Construction of Barrier in a Three-Player Pursuit-Evasion Game

Abstract

This paper addresses a particular pursuit-evasion game with two pursuers with slower speed but smaller minimum turning radius and a faster evader with bigger minimum turning radius. This is a game of kind, and what interests us is how to construct the barrier that separates the state zone into capture zone and escape zone, and what the optimal strategies for the players are on the barrier. Under some mild assumptions, we give the explicit form of the barrier near the BUP (i.e., the boundary of the usable part on the boundary of the target set) by using Isaacs’ method, and a procedure to construct the barrier when the retrogressive time is big enough by determining the optimal strategies for the players on the BUP. Then we prove that the optimal strategies remain unchanged near some special parts on the BUP, and we give two examples to illustrate these situations.