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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
    DOI: 10.1177/1043463191003001004
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    References listed on IDEAS

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    1. Anatol Rapoport, 1988. "Editorial Comments on the Article by Hirshleifer and Martinez Coll," Journal of Conflict Resolution, Peace Science Society (International), vol. 32(2), pages 399-401, June.
    2. Jack Hirshleifer & Juan Carlos Martinez Coll, 1988. "What Strategies Can Support the Evolutionary Emergence of Cooperation?," Journal of Conflict Resolution, Peace Science Society (International), vol. 32(2), pages 367-398, June.
    3. Barton Lipman, 1986. "Cooperation among egoists in Prisoners' Dilemma and Chicken games," Public Choice, Springer, vol. 51(3), pages 315-331, January.
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    Citations

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    Cited by:

    1. Henk de Vos & Rita Smaniotto & Donald A. Elsas, 2001. "Reciprocal Altruism Under Conditions Of Partner Selection," Rationality and Society, , vol. 13(2), pages 139-183, May.
    2. Angelo Antoci & Alexia Delfino & Fabio Paglieri & Fabio Sabatini, 2016. "The ecology of social interactions in online and offline environments," Papers 1601.07776, arXiv.org.
    3. Thomas Wagner, 1998. "Reciprocity And Efficiency," Rationality and Society, , vol. 10(3), pages 347-375, August.
    4. Guttman, Joel M., 2000. "On the evolutionary stability of preferences for reciprocity," European Journal of Political Economy, Elsevier, vol. 16(1), pages 31-50, March.
    5. 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.
    6. Antoci, Angelo & Russu, Paolo & Zarri, Luca, 2014. "Tax evasion in a behaviorally heterogeneous society: An evolutionary analysis," Economic Modelling, Elsevier, vol. 42(C), pages 106-115.
    7. José Molinero, 2000. "The Origins of the State from Reciprocity to Coercive Power," Constitutional Political Economy, Springer, vol. 11(3), pages 231-253, September.
    8. Kevin L. Brown, 1996. "Was Adam Smith An Economist?," Rationality and Society, , vol. 8(3), pages 343-347, August.
    9. Juan C Martinez-Coll, 2006. "Caves, Temples, Palaces and Bazaars Building with Jack Hirshleifer’s bricks," Levine's Working Paper Archive 618897000000001048, David K. Levine.
    10. Yee, Kenton K., 2003. "Ownership and trade from evolutionary games," International Review of Law and Economics, Elsevier, vol. 23(2), pages 183-197, June.
    11. Jack Hirshleifer, 1993. "The Affections and the Passions," Rationality and Society, , vol. 5(2), pages 185-202, April.
    12. Poulsen, A., 2001. "Reciprocity, Materialism and Welfare: An Evolutionary Model," Papers 01-3, Aarhus School of Business - Department of Economics.
    13. Hausken, Kjell, 1995. "The dynamics of within-group and between-group interaction," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 655-687.
    14. Jack Hirshleifer, 1992. "The Affections and the Passions: Their Economic Logic," UCLA Economics Working Papers 652, UCLA Department of Economics.
    15. Rolf Ziegler, 1997. "The Normative Structure Of Solidarity And Inequality," Rationality and Society, , vol. 9(4), pages 449-467, November.
    16. Hausken, Kjell, 2006. "Jack Hirshleifer: A Nobel Prize left unbestowed," European Journal of Political Economy, Elsevier, vol. 22(2), pages 251-276, June.
    17. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Desire for Revenge and the Dynamics of Conflicts," MPRA Paper 6746, University Library of Munich, Germany.
    18. Congleton, Roger D. & Vanberg, Viktor J., 2001. "Help, harm or avoid? On the personal advantage of dispositions to cooperate and punish in multilateral PD games with exit," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 145-167, February.

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