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Once Beaten, Never Again: Imitation in Two-Player Potential Games

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

Abstract

We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

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Bibliographic Info

Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0529.

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Date of creation: 21 Jun 2012
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Handle: RePEc:awi:wpaper:0529

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Keywords: Imitate-the-best; learning; exact potential games; symmetric games; relative payoffs; zero-sum games;

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References

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  1. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Unbeatable Imitation," Working Papers, University of Heidelberg, Department of Economics 0499, University of Heidelberg, Department of Economics.
  2. Burkhard Hehenkamp & Oddvar Kaarbøe, 2004. "Imitators and Optimizers in a Changing Environment," Discussion Papers in Economics, University of Dortmund, Department of Economics 02_01, University of Dortmund, Department of Economics.
  3. 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.
  4. 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.
  5. Brânzei, R. & Mallozzi, L. & Tijs, S.H., 2003. "Supermodular games and potential games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121822, Tilburg University.
  6. 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.
  7. 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.
  8. Josephson, Jens, 2001. "A Numerical Analysis of the Evolutionary Stability of Learning Rules," Working Paper Series in Economics and Finance 474, Stockholm School of Economics.
  9. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, Elsevier, vol. 40(2), pages 232-269, August.
  10. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(8), pages 1543-1554, August.
  11. 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.
  12. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  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, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim 07-69, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  14. 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.
  15. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1997. "Learning in Cournot Oligopoly - An Experiment," Game Theory and Information, EconWPA 9707009, EconWPA, revised 22 Jul 1997.
  16. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B, University of Bonn, Germany 296, University of Bonn, Germany.
  17. Schipper, Burkhard C., 2005. "Imitators and Optimizers in Cournot Oligopoly," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 53, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  18. 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.
  19. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, Springer, vol. 26(3), pages 497-516, October.
  20. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers, ESRC Centre on Economics Learning and Social Evolution 028, ESRC Centre on Economics Learning and Social Evolution.
  21. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer, Springer, vol. 32(4), pages 471-477, 08.
  22. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
  23. Branzei, Rodica & Mallozzi, Lina & Tijs, Stef, 2003. "Supermodular games and potential games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 39-49, February.
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Cited by:
  1. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2012. "Unbeatable Imitation," Working Papers, University of California, Davis, Department of Economics 125, University of California, Davis, Department of Economics.

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