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

  • Peter Duersch
  • Joerg Oechssler
  • Burkhard Schipper

    (Department of Economics, University of California Davis)

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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File URL: http://wp.econ.ucdavis.edu/11-12.pdf
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Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 1112.

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Length: 14
Date of creation: 09 Dec 2011
Date of revision:
Handle: RePEc:cda:wpaper:11-12
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  1. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
  2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  3. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
  4. Hehenkamp, Burkhard & Kaarbøe, Oddvar M., 2003. "Imitators and Optimizers in a Changing Environment," Working Papers in Economics 03/03, University of Bergen, Department of Economics.
  5. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2012. "Unbeatable Imitation," Working Papers 125, University of California, Davis, Department of Economics.
  6. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 471-477, 08.
  7. 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.
  8. 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.
  9. José Apesteguía & Steffen Huck & Jorg Oechssler, 2003. "Imitation-Theory and Experimental Evidence-," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0306, Departamento de Economía - Universidad Pública de Navarra.
  10. Josephson, Jens, 2001. "A Numerical Analysis of the Evolutionary Stability of Learning Rules," SSE/EFI Working Paper Series in Economics and Finance 474, Stockholm School of Economics.
  11. 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.
  12. Brânzei, R. & Mallozzi, L. & Tijs, S.H., 2003. "Supermodular games and potential games," Other publications TiSEM 87c16860-0596-4448-808d-c, Tilburg University, School of Economics and Management.
  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. 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. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
  16. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
  17. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 407-430, June.
  18. Offerman, T.J.S. & Potters, J.J.M. & Sonnemans, J., 2002. "Imitation and belief learning in an oligopoly experiment," Other publications TiSEM a6a771c5-31ba-4193-8f76-a, Tilburg University, School of Economics and Management.
  19. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
  20. 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.
  21. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  22. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  23. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1997. "Learning in Cournot Oligopoly - An Experiment," Game Theory and Information 9707009, EconWPA, revised 22 Jul 1997.
  24. 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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