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Evolutionary stability in a reputational model of bargaining

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  • Abreu, Dilip
  • Sethi, Rajiv

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.
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  • Abreu, Dilip & Sethi, Rajiv, 2003. "Evolutionary stability in a reputational model of bargaining," Games and Economic Behavior, Elsevier, vol. 44(2), pages 195-216, August.
    • Handle: RePEc:eee:gamebe:v:44:y:2003:i:2:p:195-216
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    Cited by:

    1. Daniel G. Stephenson & Alexander L. Brown, 2021. "Playing the field in all-pay auctions," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 489-514, June.
    2. Friedman, Daniel & Singh, Nirvikar, 2009. "Equilibrium vengeance," Games and Economic Behavior, Elsevier, vol. 66(2), pages 813-829, July.
    3. 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.
    4. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2009. "Voluntarily Separable Repeated Prisoner's Dilemma," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 993-1021.
    5. Selçuk Özyurt, 2015. "Searching for a Bargain: Power of Strategic Commitment," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 320-353, February.
    6. 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.
    7. Send, Jonas & Serena, Marco, 2022. "An empirical analysis of insistent bargaining," Journal of Economic Psychology, Elsevier, vol. 90(C).
    8. 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.
    9. Thierry Vignolo, 2010. "Imitation and selective matching in reputational games," Journal of Evolutionary Economics, Springer, vol. 20(3), pages 395-412, June.
    10. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    11. Anna Sanktjohanser, 2020. "Optimally Stubborn," Cowles Foundation Discussion Papers 2255, Cowles Foundation for Research in Economics, Yale University.
    12. 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.
    13. Heggedal, Tom-Reiel & Helland, Leif & Våge Knutsen, Magnus, 2022. "The power of outside options in the presence of obstinate types," Games and Economic Behavior, Elsevier, vol. 136(C), pages 454-468.
    14. Sanktjohanser, Anna, 2022. "Optimally Stubborn," TSE Working Papers 22-1367, Toulouse School of Economics (TSE).
    15. Jonas Send & Marco Serena, 2021. "An Empirical Analysis of Stubborn Bargaining," Working Papers tax-mpg-rps-2021-05, Max Planck Institute for Tax Law and Public Finance.

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    JEL classification:

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

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