Stochastic Approximation, Momentum, and Nash Play

Helge Berglann () and Sjur Flåm
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Helge Berglann: University of Bergen, Department of Economics, Postal: Hermann Fossgt. 6, N-5007 Bergen, Norway

No 09/02, Working Papers in Economics from University of Bergen, Department of Economics

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.

Keywords: Noncooperative games; Nash equilibrium; stochastic programming and approximation; the heavy ball method. (search for similar items in EconPapers)
JEL-codes: C02 C61 C71 (search for similar items in EconPapers)
Pages: 9 pages
Date: 2002-04-03
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