Guaranteed approach with the farthest of the runaways

Games of the family $\{\Lambda_N\}_{N\ge2}$ are formulated and studied with the application of generalized Isaacs's approach. The game $\Lambda_N$ is a simplest model of the counteraction of one persecutor $P$ and coalition $N$ of $E^N$ runaways for the case when the payoff is the distance up to the coalition of $E^N$ equal to the Euclidean distance between $P$ and the farthest from the runaways; $P$ is in command of the termination moment. Moreover, an approach within the limits of which in games with a smooth terminal payoff are generated strategies prescribing players' motions in the directions of local gradients of the payoff is described. The approach is used for constructing pursuit strategies in games in which smooth approximations of the maximum of Euclidean distances up to the runaways are in place of payoffs. Pursuit strategies prescribing the motion in the direction of the farthest of the runaways are studied. A numerical simulation of the development of the games $\Lambda_2$ and $\Lambda_3$ is conducted in using different strategies by the players.