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Payoff Information and Self-Confirming Equilibrium

  • Dekel, Eddie
  • Fudenberg, Drew
  • Levine, David K.

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 89 (1999)
Issue (Month): 2 (December)
Pages: 165-185

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Handle: RePEc:eee:jetheo:v:89:y:1999:i:2:p:165-185
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. A. Rubinstein & A. Wolinsky, 2010. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Levine's Working Paper Archive 369, David K. Levine.
  2. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  3. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  4. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  5. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  6. Drew Fudenberg & David M. Kreps & David K. Levine, 1986. "On the Robustness of Equilibrium Refinements," UCLA Economics Working Papers 398, UCLA Department of Economics.
  7. Kaushik Basu, 2010. "Strategic Irrationality in Extensive Games," Levine's Working Paper Archive 375, David K. Levine.
  8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  9. 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.
  10. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
  11. 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.
  12. Miguel Costa-Gomes & Vincent P. Crawford & Bruno Broseta, . "Cognition and Behavior in Normal-Form Games:An Experimental Study," Discussion Papers 00/45, Department of Economics, University of York.
  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. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
  15. D. Fudenberg & D. M. Kreps, 2010. "Learning in Extensive Games, I: Self-Confirming Equilibrium," Levine's Working Paper Archive 382, David K. Levine.
  16. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  17. 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).
  18. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  19. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
  20. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  21. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  22. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
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