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We consider two-player non-zero-sum linear-quadratic Gaussian games in whichboth players aim to minimize a quadratic cost function while controlling alinear and stochastic state process {using linear policies}. The system ispartially observable with asymmetric information available to the players. Inparticular, each player has a private and noisy measurement of the stateprocess but can see the history of their opponent's actions. The challenge ofthis asymmetry is that it introduces correlations into the players' beliefprocesses for the state and leads to circularity in their beliefs about theiropponents beliefs. We show that by leveraging the information available throughtheir opponent's actions, both players can enhance their state estimates andimprove their overall outcomes. In addition, we provide a closed-form solutionfor the Bayesian updating rule of their belief process. We show that there is aNash equilibrium which is linear in the estimation of the state and with avalue function incorporating terms that arise due to errors in the stateestimation. We illustrate the results through an application to bargainingwhich demonstrates the value of these information corrections.

Linear-quadratic Gaussian Games with Asymmetric Information: Belief Corrections Using the Opponents Actions