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Unbeatable Imitation

Author

Listed:
  • Peter Duersch
  • Joerg Oechssler
  • Burkhard Schipper

    (Department of Economics, University of California Davis)

Abstract

We show that for many classes of symmetric two-player games, the simple decision rule ``imitate-if-better'' can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a money pump. In particular, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rock-scissors-paper variety. We also show that a sufficient condition for imitation not being subject to a money pump is that the relative payoff game is a generalized ordinal potential game or a quasiconcave game. Our results apply to many interesting examples of symmetric games including 2 x 2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

Suggested Citation

  • Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2012. "Unbeatable Imitation," Working Papers 125, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:12-5
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    References listed on IDEAS

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    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, vol. 145(5), pages 1603-1617, September.
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    Cited by:

    1. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    2. Buckert, Magdalena & Oechssler, Jörg & Schwieren, Christiane, 2017. "Imitation under stress," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 252-266.
    3. Tsakas, Nikolas, 2017. "Diffusion by imitation: The importance of targeting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 118-151.
    4. Fosco, Constanza & Mengel, Friederike, 2011. "Cooperation through imitation and exclusion in networks," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 641-658, May.
    5. repec:zbw:rwirep:0497 is not listed on IDEAS
    6. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
    7. García-Martínez, José A. & Vega-Redondo, Fernando, 2015. "Social cohesion and the evolution of altruism," Games and Economic Behavior, Elsevier, vol. 92(C), pages 74-105.
    8. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    9. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    10. Wood, Aaron D. & Mason, Charles F. & Finnoff, David, 2016. "OPEC, the Seven Sisters, and oil market dominance: An evolutionary game theory and agent-based modeling approach," Journal of Economic Behavior & Organization, Elsevier, vol. 132(PB), pages 66-78.
    11. Christian Ewerhart, 2017. "Ordinal potentials in smooth games," ECON - Working Papers 265, Department of Economics - University of Zurich.
    12. Tsakas, Nikolas, 2015. "Beatable imitation in symmetric games with perturbed payoffs," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 34-40.
    13. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2014. "Imitation and the role of information in overcoming coordination failures," Games and Economic Behavior, Elsevier, vol. 87(C), pages 397-411.
    14. 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.
    15. Leininger, Wolfgang & Moghadam, Hamed M., 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 497, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    16. Schipper, Burkhard C, 2011. "Strategic control of myopic best reply in repeated games," MPRA Paper 30219, University Library of Munich, Germany.
    17. Hilbe, Christian & Traulsen, Arne & Sigmund, Karl, 2015. "Partners or rivals? Strategies for the iterated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 92(C), pages 41-52.
    18. Takuya Iimura & Takahiro Watanabe, 2016. "Pure strategy equilibrium in finite weakly unilaterally competitive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 719-729, August.
    19. Accinelli, Elvio & Covarrubias, Enrique, 2015. "Evolution in a Walrasian setting," MPRA Paper 64736, University Library of Munich, Germany.
    20. David M. Newbery & Thomas P. Greve, 2015. "The robustness of industrial commodity oligopoly pricing strategies," Cambridge Working Papers in Economics 1540, Faculty of Economics, University of Cambridge.
    21. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2011. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 1112, University of California, Davis, Department of Economics.
    22. Wolfgang Leininger & Hamed Moghadam, 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 0497, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.

    More about this item

    Keywords

    Imitate-the-best; learning; symmetric games; relative payoffs; zero-sum games; rock-paper-scissors; finite population ESS; generalized ordinal potential games; quasiconcave 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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