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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. Drew Fudenberg & David K. Levine, 1996. "Consistency and Cautious Fictitious Play," Levine's Working Paper Archive 470, David K. Levine.
  2. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  3. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  4. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  5. 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.
  6. Eddie Dekel & Drew Fudenberg & David K. Levine, 2001. "Learning to Play Bayesian Games," Harvard Institute of Economic Research Working Papers 1926, Harvard - Institute of Economic Research.
  7. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic Uncoupled Dynamics and Nash Equilibrium," Working Papers 174, Barcelona Graduate School of Economics.
  8. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  9. 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.
  10. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September.
  11. 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.
  12. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  13. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  14. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
  15. 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.
  16. Lawrence E. Blume & William R. Zame, 1993. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Game Theory and Information 9309001, EconWPA.
  17. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  18. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  19. 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.
  20. Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer, vol. 33(1), pages 21-40, January.
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