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When is tit-for-tat unbeatable?

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  • Peter Duersch
  • Jörg Oechssler
  • Burkhard Schipper

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 2 $$\times $$ 2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2014. "When is tit-for-tat unbeatable?," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 25-36, February.
  • Handle: RePEc:spr:jogath:v:43:y:2014:i:1:p:25-36
    DOI: 10.1007/s00182-013-0370-1
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    4. Ding, Hong & Zhang, Geng-shun & Wang, Shi-hao & Li, Juan & Wang, Zhen, 2019. "Q-learning boosts the evolution of cooperation in structured population by involving extortion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    5. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    6. Burkhard C. Schipper, 2019. "Dynamic Exploitation of Myopic Best Response," Dynamic Games and Applications, Springer, vol. 9(4), pages 1143-1167, December.

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    More about this item

    Keywords

    Imitation; Tit-for-tat; Decision rules; Learning; Exact potential games; Symmetric games; Repeated games; Relative payoffs; Zero-sum games; C72; C73; D43;
    All these keywords.

    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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