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Stochastic approximation, Momentum, and Nash play

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Author Info
Berglann, Helge ()
Flåm, Sjur () (Department of Economics, University of Bergen.)

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Abstract

Main objects here are normal-form games, featuring uncertainty and noncooperative players who entertain local visions, form local approximations, and hesitate in making large, swift adjustments. For the purpose of reaching Nash equilibrium, or learning such play, we advocate and illustrate an algorithm that combines stochastic gradient projection with the heavyball method. What emerges is a coupled, constrained, second-order stochastic process. Some friction feeds into and stabilizes myopic approximations. Convergence to Nash play obtains under seemingly weak and natural conditions, an important one being that accumulated marginal payoffs remains bounded above.

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Publisher Info
Paper provided by Department of Economics, University of Bergen in its series Working paper Series with number 0209.

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Length: 9 pages
Date of creation: 03 Apr 2002
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Handle: RePEc:uib:bereco:0209

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Related research
Keywords: Noncooperative games; Nash equilibrium; stochastic programming and approximation; the heavy ball method.;

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Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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References listed on IDEAS
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. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
  2. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December. [Downloadable!] (restricted)
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  3. Flam, S.D., 1999. "Learning Equilibrium Play: a Myopic Approach," Norway; Department of Economics, University of Bergen 189, Department of Economics, University of Bergen.
  4. Flam, Sjur Didrik, 1996. "Approaches to economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1505-1522. [Downloadable!] (restricted)
  5. Flam, S.D., 2001. "Approaching Equilibrium in Parallel," Norway; Department of Economics, University of Bergen 0601, Department of Economics, University of Bergen.
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