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Stochastic Approximations and Differential Inclusions; Part II: Applications

Author

Listed:
  • Michel Benaïm

    () (Université de Neuchâtel)

  • Josef Hofbauer

    (UCL - University College of London [London])

  • Sylvain Sorin

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

We apply the theoretical results on ``stochastic approximations and differential inclusions'' developed in Benaïm Hofbauer and Sorin (2003) to several adaptive processes used in game theory including: classical and generalized approachability, no-regrets procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine)

Suggested Citation

  • Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
  • Handle: RePEc:hal:wpaper:hal-00242974
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00242974
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    File URL: https://hal.archives-ouvertes.fr/hal-00242974/document
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    References listed on IDEAS

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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
    3. 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.
    4. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    5. 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.
    6. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    7. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    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. Michel Benaïm & Gerard Ben Arous, 2003. "A two armed bandit type problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 3-16, December.
    10. 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.
    11. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    12. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
    13. 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.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
    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. Viossat, Yannick & Zapechelnyuk, Andriy, 2013. "No-regret dynamics and fictitious play," Journal of Economic Theory, Elsevier, vol. 148(2), pages 825-842.
    5. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    6. Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.
    7. 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.
    8. repec:eee:gamebe:v:103:y:2017:i:c:p:41-66 is not listed on IDEAS
    9. repec:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0198-y is not listed on IDEAS
    10. repec:spr:eurjdp:v:5:y:2017:i:1:d:10.1007_s40070-017-0068-x is not listed on IDEAS
    11. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    12. 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.
    13. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
    14. repec:hal:wpaper:hal-00713871 is not listed on IDEAS
    15. 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.
    16. repec:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0978-y is not listed on IDEAS
    17. Michel Benaim & Olivier Raimond, 2007. "Simulated Annealing, Vertex-Reinforced Random Walks and Learning in Games," Levine's Bibliography 122247000000001702, UCLA Department of Economics.
    18. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.

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