In addition to the classical formulation of a general two-player zero-sum differential game it is assumed that the minimizing player chooses the values of certain parameters to further decrease the pay-off functional at the expense of the maximizing player. To solve this problem in the best possible way for the minimizing player, a set of necessary optimality conditions is derived, which not only enable the determination of the saddle-point strategies for both participating players, but also the optimal parameters. Based on these conditions an iterative numerical algorithm of gradient type is suggested. As an illustration, several examples are solved applying the described algorithm.

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