IDEAS home Printed from https://ideas.repec.org/p/bro/econwp/2013-5.html
   My bibliography  Save this paper

The Evolutionary Robustness of Forgiveness and Cooperation

Author

Listed:

Abstract

We study the evolutionary robustness of strategies in innitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator dynamics. We show that there are strategies with a uniformly large basin of attraction independent of the size of the population. Moreover, we show that those strategies forgive defections and, assuming that they are symmetric, they cooperate. We provide partial eciency results for asymmetric strategies.

Suggested Citation

  • Pedro Dal BÛ & Enrique R. Pujals, 2013. "The Evolutionary Robustness of Forgiveness and Cooperation," Working Papers 2013-5, Brown University, Department of Economics.
    • Handle: RePEc:bro:econwp:2013-5
    as

    Download full text from publisher

    File URL: https://economics.brown.edu/sites/g/files/dprerj726/files/papers/2013-5_paper.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
    2. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-749, April.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    4. Bendor, Jonathan & Swistak, Piotr, 1997. "The Evolutionary Stability of Cooperation," American Political Science Review, Cambridge University Press, vol. 91(2), pages 290-307, June.
    5. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
    6. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    7. Johnson, Philip & Levine, David K. & Pesendorfer, Wolfgang, 2001. "Evolution and Information in a Gift-Giving Game," Journal of Economic Theory, Elsevier, vol. 100(1), pages 1-21, September.
    8. Volij, Oscar, 2002. "In Defense of DEFECT," Games and Economic Behavior, Elsevier, vol. 39(2), pages 309-321, May.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
    11. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    12. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    13. Cooper, David J., 1996. "Supergames Played by Finite Automata with Finite Costs of Complexity in an Evolutionary Setting," Journal of Economic Theory, Elsevier, vol. 68(1), pages 266-275, January.
    14. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    15. Kim, Yong-Gwan, 1994. "Evolutionarily stable strategies in the repeated prisoner's dilemma," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 167-197, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ravi Bapna & Liangfei Qiu & Sarah Rice, 2014. "Repeated Interactions vs. Social Ties: Quantifying the Economic Value of Trust, Forgiveness, and Reputation Using a Field Experiment," Working Papers 14-07, NET Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    2. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    3. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    4. Oscar Volij, 1998. "In Defense of DEFECT or Cooperation does not Justify the Solution Concept," Economic theory and game theory 007, Oscar Volij, revised 26 Aug 1999.
    5. Volij, Oscar, 2002. "In Defense of DEFECT," Games and Economic Behavior, Elsevier, vol. 39(2), pages 309-321, May.
    6. Anderlini, Luca & Sabourian, Hamid, 2001. "Cooperation and computability in n-player games," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 99-137, September.
    7. Jones, Matthew T., 2014. "Strategic complexity and cooperation: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 352-366.
    8. van Veelen, Matthijs & García, Julián, 2019. "In and out of equilibrium II: Evolution in repeated games with discounting and complexity costs," Games and Economic Behavior, Elsevier, vol. 115(C), pages 113-130.
    9. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February.
    10. Samuelson, Larry & Swinkels, Jeroen M., 2003. "Evolutionary stability and lexicographic preferences," Games and Economic Behavior, Elsevier, vol. 44(2), pages 332-342, August.
    11. Samuelson, Larry & Swinkels, Jeroen M., 2003. "Evolutionary stability and lexicographic preferences," Games and Economic Behavior, Elsevier, vol. 44(2), pages 332-342, August.
    12. Luis A Martinez-Vaquero & José A Cuesta & Angel Sánchez, 2012. "Generosity Pays in the Presence of Direct Reciprocity: A Comprehensive Study of 2×2 Repeated Games," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-12, April.
    13. Jonathan Bendor & Piotr Swistak, 1998. "Evolutionary Equilibria: Characterization Theorems and Their Implications," Theory and Decision, Springer, vol. 45(2), pages 99-159, October.
    14. Christos Ioannou, 2014. "Coevolution of finite automata with errors," Journal of Evolutionary Economics, Springer, vol. 24(3), pages 541-571, July.
    15. Westhoff, Frank H. & Yarbrough, Beth V. & Yarbrough, Robert M., 1996. "Complexity, organization, and Stuart Kauffman's The Origins of Order," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 1-25, January.
    16. Amit Pazgal, 1995. "Satisficing Leads to Cooperation in Mutual Interests Games," Discussion Papers 1126, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Vega-Redondo, Fernando, 2014. "Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 91-113.
    18. van Damme, E.E.C., 1995. "Game theory : The next stage," Other publications TiSEM 7779b0f9-bef5-45c7-ae6b-7, Tilburg University, School of Economics and Management.
    19. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    20. David K Levine, 2022. "Phoenix From the Ashes: The Evolution of Mechanism Designers," Levine's Working Paper Archive 11694000000000141, David K. Levine.

    More about this item

    Keywords

    #;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bro:econwp:2013-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brown Economics Webmaster (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.