Problems particular to N versus 1 differential games are investigated based on a 2 versus 1 game. A differential game arises between two sonar (or radar) systems and a target. The target uses a mixed strategy by adding white noise into its controller to hamper the tracking of the sonars. The two structures studied, a centralized and a decentralized structure that correspond to a 1 versus 1 or a 2 versus 1 game formulation, are shown to yield different results. Nash-optimality of each structure is shown to depend on the dynamics of the evader. The study provides insight into the solution of difficult problems specific to N versus 1 games. To illustrate further N versus 1 game problems, a nonoptimal scalar case is presented in which the decentralized structure is proven superior. In the same context, this stochastic problem also yields a matrix game, a bimatrix game, and a hierarchical (Stackelberg) game.

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