This paper is concerned with the development of a general theory for the class of multistage linear\3-quadratic\3-Gaussian (LQG) decision problems characterized by (i) two decision makers (DM) each with a different objective functional to optimize, (ii) one-step delay observation sharing information pattern which provides each DM with the observation (but not the action) of the other DM with a one-step delay, (iii) a noncooperative equilibrium solution concept. In particular, it is proven that, under certain conditions, this class of optimization problems admit unique equilibrium strategies for each DM, which are linear in the information available. Moreover, exact expressions for those unique strategies are given in the paper. When specialized to the case of a single objective functional, the theory developed generalizes and unifies some of the results found in the literature on dynamic LQG team and zero-sum game problems.
