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Global Nash convergence of Foster and Young's regret testing

We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about the game. In fact, players' actions are based only on their own past payoffs and, in a variant of the strategy, players need not even know that their payoffs are determined through other players' actions. The procedure works for general finite games and is based on appropriate modifications of a simple stochastic learning rule introduced by Foster and Young.

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File URL: http://www.econ.upf.edu/docs/papers/downloads/788.pdf
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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 788.

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Date of creation: Oct 2004
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Handle: RePEc:upf:upfgen:788
Contact details of provider: Web page: http://www.econ.upf.edu/

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  1. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  2. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September.
  3. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series dp372, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  4. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, vol. 59(1), pages 187-208, April.
  5. Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001.
  6. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  7. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  8. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  9. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic uncoupled dynamics and Nash equilibrium," Economics Working Papers 783, Department of Economics and Business, Universitat Pompeu Fabra.
  10. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
  11. 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.
  12. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  13. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
  14. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
  15. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-36.
  16. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  17. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  18. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  19. Lawrence E. Blume & William R. Zame, 1993. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Game Theory and Information 9309001, EconWPA.
  20. Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 21-40, January.
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