On the Global Convergence of Stochastic Fictitious Play

Josef Hofbauer () and William H. Sandholm ()
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Josef Hofbauer: Universitat Wien, Austria
William H. Sandholm: University of Wisconsin

Econometrica, 2002, vol. 70, issue 6, 2265-2294

Abstract: We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities. Copyright The Econometric Society 2002.

Date: 2002
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