Abstract
The three agent zero-sum differential game of active defence is investigated; in this pursuit-evader game, agent A attempts to capture agent T, and agents T and D coordinate to achieve the opposite goal. A novel geometric approach is introduced as an alternative to the standard algebraic approach where the pursuit-evader game is reformulated as a discrete-time turn-based dynamic game, in which the corresponding strategies are proved to be a Nash equilibrium. Via a recursive application of the main results, in view of the fact that no limits were placed on the infinitesimalness of the time increment, it is argued that the strategies also constitute a Nash equilibrium in the original continuous time formulation. Finally we simulate the Nash equilibrium strategies to verify its optimality and its robustness against other guidance laws.
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