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Unbeatable imitation

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Author Info

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

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 2×2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 76 (2012)
Issue (Month): 1 ()
Pages: 88-96

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Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:88-96

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Imitate-the-best; Learning; Symmetric games; Relative payoffs; Zero-sum games; Rock–paper–scissors; Finite population ESS; Generalized ordinal potential games; Quasiconcave games;

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References

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  1. 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.
  2. Burkhard C. Schipper, 2005. "Imitators and Optimizers in Cournot oligopoly," Working Papers 537, University of California, Davis, Department of Economics.
  3. Jose Apesteguia & Steffen Huck & Jorg Oechssler, 2003. "Imitation - Theory and Experimental Evidence," Experimental 0309001, EconWPA.
  4. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," MPRA Paper 20864, University Library of Munich, Germany.
  5. J. B. Van Huyck & R. C. Battalio & R. O. Beil, 2010. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 661465000000000393, David K. Levine.
  6. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 973-997.
  7. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer, vol. 32(4), pages 471-477, 08.
  8. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  9. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  10. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2010. "Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games," Working Papers 1021, University of California, Davis, Department of Economics.
  11. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  12. 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.
  13. 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.
  14. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
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  16. 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.
  17. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  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. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  20. 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.
  21. 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.
  22. 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.
  23. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  24. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  25. 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.
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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
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:
  1. Mengel, Friederike & Fosco, Constanza, 2007. "Cooperation through Imitation and Exclusion in Networks," MPRA Paper 5258, University Library of Munich, Germany.
  2. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2013. "When is Tit-For-Tat unbeatable?," Working Papers 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, vol. 41(3), pages 553-564, August.
  4. Burkhard Schipper, 2011. "Strategic Control of Myopic Best Reply in Repeated Games," Working Papers 115, University of California, Davis, Department of Economics.
  5. 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.
  6. 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.
  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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