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The Evolutionary Robustness of Forgiveness and Cooperation

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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.

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  • Pedro Dal Bó & 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
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    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. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
    3. 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.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    5. 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.
    6. repec:cup:apsrev:v:91:y:1997:i:02:p:290-307_20 is not listed on IDEAS
    7. 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.
    8. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    9. 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.
    10. 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.
    11. Kim, Yong-Gwan, 1994. "Evolutionarily stable strategies in the repeated prisoner's dilemma," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 167-197, December.
    12. 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.
    13. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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    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.

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