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Stochastic differential games characterized by linear systems and quadratic cost functionals are known to have solutions wherein the optimal strategies are formed as linear transformations of the noisy state observations. These linear transformations are generally unsuitable for use in a situation where the strategies must be computed "on board," since they require retention of the entire observation record. In this paper it is shown that restriction of the players to a class of "filter-like" strategies can yield solutions which are optimal within their class and require storage of only a finite-dimensional data array. The time-varying filter gains are expressible as solutions to nonlinear two-point boundary value problems.