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On the Global Convergence of Stochastic Fictitious Play

Author

Listed:
  • Josef Hofbauer

    () (Universitat Wien, Austria)

  • William H. Sandholm

    () (University of Wisconsin)

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.

Suggested Citation

  • Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:6:p:2265-2294
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