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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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References

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  1. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  2. 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.
  3. Offerman, Theo & Potters, Jan & Sonnemans, Joep, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Wiley Blackwell, vol. 69(4), pages 973-97, October.
  4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  5. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  6. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  7. 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.
  8. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, vol. 41(3), pages 553-564, August.
  9. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  10. 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).
  11. Hehenkamp, B. & Leininger, W. & Possajennikov, A., 2004. "Evolutionary equilibrium in Tullock contests: spite and overdissipation," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1045-1057, November.
  12. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  13. 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.
  14. 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.
  15. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 0529, University of Heidelberg, Department of Economics.
  16. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  17. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  18. 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.
  19. Burkhard C. Schipper, 2005. "Imitators and Optimizers in Cournot oligopoly," Working Papers 537, University of California, Davis, Department of Economics.
  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. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer, vol. 32(4), pages 471-477, 08.
  22. 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.
  23. 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.
  24. 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.
  25. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer, vol. 43(3), pages 407-430, June.
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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. Constanza Fosco & Friederike Mengel, 2009. "Cooperation through Imitation and Exclusion in Networks," Working Papers 2009.37, Fondazione Eni Enrico Mattei.
  3. Burkhard Schipper, 2011. "Strategic Control of Myopic Best Reply in Repeated Games," Working Papers 115, University of California, Davis, Department of Economics.
  4. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 0529, University of Heidelberg, Department of Economics.
  5. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2013. "When is Tit-For-Tat unbeatable?," Working Papers 131, University of California, Davis, Department of Economics.
  6. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
  7. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, vol. 41(3), pages 553-564, August.

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