Cooperative versus non-cooperative strategies in three-pursuer single-evader games

The value of cooperation in pursuit-evasion games is investigated. The considered setting is that of three pursuers chasing one evader in a planar environment. The optimal evader trajectory for a well-known non-cooperative pursuer strategy is characterized. This result is instrumental to derive upper and lower bounds to the game length, in the case in which the pursuers cooperate in the chasing strategy. It is shown that the cooperation cannot reduce the capture time by more than one half with respect to the non-cooperative case, and that such bound is tight.