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In this manuscript we formulate the general Target–Attacker–Defender differential game of degree in both its continuous-time and discrete-time turn-based variants in n-dimensional euclidean space. In this three-agent engagement, the Attackers goal is to get as close as possible to the Target before collision with the Defender, whilst the Target and Defender coordinate to achieve the opposite. The most general setting for this zero-sum differential game is considered, where the agents move at speeds not necessarily equal, and the Nash equilibrium strategies are proven in the discrete-time turn-based variant.

A state-feedback Nash equilibrium for the general Target–Attacker–Defender differential game of degree in arbitrary dimensions