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Evolutionary Stability in a Reputational Model of Bargaining

Author

Listed:
  • Dilip Abreu

    (Princeton University)

  • Rajiv Sethi

    (Barnard College, Columbia University)

Abstract

A large and growing literature on reputation in games builds on the insight that the possibility of one or more players being other than fully rational can have significant effects on equilibrium behavior. This literature leaves unexplained the presence of behavioral players in the first place, and the particular forms of irrationality assumed. In this paper we endogenize departures from rationality on the basis of an evolutionary stability criterion, under the assumption that rational players incur a cost which reflects the greater sophistication of their behavior. This cost may be arbitrarily small. Within the context of a reputational model of bargaining, we show that evolutionary stability necessitates the presence of behavioral players, and places significant restrictions on the set of behavioral types that can coexist. It is consistent, however, with a broad variety of outcomes ranging from immediate agreement to complete surplus dissipation. The long run population share of behavioral types is greatest at states in which surplus dissipation is either negligible or almost complete.

Suggested Citation

  • Dilip Abreu & Rajiv Sethi, 2001. "Evolutionary Stability in a Reputational Model of Bargaining," Game Theory and Information 0103001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0103001
    Note: Type of Document - Tex; prepared on IBM PC ; to print on HP/PostScript; pages: 29 ; figures: included
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    References listed on IDEAS

    as
    1. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    2. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    3. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    4. Guttman, Joel M., 1996. "Rational actors, tit-for-tat types, and the evolution of cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 27-56, January.
    5. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    6. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    7. Kalyan Chatterjee & Larry Samuelson, 1987. "Bargaining with Two-sided Incomplete Information: An Infinite Horizon Model with Alternating Offers," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 175-192.
    8. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    9. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
    10. Simon, Herbert A, 1978. "Rationality as Process and as Product of Thought," American Economic Review, American Economic Association, vol. 68(2), pages 1-16, May.
    11. Conlisk, John, 1980. "Costly optimizers versus cheap imitators," Journal of Economic Behavior & Organization, Elsevier, vol. 1(3), pages 275-293, September.
    12. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    13. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
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    Cited by:

    1. Friedman, Daniel & Singh, Nirvikar, 2009. "Equilibrium vengeance," Games and Economic Behavior, Elsevier, vol. 66(2), pages 813-829, July.
    2. Thierry Vignolo, 2010. "Imitation and selective matching in reputational games," Journal of Evolutionary Economics, Springer, vol. 20(3), pages 395-412, June.
    3. Heller, Yuval & Mohlin, Erik, 2014. "Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli," MPRA Paper 58255, University Library of Munich, Germany.
    4. Jack Robles, 2008. "Evolution, bargaining, and time preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 19-36, April.
    5. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2009. "Voluntarily Separable Repeated Prisoner's Dilemma," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 993-1021.
    6. Konrad, Kai A. & Morath, Florian, 2016. "Bargaining with incomplete information: Evolutionary stability in finite populations," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 118-131.
    7. Vincent P. Crawford, 2003. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," American Economic Review, American Economic Association, vol. 93(1), pages 133-149, March.
    8. Kai A. Konrad & Florian Morath, 2011. "Evolutionarily stable in-group favoritism and out-group spite in intergroup conflict," Working Papers evolutionarily_stable, Max Planck Institute for Tax Law and Public Finance.

    More about this item

    Keywords

    Reputation; Evolutionary Stability; Bargaining;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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