A linear differential game on a plane with a minimum-type functional

A differential game on a plane with a functional in the form of the minimum, with respect to time, of a certain prescribed phase vector function (quality function) is considered. It is proved that the game value is constant outside a certain bounded region, consisting of two parts. In the first subregion, the value is equal to the quality function, and in the second it satisfies Bellman's equation. For the constant-value region, where the players’ optimum strategies are not unique, single-valued guaranteeing players’ strategies are proposed. The results of a numerical investigation of the problem are presented.