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Learning in Perturbed Asymmetric Games

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Author Info
Josef Hofbauer
Ed Hopkins ()

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Abstract

We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is shown also for (rescaled) partnership games (also know as games of identical interest). Some applications of these result to stochastic learning models are given.

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Publisher Info
Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 53.

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Length: 16
Date of creation: Apr 2004
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Handle: RePEc:edn:esedps:53

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Related research
Keywords: Games; Learning; Best Response Dynamics; Stochastic Fictitious Play; Mixed Strategy Equilibria; Zero Sum Games;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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References listed on IDEAS
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    Other versions:
  3. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October. [Downloadable!] (restricted)
    Other versions:
  4. Duffy, John & Hopkins, Ed, 2005. "Learning, information, and sorting in market entry games: theory and evidence," Games and Economic Behavior, Elsevier, vol. 51(1), pages 31-62, April. [Downloadable!] (restricted)
    Other versions:
  5. repec:att:wimass:199325 is not listed on IDEAS
  6. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Blackwell Publishing, vol. 66(2), pages 363-93, April. [Downloadable!] (restricted)
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  11. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April. [Downloadable!] (restricted)
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  19. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October. [Downloadable!] (restricted)
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    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. repec:att:wimass:1920321 is not listed on IDEAS
  2. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics. [Downloadable!]
    Other versions:
  3. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics. [Downloadable!]
  4. Friederike Mengel, 2007. "Learning Across Games," Working Papers. Serie AD 2007-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  5. Kets, W., 2007. "The Minority Game: An Economics Perspective," Discussion Paper 2007-53, Tilburg University, Center for Economic Research. [Downloadable!]
  6. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Bibliography 506439000000000350, UCLA Department of Economics. [Downloadable!]
    Other versions:
  7. Willemien Kets, 2007. "The minority game: An economics perspective," Quantitative Finance Papers 0706.4432, arXiv.org. [Downloadable!]
  8. Josef Hofbauer & William H. Sandholm, 2001. "Evolution and Learning in Games with Randomly Disturbed Payoffs," Vienna Economics Papers 0205, University of Vienna, Department of Economics. [Downloadable!]
  9. repec:att:wimass:192035 is not listed on IDEAS
  10. Federico Echenique & Aaron Edlin, 2002. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Department of Economics, Working Paper Series 1037, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
  11. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning: The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research. [Downloadable!]
  12. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine. [Downloadable!]
  13. repec:att:wimass:1920320 is not listed on IDEAS
  14. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," CIRANO Working Papers 2006s-30, CIRANO. [Downloadable!]
    Other versions:
  15. Ed Hopkins, 2004. "Two Competing Models of How People Learn in Games," ESE Discussion Papers 51, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  16. repec:att:wimass:192015 is not listed on IDEAS
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