  We formulate a new class of two-person zero-sum differential games, in a
stochastic setting, where a specification on a target terminal state
distribution is imposed on the players. We address such added specification by
introducing incentives to the game that guides the players to steer the join
distribution accordingly. In the present paper, we only address linear
quadratic games with Gaussian target distribution. The solution is
characterized by a coupled Riccati equations system, resembling that in the
standard linear quadratic differential games. Indeed, once the incentive
function is calculated, our problem reduces to a standard one. Tthe framework
developed in this paper extends previous results in covariance control, a fast
growing research area. On the numerical side, problems herein are reformulated
as convex-concave minimax problems for which efficient and reliable algorithms
are available.
