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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: https://econ-papers.upf.edu/papers/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 K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  2. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-94, July.
  3. Eddie Dekel & Drew Fudenberg & David K Levine, 2002. "Learning to Play Bayesian Games," Levine's Working Paper Archive 625018000000000151, David K. Levine.
  4. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic Uncoupled Dynamics and Nash Equilibrium," Working Papers 174, Barcelona Graduate School of Economics.
  5. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  6. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  7. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series dp372, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  9. 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.
  10. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series dp309, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Apr 2003.
  11. 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.
  12. 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.
  13. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  14. 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.
  15. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  16. 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.
  17. 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.
  18. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  19. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
  20. Drew Fudenberg & David K. Levine, 1996. "Consistency and Cautious Fictitious Play," Levine's Working Paper Archive 470, David K. Levine.
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