TY - GEN

T1 - Mean field stochastic games

T2 - Convergence, Q/H-learning and optimality

AU - Tembine, Hamidou

PY - 2011

Y1 - 2011

N2 - We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting players when the total number of possible players grow without bound. We provide sufficient conditions for mean field convergence. We characterize the mean field payoff optimality by solutions of a coupled system of backward-forward equations. The limiting games are equivalent to discrete time anonymous sequential population games or to differential population games. Using multidimensional diffusion processes, a general mean field convergence to coupled stochastic differential equation is given. Finally, the computation of mean field equilibria is addressed using Q/H learning.

AB - We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting players when the total number of possible players grow without bound. We provide sufficient conditions for mean field convergence. We characterize the mean field payoff optimality by solutions of a coupled system of backward-forward equations. The limiting games are equivalent to discrete time anonymous sequential population games or to differential population games. Using multidimensional diffusion processes, a general mean field convergence to coupled stochastic differential equation is given. Finally, the computation of mean field equilibria is addressed using Q/H learning.

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U2 - 10.1109/acc.2011.5991087

DO - 10.1109/acc.2011.5991087

M3 - Conference contribution

AN - SCOPUS:80053146604

SN - 9781457700804

T3 - Proceedings of the American Control Conference

SP - 2423

EP - 2428

BT - Proceedings of the 2011 American Control Conference, ACC 2011

PB - Institute of Electrical and Electronics Engineers Inc.

ER -