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When is Tit-For-Tat unbeatable?

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  • Peter Duersch
  • Joerg Oechssler
  • Burkhard Schipper

    (Department of Economics, University of California Davis)

Abstract

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

Suggested Citation

  • Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2013. "When is Tit-For-Tat unbeatable?," Working Papers 131, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:13-1
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    File URL: http://wp.econ.ucdavis.edu/13-1.pdf
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    References listed on IDEAS

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    1. Apesteguia, Jose & Huck, Steffen & Oechssler, Jorg, 2007. "Imitation--theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 136(1), pages 217-235, September.
    2. Apesteguia, Jose & Huck, Steffen & Oechssler, Jörg & Weidenholzer, Simon, 2010. "Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust," Journal of Economic Theory, Elsevier, pages 1603-1617.
    3. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    5. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 407-430, June.
    6. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
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    Cited by:

    1. repec:elg:eechap:15532_7 is not listed on IDEAS
    2. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    3. Andreas Ortmann & Leonidas Spiliopoulos, 2017. "The beauty of simplicity? (Simple) heuristics and the opportunities yet to be realized," Chapters,in: Handbook of Behavioural Economics and Smart Decision-Making, chapter 7, pages 119-136 Edward Elgar Publishing.

    More about this item

    Keywords

    Imitation; tit-for-tat; decision rules; learning; exact potential games; symmetric games; repeated games; relative payoffs; zero-sum games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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