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Tit-for-Tat or Win-Stay, Lose-Shift?

Author

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  • Imhof, Lorens
  • Nowak, Martin
  • Fudenberg, Drew

Abstract

The repeated Prisoner's Dilemma is usually known as a story of tit-for-tat (TFT). This remarkable strategy has won both of Robert Axelrod's tournaments. TFT does whatever the opponent has done in the previous round. It will cooperate if the opponent has cooperated, and it will defect if the opponent has defected. But TFT has two weaknesses: (i) it cannot correct mistakes (erroneous moves) and (ii) a population of TFT players is undermined by random drift when mutant strategies appear which play always-cooperate (ALLC). Another equally simple strategy called ‘win-stay, lose-shift’ (WSLS) has neither of these two disadvantages. WSLS repeats the previous move if the resulting payoff has met its aspiration level and changes otherwise. Here, we use a novel approach of stochastic evolutionary game dynamics in finite populations to study mutation–selection dynamics in the presence of erroneous moves. We compare four strategies: always-defect (ALLD), ALLC, TFT and WSLS. There are two possible outcomes: if the benefit of cooperation is below a critical value then ALLD is selected; if the benefit of cooperation is above this critical value then WSLS is selected. TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS.

Suggested Citation

  • Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:3200671
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    File URL: http://dash.harvard.edu/bitstream/handle/1/3200671/fudenberg_titfortat.pdf
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    References listed on IDEAS

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    1. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
    2. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, January.
    3. 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.
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    Cited by:

    1. repec:eee:apmaco:v:277:y:2016:i:c:p:44-53 is not listed on IDEAS
    2. repec:eee:phsmap:v:494:y:2018:i:c:p:236-241 is not listed on IDEAS
    3. Ochea, M., 2012. "Evolution of Repeated Prisoner's Dilemma Play under Logit Dynamics," CeNDEF Working Papers 12-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    4. Duffy, Sean & Naddeo, JJ & Owens, David & Smith, John, 2016. "Cognitive load and mixed strategies: On brains and minimax," MPRA Paper 71878, University Library of Munich, Germany.
    5. Nicklisch, Andreas & Köke, Sonja & Lange, Andreas, 2016. "Is Adversity a School of Wisdom? Experimental Evidence on Cooperative Protection Against Stochastic Losses," Annual Conference 2016 (Augsburg): Demographic Change 145716, Verein für Socialpolitik / German Economic Association.
    6. repec:eee:phsmap:v:490:y:2018:i:c:p:419-425 is not listed on IDEAS
    7. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    8. Ochea, Marius-Ionut, 2013. "Evolution of repeated prisoner's dilemma play under logit dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2483-2499.
    9. Wang, Xu-Wen & Nie, Sen & Jiang, Luo-Luo & Wang, Bing-Hong & Chen, Shi-Ming, 2017. "Role of delay-based reward in the spatial cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 153-158.
    10. repec:eee:gamebe:v:107:y:2018:i:c:p:203-219 is not listed on IDEAS
    11. 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.
    12. Mike Farjam & Wladislaw Mill & Marian Panganiban, 2016. "Ignorance Is Bliss, But for Whom? The Persistent Effect of Good Will on Cooperation," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-19, October.
    13. Pedro Dal Bó & Enrique R. Pujals, 2013. "The Evolutionary Robustness of Forgiveness and Cooperation," Working Papers 2013-5, Brown University, Department of Economics.
    14. repec:eee:apmaco:v:282:y:2016:i:c:p:117-127 is not listed on IDEAS
    15. Wang, Tao & Chen, Zhigang & Li, Kenli & Deng, Xiaoheng & Li, Deng, 2014. "Memory does not necessarily promote cooperation in dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 218-227.
    16. Dal Bó, Pedro & Fréchette, Guillaume R., 2013. "Strategy choice in the infinitely repeated prisoners' dilemma," Discussion Papers, Research Unit: Economics of Change SP II 2013-311, Social Science Research Center Berlin (WZB).

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