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The Limits of Reciprocity

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  • JUAN CARLOS MARTINEZ COLL

    (Universidad de Málaga)

  • JACK HIRSHLEIFER

    (University of California, Los Angeles)

Abstract

Besides meeting the Nash condition (Axelrod's so-called “collective stability†), an evolutionary equilibrium must be an attractor—either an evolutionary equilibrium point (EEP) or an evolutionary equilibrium region (EER). In this analysis of Prisoners' Dilemma and Chicken environments, the “archetype†strategies (COOPERATE and DEFECT in Prisoners' Dilemma and COWARD and DAREDEVIL in Chicken) were augmented by the “reactive†strategies TIT FOR TAT and BULLY—entering separately in 3 x 3 interactions and jointly in 4 x 4 interactions. An instant-response assumption was employed that stacked the deck somewhat in favor of TIT FOR TAT. Nevertheless, in no case was all-TIT FOR TAT ever an EEP, although some conditions generated a mixed EER with only “nice†behaviors represented. A credible model should imply an equilibrium in which both “mean†and “nice†behaviors are represented. Remarkably, none of the conditions postulated here led to such an outcome. This unsatisfying result suggests the importance of introducing a PUNISHER strategy as described elsewhere by the authors.

Suggested Citation

  • Juan Carlos Martinez Coll & Jack Hirshleifer, 1991. "The Limits of Reciprocity," Rationality and Society, , vol. 3(1), pages 35-64, January.
  • Handle: RePEc:sae:ratsoc:v:3:y:1991:i:1:p:35-64
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    Cited by:

    1. Angelo Antoci & Alexia Delfino & Fabio Paglieri & Fabio Sabatini, 2016. "The ecology of social interactions in online and offline environments," Papers 1601.07776, arXiv.org.
    2. J. Atsu Amegashie & Marco Runkel, 2012. "The Paradox of Revenge in Conflicts," Journal of Conflict Resolution, Peace Science Society (International), vol. 56(2), pages 313-330, April.
    3. Poulsen, A., 2001. "Reciprocity, Materialism and Welfare: An Evolutionary Model," Papers 01-3, Aarhus School of Business - Department of Economics.
    4. Angelo Antoci & Pier Sacco & Luca Zarri, 2004. "Coexistence of Strategies and Culturally-Specific Common Knowledge: An Evolutionary Analysis," Journal of Bioeconomics, Springer, vol. 6(2), pages 165-194, May.
    5. Jack Hirshleifer, 1992. "The Affections and the Passions: Their Economic Logic," UCLA Economics Working Papers 652, UCLA Department of Economics.
    6. Bruni, Luigino & Smerilli, Alessandra, 2010. "Cooperation and diversity. An evolutionary approach," MPRA Paper 20564, University Library of Munich, Germany.
    7. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Desire for Revenge and the Dynamics of Conflicts," MPRA Paper 6746, University Library of Munich, Germany.

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