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The optimal control sequence is found for the capture by a pursuer of the identities of an arbitrary number of evaders. The pursuer moves to observe the face of each evader, which each evader simultaneously moves to conceal. A dynamic game model is used, with metrics defining evader observability and utility functions embodying pursuer and evader control objectives. Nash equilibria are found specifying player strategies in a repeated game with perfect but either complete or incomplete information. The evolution of evasive runaway, identity capture, and stopping is characterized, and an exact solution with proof is found for the optimal sequence of pursuer controls which results in the identification of an arbitrary number of evaders in minimum time. Performance illustrations of the optimal sequencing are provided.1. Introduction. This paper develops control strategies in a dynamic game of identity evasion and capture. Players in the game are vehicles or persons moving in two or three dimensions. One player, the pursuer, seeks to identify the other players, the evaders, by sequentially moving to observe the face of each evader. Each evader simultaneously moves to conceal its face from the pursuer. All players have perfect information on past moves, but we consider cases in which the evaders have either complete or incomplete information on pursuer objectives. We develop a model for the pursuer and evader dynamics, followed by construction of an observability metric for specifying evader identity capture. The observability metric is used to generate utility functions embodying pursuer and evader control objectives. Using the utility functions, the pure strategy Nash equilibria are found that specify individual player strategies in a repeated game consisting of a single pursuer and an arbitrary number of evaders. With the solution to the repeated game, a stopping criterion is developed defining when an individual evader is identified. A difference equation for the dynamical evolution of stopping and capture is then used to model the sequential identification of all evaders. An exact solution with proof is found for the optimal sequence of pursuer controls which results in the identification of an arbitrary number of evaders in minimum time. Examples are provided to illustrate the performance using the optimal control sequence.The pursuit-evasion game between a single pursuer and an arbitrary number of evaders solved in this work uses a game formulation that departs from traditional approaches based on control over a finite horizon or search on a closed gridded graph. The overall volume of research in the theory and application of pursuit-evasion games is substantial. Historically, much of the analytical work in pursuit-evasion has focused on the solution of differential games in continuous time [4], [9], [10], [11], [12]. A central class of problems underpinning this theory focuses on variants of quadratic games

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