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Unbeatable Imitation

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  • Duersch, Peter
  • Oechssler, Joerg
  • Schipper, Burkhard C

Abstract

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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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 20856.

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Date of creation: 18 Feb 2010
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Handle: RePEc:pra:mprapa:20856

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Keywords: Imitate-the-best; learning; symmetric games; relative payoffs; zero-sum games; rock-paper-scissors; finite population ESS; potential games; quasisubmodular games; quasisupermodular games; quasiconcave games; aggregative games;

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  1. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 12(1), pages 29-45, August.
  2. Burkhard Schipper, 2002. "Submodularity and the Evolution of Walrasian Behavior," Bonn Econ Discussion Papers, University of Bonn, Germany bgse4_2003, University of Bonn, Germany.
  3. Apesteguia, Jose & Huck, Steffen & Oechssler, Joerg, 2003. "Imitation - Theory and Experimental Evidence," University of California at Santa Barbara, Economics Working Paper Series qt3h0887tj, Department of Economics, UC Santa Barbara.
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  5. Schipper, Burkhard C., 2005. "Imitators and Optimizers in Cournot Oligopoly," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University 53, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  6. 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.
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  8. Apesteguia, Jose & Huck, Steffen & Oechssler, Jörg & Weidenholzer, Simon, 2007. "Imitation and the Evolution of Walrasian Behavior: Theoretically Fragile but Behaviorally Robust," Sonderforschungsbereich 504 Publications, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim 07-69, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  9. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer, Springer, vol. 43(3), pages 407-430, June.
  10. Burkhard Hehenkamp & Wolfgang Leininger & Alex Possajennikov, 2003. "Evolutionary Equilibrium in Tullock Contests: Spite and Overdissipation," Discussion Papers in Economics, University of Dortmund, Department of Economics 03_01, University of Dortmund, Department of Economics.
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  12. Offerman, Theo & Potters, Jan & Sonnemans, Joep, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 69(4), pages 973-97, October.
  13. 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, American Economic Association, vol. 80(1), pages 234-48, March.
  14. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, Econometric Society, vol. 65(2), pages 375-384, March.
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  16. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  17. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers, University of Heidelberg, Department of Economics 0500, University of Heidelberg, Department of Economics.
  18. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, Springer, vol. 41(3), pages 553-564, August.
  19. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, Elsevier, vol. 39(1), pages 71-90, April.
  20. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
  21. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, Elsevier, vol. 78(1), pages 130-156, January.
  22. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, Econometric Society, vol. 62(1), pages 157-80, January.
  23. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1255-77, November.
  24. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers, University of Heidelberg, Department of Economics 0529, University of Heidelberg, Department of Economics.
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Citations

Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. “Unbeatable Imitation,” P. Duersch, J. Oechssler & B. C. Schipper (2012)
    by afinetheorem in A Fine Theorem on 2012-09-25 08:38:20
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Cited by:
  1. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," MPRA Paper 20864, University Library of Munich, Germany.
  2. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2013. "When is Tit-For-Tat unbeatable?," Working Papers, University of California, Davis, Department of Economics 131, University of California, Davis, Department of Economics.
  3. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, Springer, vol. 41(3), pages 553-564, August.
  4. Constanza Fosco & Friederike Mengel, 2009. "Cooperation through Imitation and Exclusion in Networks," Working Papers, Fondazione Eni Enrico Mattei 2009.37, Fondazione Eni Enrico Mattei.
  5. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers, University of Heidelberg, Department of Economics 0529, University of Heidelberg, Department of Economics.
  6. Schipper, Burkhard C, 2011. "Strategic control of myopic best reply in repeated games," MPRA Paper 30219, University Library of Munich, Germany.
  7. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.

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