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Unbeatable Imitation

  • Duersch, Peter
  • Oechssler, Jörg
  • Schipper, Burkhard C.

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 and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent.

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Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0499.

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Date of creation: 30 Mar 2010
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Handle: RePEc:awi:wpaper:0499
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  1. 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.
  2. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  3. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  4. 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.
  5. 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.
  6. 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.
  7. Burkhard Schipper, 2002. "Imitators and Optimizers in Cournot Oligopoly," Bonn Econ Discussion Papers bgse29_2002, University of Bonn, Germany.
  8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  9. 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.
  10. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
  11. 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.
  12. Theo Offerman & Jan Potters & Joep Sonnemans, 1997. "Imitation and Belief Learning in an Oligopoly Experiment," Tinbergen Institute Discussion Papers 97-116/1, Tinbergen Institute.
  13. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  14. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 471-477, 08.
  15. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  16. Peter Duersch & Joerg Oechssler & Burkhard C. Schipper, 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 104, University of California, Davis, Department of Economics.
  17. Jose Apesteguia & Steffen Huck & Jörg Oechssler & Simon Weidenholzer, 2007. "Imitation and the Evolution of Walrasian Behavior: Theoretically Fragile but Behaviorally Robust," Working Papers 0461, University of Heidelberg, Department of Economics, revised Nov 2007.
  18. 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.
  19. AMIR, Rabah, 1994. "Cournot Oligopoly and the Theory of Supermodular Games," CORE Discussion Papers 1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  20. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-48, March.
  21. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
  22. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1997. "Learning in Cournot Oligopoly - An Experiment," Game Theory and Information 9707009, EconWPA, revised 22 Jul 1997.
  23. 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.
  24. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  25. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  26. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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