VALUE OF A DIFFERENTIAL GAME PROBLEM WITH MULTIPLE PLAYERS IN A CERTAIN HILBERT SPACE

Abstract

We study differential game problem involving countable number of pursuers and one evader in the space l2. Players’ motion obey ordinary differential equations with integral constraints subjected to the control functions of the players. Termination time of the game is fixed. The payoff functional is the greatest lower bound of distances between pursuers and the evader when the game is terminated. Optimal strategies of the players are constructed and value of the game is found.