A Pursuit-Evasion Differential Game with Many Pursuers and One Evader

We study a pursuit-evasion differential game of many players with geometric constraints being imposed on the control parameters of players. Game is described by an infinite system of differential equations of second order in Hilbert space. Duration of the game is fixed. Payoff is the infimum of the distances between the evader and pursuers when the game is terminated. The pursuers’ goal is to minimize the payoff, and the evaderʹs goal is to maximize it. A condition to find the value of the differential game is obtained. Optimal strategies of players are also constructed.