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

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  1. 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.
  2. Jose Alpesteguia & Steffen Huck & Jörg Oechssler, 2003. "Imitation - Theory and Experimental Evidence," CESifo Working Paper Series 1049, CESifo Group Munich.
  3. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2012. "Unbeatable Imitation," Working Papers 125, University of California, Davis, Department of Economics.
  4. 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.
  5. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  6. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Burkhard Schipper, 2002. "Imitators and Optimizers in Cournot Oligopoly," Bonn Econ Discussion Papers bgse29_2002, University of Bonn, Germany.
  8. 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.
  9. 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.
  10. 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.
  11. Peleg, Bezalel, 1998. "Almost all equilibria in dominant strategies are coalition - proof," Economics Letters, Elsevier, vol. 60(2), pages 157-162, August.
  12. 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.
  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. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  15. 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.
  16. 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.
  17. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  18. 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.
  19. 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.
  20. Erik J. Balder, 1996. "Remarks on Nash equilibria for games with additively coupled payoffs (*)," Economic Theory, Springer, vol. 9(1), pages 161-167.
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