The paper deals with the game between a pursuer P and a slower evader E confined to a plane. The scenario considered by Skowronski and Stonier [1] required P to capture E before the latter reaches a shelter, and E to escape before he is captured, the objective achieved via Liapunov conditions. This paper augments the above work by considering a third game and introducing Isaacs’ barriers which interface with the Liapunov approach.

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