On the saddle-point solutions of a class of stochastic differential games

This paper deals with the saddle-point solutions of a class of stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that both players have access to a common noisy linear measurement of the state and they are permitted to utilize only this information in constructing their controls. The saddle-point solution of such differential game problems have been discussed earlier in Ref. 1, but the conclusions arrived there are incorrect as it is explicitly shown in this paper. We extensively discuss the role of information structure on the saddle-point solution of such stochastic games (specifically within the context of an illustrative discrete-time example) and then obtain the saddle-point solution of the originally formulated problem by employing an indirect approach.