LEARNING DYNAMICS IN GAMES WITH STOCHASTIC PERTURBATIONS

Consider a generalization of fictitious play in which agents' choices are perturbed by incomplete information about what the other side has done, variability in their payoffs, and unexplained trembles. These pe rturbed best reply dynamics define a nonstationary Markov process on a n infinite state space. It is shown, using results from stochastic app roximation theory, that for 2 X 2 games it converges almost surely to a point that lies close to a stable Nash equilibrium, whether pure or mixed. This generalizes a result of Fudenberg and Kreps, who demonstra te convergence when the game has a unique mixed equilibrium. (C) 1995 Academic Press, Inc.