14. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
  15. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-94, July.
  16. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  17. 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.
  18. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  19. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  20. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  21. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
  22. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
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