DISTRIBUTED ALGORITHM FOR THE COMPUTATION OF NASH EQUILIBRIA IN LINEAR STOCHASTIC DIFFERENTIAL GAMES.

In this paper, we study a class of two-person stochastic linear-quadratic differential games under multiple probabilistic modeling, and with each player acquiring a noisy measurement of the initial state. We obtain conditions for the existence and uniqueness of Nash equilibrium, and provide a method for iterative distributed computation of the solution. The distributed algorithm involves learning in the policy space, and it does not require that the players know each other's perception of the probabilistic model underlying the decision process. Such an iteration converges whenever the length of the time horizon is sufficiently small, and the limit is an affine policy for both players if the underlying distributions are jointly Gaussian.