In the framework of Pursuit-Evasion Games (PEGs), the so-called Lion and Man problem has been studied. In this game, a lion (pursuer) and a man (evader) move alternately in the positive quadrant of the plane, traveling a distance of at most one unit at each move. Capture occurs when the players’ locations coincide. Novel strategies outperforming existing ones have been proposed as well as associated bounds on the capture time. Such results have also been extended to polynomial environments.
Pursuit-Evasion Games involving one evader and multiple pursuers have been investigated as well. In particular, games involving three pursuers and one evader has been analyzed, deriving results on how pursuer cooperation may improve capture time with respect to the decentralized case.
You can find more information in the following publications.
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