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We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game withasymmetric information. Each player observes privately a noisy version of a(hidden) state of the world $V$, resulting in dependent private observations.We study perfect Bayesian equilibria (PBE) for this game with equilibriumstrategies that are linear in players' private estimates of $V$. The maindifficulty arises from the fact that players need to construct estimates onother players' estimate on $V$, which in turn would imply that an infinitehierarchy of estimates on estimates needs to be constructed, rendering theproblem unsolvable. We show that this is not the case: each player's estimateon other players' estimates on $V$ can be summarized into her own estimate on$V$ and some appropriately defined public information. Based on this finding wecharacterize the PBE through a backward/forward algorithm akin to dynamicprogramming for the standard LQG control problem. Unlike the standard LQGproblem, however, Kalman filter covariance matrices, as well as some otherrequired quantities, are observation-dependent and thus cannot be evaluatedoff-line through a forward recursion.

Linear Equilibria for Dynamic LQG Games with Asymmetric Information and Dependent Types