  We consider a stochastic dynamic game where players have their own linear
state dynamics and quadratic cost functions. Players are coupled through some
environment variables, generated by another linear system driven by the states
and decisions of all players. Each player observes his own states realized up
to the current time as well as the past realizations of his own decisions and
the environment variables. Each player (incorrectly) believes that the
environment variables are generated by an independent exogenous stochastic
process. In this setup, we study the notion of ``subjective equilibrium under
beliefs of exogenous uncertainty (SEBEU)'' introduced in our recent work
arXiv:2005.01640. At an SEBEU, each player's strategy is optimal with respect
to his subjective belief; moreover, the objective probability distribution of
the environment variables is consistent with players' subjective beliefs. We
construct an SEBEU in pure strategies, where each player strategy is an affine
function of his own state and his estimate of the system state.
