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Fictitious play in zero-sum stochastic games · Around

2020

Fictitious play in zero-sum stochastic games

Sayin, Muhammed O., Parise, Francesca, Ozdaglar, Asuman

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We present a novel variant of fictitious play dynamics combining classical fictitious play with Q-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games.

Our dynamics involves players forming beliefs on the opponent strategy and their own continuation payoff (Q-function), and playing a greedy best response by using the estimated continuation payoffs.
Players update their beliefs from observations of opponent actions.
A key property of the learning dynamics is that update of the beliefs on Q-functions occurs at a slower timescale than update of the beliefs on strategies.

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