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Unbeatable Imitation

  • Peter Duersch
  • Joerg Oechssler
  • Burkhard C. Schipper

    (Department of Economics, University of California Davis)

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that, even against a very clever opponent, 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. For many interesting classes of games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games, we obtain an even stronger notion of the unbeatability of imitation.

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Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 103.

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Length: 31
Date of creation: 16 Mar 2011
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Handle: RePEc:cda:wpaper:10-3
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  1. Theo Offerman & Jan Potters & Joep Sonnemans, 1997. "Imitation and Belief Learning in an Oligopoly Experiment," Tinbergen Institute Discussion Papers 97-116/1, Tinbergen Institute.
  2. Apestgeguia, Jose & Huck, Steffen & Oechssler, Jörg, 2005. "Imitation - Theory and Experimental Evidence," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 54, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  3. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  4. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  5. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  6. Apesteguia, Jose & Huck, Steffen & Oechssler, Jörg & Weidenholzer, Simon, 2007. "Imitation and the Evolution of Walrasian Behavior: Theoretically Fragile but Behaviorally Robust," Sonderforschungsbereich 504 Publications 07-69, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  7. 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.
  8. Ana B. Ania, 2005. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Vienna Economics Papers 0601, University of Vienna, Department of Economics.
  9. 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.
  10. 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.
  11. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  12. John B Van Huyck & Raymond C Battalio & Richard O Beil, 1997. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 1225, David K. Levine.
  13. Schipper, Burkhard C., 2005. "Imitators and Optimizers in Cournot Oligopoly," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 53, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  14. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
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  16. Walker, James M. & Gardner, Roy & Ostrom, Elinor, 1990. "Rent dissipation in a limited-access common-pool resource: Experimental evidence," Journal of Environmental Economics and Management, Elsevier, vol. 19(3), pages 203-211, November.
  17. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  18. Burkhard Hehenkamp & Wolfgang Leininger & Alex Possajennikov, 2003. "Evolutionary Equilibrium in Tullock Contests: Spite and Overdissipation," Discussion Papers in Economics 03_01, University of Dortmund, Department of Economics.
  19. Burkhard Schipper, 2002. "Submodularity and the Evolution of Walrasian Behavior," Bonn Econ Discussion Papers bgse4_2003, University of Bonn, Germany.
  20. 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.
  21. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  22. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages C80-95, March.
  23. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
  24. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  25. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  26. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
  27. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
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