We consider a finite horizon dynamic game with two players who observe their
types privately and take actions, which are publicly observed. Players' types
evolve as independent, controlled linear Gaussian processes and players incur
quadratic instantaneous costs. This forms a dynamic linear quadratic Gaussian
(LQG) game with asymmetric information. We show that under certain conditions,
players' strategies that are linear in their private types, together with
Gaussian beliefs form a perfect Bayesian equilibrium (PBE) of the game.
Furthermore, it is shown that this is a signaling equilibrium due to the fact
that future beliefs on players' types are affected by the equilibrium
strategies. We provide a backward-forward algorithm to find the PBE. Each step
of the backward algorithm reduces to solving an algebraic matrix equation for
every possible realization of the state estimate covariance matrix. The forward
algorithm consists of Kalman filter recursions, where state estimate covariance
matrices depend on equilibrium strategies