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When is Tit-For-Tat unbeatable?

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  • Peter Duersch
  • Joerg Oechssler
  • Burkhard Schipper

    (Department of Economics, University of California Davis)

Abstract

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of 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/13-1.pdf
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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 131.

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Length: 15
Date of creation: 22 Jan 2013
Date of revision:
Handle: RePEc:cda:wpaper:13-1

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Related research

Keywords: Imitation; tit-for-tat; decision rules; learning; exact potential games; symmetric games; repeated games; relative payoffs; zero-sum games;

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References

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  1. Peleg, Bezalel, 1998. "Almost all equilibria in dominant strategies are coalition - proof," Economics Letters, Elsevier, vol. 60(2), pages 157-162, August.
  2. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  3. 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.
  4. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  5. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-48, March.
  6. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
  7. Jose Apesteguia & Steffen Huck & Jörg Oechssler, 2005. "Imitation - Theory and Experimental Evidence -," Working Papers 0419, University of Heidelberg, Department of Economics, revised Apr 2005.
  8. Jose Apesteguia & Steffen Huck & Jörg Oechssler & Simon Weidenholzer, 2008. "Imitation and the Evolution of Walrasian Behavior: Theoretically Fragile but Behaviorally Robust," CESifo Working Paper Series 2224, CESifo Group Munich.
  9. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  10. Peter Duersch & Joerg Oechssler & Burkhard C. Schipper, 2011. "Unbeatable Imitation," Working Papers 103, University of California, Davis, Department of Economics.
  11. 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.
  12. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  13. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1997. "Learning in Cournot Oligopoly - An Experiment," Game Theory and Information 9707009, EconWPA, revised 22 Jul 1997.
  14. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  15. 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.
  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. 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.
  18. Erik J. Balder, 1996. "Remarks on Nash equilibria for games with additively coupled payoffs (*)," Economic Theory, Springer, vol. 9(1), pages 161-167.
  19. 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.
  20. 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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