In this paper, closed-loop Nash equilibrium strategies for an N-pursuer single-evader differential game over a finite time horizon with limited observations is considered. The game setting is such that each pursuer has limited sensing range and can observe the state vector of another player only if that player is within the pursuer's sensing range. The evader, on the other hand, has unlimited sensing range which allows it to observe the state of all pursuers at all times and implement a standard closed-loop Nash strategy. To derive strategies for the pursuers, a new concept of best achievable performance indices is proposed. These indices are derived in a way to be the closest to the original performance indices and such that the resulting pursuers' collective strategy satisfies a Nash equilibrium against the evader's strategy. The strategies obtained by such an approach are independent of the initial state vector. An illustrative example is solved and simulation results corresponding to different sensing ranges and performance indices of the game are presented.
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