  We consider a class of two-player dynamic stochastic nonzero-sum games where
the state transition and observation equations are linear, and the primitive
random variables are Gaussian. Each controller acquires possibly different
dynamic information about the state process and the other controller's past
actions and observations. This leads to a dynamic game of asymmetric
information among the controllers. Building on our earlier work on finite games
with asymmetric information, we devise an algorithm to compute a Nash
equilibrium by using the common information among the controllers. We call such
equilibria common information based Markov perfect equilibria of the game,
which can be viewed as a refinement of Nash equilibrium in games with
asymmetric information. If the players' cost functions are quadratic, then we
show that under certain conditions a unique common information based Markov
perfect equilibrium exists. Furthermore, this equilibrium can be computed by
solving a sequence of linear equations. We also show through an example that
there could be other Nash equilibria in a game of asymmetric information, not
corresponding to common information based Markov perfect equilibria.
