On Nash equilibrium solutions in stochastic dynamic games

We consider Nash equilibrium solutions in linear, quadratic, Gaussian stochastic differential games where the two players have access to noise-corrupted information. A class of such games is identified for which each player has optimal solutions which are finite-dimensionally implementable. Utilizing these solutions, we propose, for either player, a finite-dimensionally implementable suboptimal solution to the general linear quadratic, Gaussian zero-sum stochastic differential game where both players have access to differing noise-corrupted observations. This solution possesses the property that it guarantees a computable lower bound for the performance of a player adopting it.