Two General Properties of the Saddle-Point Solutions of Dynamic Games

In deterministic team problems every closed-loop representation of an optimal open-loop solution is also optimal This property, however, no longer holds true when the optimization problem is a zero-sum or a nonzero-sum game. In zero-sum games, two weaker (but still general enough) versions of this statement are valid, which still fail to hold in the case of nonzero-sum games. In this correspondence we state and prove these two general properties of the saddle-point solution in dynamic games.