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On the global convergence of stochastic fictitious play. (English) Zbl 1141.91336
Summary: 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.

MSC:
91A26 Rationality and learning in game theory
60E15 Inequalities; stochastic orderings
91A15 Stochastic games, stochastic differential games
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