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Limit Behavior of No-regret Dynamics

  • Andriy Zapechelnyuk

    ()

    (University of Bonn and Kyiv School of Economics)

Consider a repeated game where all players follow no-regret strategies by reinforcing the actions that they regret not having played enough in the past. We show that a resulting no-regret dynamic approaches in the long run a best-response dynamic and leads to its invariant sets: rest points (Nash equilibria) or periodic orbits. The convergence results for best-response dynamics known in the literature immediately apply to no-regret dynamics. Thus, every no-regret dynamic leads to Nash equilibrium in zero-sum games, weighted potential and two-player ordinal potential games, supermodular games with diminishing returns, and some other special classes.

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File URL: http://repec.kse.org.ua/pdf/KSE_dp21.pdf
File Function: First version, October 2009
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Paper provided by Kyiv School of Economics in its series Discussion Papers with number 21.

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Date of creation: Oct 2009
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Handle: RePEc:kse:dpaper:21
Note: Under review in Journal of Economic Theory
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  1. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  2. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  3. Basu, K. & Weibull, J., 1990. "Strategy Subsets Closed Under Rational Behavior," Papers 62, Princeton, Woodrow Wilson School - Discussion Paper.
  4. Sparrow, Colin & van Strien, Sebastian & Harris, Christopher, 2008. "Fictitious play in 3x3 games: The transition between periodic and chaotic behaviour," Games and Economic Behavior, Elsevier, vol. 63(1), pages 259-291, May.
  5. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
  6. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  7. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
  8. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  9. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
  10. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
  11. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
  12. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  13. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  14. Harris, Christopher, 1998. "On the Rate of Convergence of Continuous-Time Fictitious Play," Games and Economic Behavior, Elsevier, vol. 22(2), pages 238-259, February.
  15. Ed Hopkins, 2000. "Two Competing Models of How People Learn in Games," ESE Discussion Papers 51, Edinburgh School of Economics, University of Edinburgh.
  16. Ed Hopkins, 1997. "A Note on Best Response Dynamics," ESE Discussion Papers 3, Edinburgh School of Economics, University of Edinburgh.
  17. Sela, Aner, 2000. "Fictitious Play in 2 x 3 Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 152-162, April.
  18. Lawrence Blume, 1996. "Population Games," Game Theory and Information 9607001, EconWPA.
  19. Ehud Lehrer & Dinah Rosenberg, 2003. "A Wide Range No-Regret Theorem," Game Theory and Information 0312004, EconWPA.
  20. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
  21. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  22. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  23. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  24. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  25. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  26. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
  27. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
  28. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
  29. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
  30. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
  31. Matros, Alexander, 2000. "Clever agents in adaptive learning," SSE/EFI Working Paper Series in Economics and Finance 403, Stockholm School of Economics.
  32. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
  33. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
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