Mean field stochastic games: convergence, Q/H learning, optimality

Hamidou Tembine (1)

1 E3S - Supélec Sciences des Systèmes

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.

Domaines: Informatique et théorie des jeux [cs.GT]; Réseaux et télécommunications [cs.NI]

Hamidou Tembine. Mean field stochastic games: convergence, Q/H learning, optimality. American Control Conference 2011, Jun 2011, San Francisco, CA, USA, United States. pp.2423-2428, ⟨10.1109/ACC.2011.5991087⟩. ⟨hal-00643566⟩