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The Evolutionary Robustness of Forgiveness and Cooperation

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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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File URL: http://www.brown.edu/Departments/Economics/Papers/2013/2013-5_paper.pdf
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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2013-5.

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Date of creation: 2013
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Handle: RePEc:bro:econwp:2013-5

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Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-79, May.
  2. Philip Johnson & David K. Levine & Wolfgang Pesendorfer, 2000. "Evolution and Information in a Gift Giving Game," Levine's Working Paper Archive 162, David K. Levine.
  3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
  4. 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.
  5. Kim, Yong-Gwan, 1994. "Evolutionarily stable strategies in the repeated prisoner's dilemma," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 167-197, December.
  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. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  8. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
  9. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
  10. 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.
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