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Unbeatable imitation

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  • 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. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1997. "Learning in Cournot Oligopoly - An Experiment," Game Theory and Information 9707009, EconWPA, revised 22 Jul 1997.
  2. 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.
  3. 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.
  4. 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.
  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. 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.
  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. Burkhard Schipper, 2002. "Submodularity and the Evolution of Walrasian Behavior," Bonn Econ Discussion Papers bgse4_2003, University of Bonn, Germany.
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  10. Offerman, T.J.S. & Potters, J.J.M. & Sonnemans, J., 2002. "Imitation and belief learning in an oligopoly experiment," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91663, Tilburg University.
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  13. 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.
  14. 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.
  15. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  16. 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.
  17. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  18. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  19. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  20. 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.
  21. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  22. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  23. 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).
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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. Constanza Fosco & Friederike Mengel, 2009. "Cooperation through Imitation and Exclusion in Networks," Working Papers 2009.37, Fondazione Eni Enrico Mattei.
  2. 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.
  3. 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.
  4. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
  5. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2014. "When is tit-for-tat unbeatable?," International Journal of Game Theory, Springer, vol. 43(1), pages 25-36, February.
  6. 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.
  7. Burkhard Schipper, 2011. "Strategic Control of Myopic Best Reply in Repeated Games," Working Papers 115, University of California, Davis, Department of Economics.

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