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Stochastic Approximations and Differential Inclusions; Part II: Applications

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Author Info

  • Michel Benaïm

    ()
    (Université de Neûchatel)

  • Josef Hofbauer

    (University College of London)

  • Sylvain Sorin

    (CECO - Laboratoire d'econometrie de l'école polytechnique - CNRS : UMR7657 - Polytechnique - X)

Abstract

Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures adapatatives utilisées en théorie des jeux en particulier: approchabilité classique et généralisées, procédures de non regret (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine)

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00242974.

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Date of creation: 2005
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Handle: RePEc:hal:wpaper:hal-00242974

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References

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  1. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
  2. 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.
  3. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  4. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  6. Nimrod Megiddo, 1979. "On Repeated Games with Incomplete Information Played by Non-Bayesian Players," Discussion Papers 373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  8. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
  9. 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.
  10. Michel Benaïm & Gerard Ben Arous, 2003. "A two armed bandit type problem," International Journal of Game Theory, Springer, vol. 32(1), pages 3-16, December.
  11. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series dp309, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Apr 2003.
  12. 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.
  13. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  14. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
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Citations

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Cited by:
  1. Cason, Timothy N. & Friedman, Daniel UC & Hopkins, Ed, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," SIRE Discussion Papers 2009-15, Scottish Institute for Research in Economics (SIRE).
  2. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
  3. Cominetti, Roberto & Melo, Emerson & Sorin, Sylvain, 2010. "A payoff-based learning procedure and its application to traffic games," Games and Economic Behavior, Elsevier, vol. 70(1), pages 71-83, September.
  4. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics.
  5. Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.
  6. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  7. 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.
  8. van Strien, Sebastian & Sparrow, Colin, 2011. "Fictitious play in 3x3 games: Chaos and dithering behaviour," Games and Economic Behavior, Elsevier, vol. 73(1), pages 262-286, September.
  9. Michel Benaim & Olivier Raimond, 2007. "Simulated Annealing, Vertex-Reinforced Random Walks and Learning in Games," Levine's Bibliography 122247000000001702, UCLA Department of Economics.
  10. Yannick Viossat & Andriy Zapechelnyuk, 2013. "No-regret Dynamics and Fictitious Play," Post-Print hal-00713871, HAL.
  11. repec:hal:wpaper:hal-00713871 is not listed on IDEAS
  12. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
  13. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.

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