Pursuit Games with Costly Information: Application to the ASW Helicopter Versus Submarine Game

Abstract

This paper deals with an application of game theory to a problem of an ASW (Anti Submarine Warfare) helicopter versus a submarine pursuit game: the helicopter (the pursuer) tries to reach, with respect to duration constraints (autonomy), a relative location to the submarine close enough to deliver a weapon; the submarine (the evader) maneuvers in order to escape to a secure position. Under realistic assumptions, the game therefore consists of a two-player pursuit game, in which each player gets information about the other one only at discrete dates (corresponding to helicopter dipping stations), these dates being chosen by the pursuer. Furthermore, information access is costly for the helicopter due to the intrinsic duration of a dipping station. Then the pursuit game is characterized by the fact that the pursuer suffers some penalty when he wants to obtain information about the position of the evader, and the evader remains blind except when the pursuer takes information.

Theoretical aspects of this problem have been previously treated. Assuming order one dynamics for both players, and a limited capture zone, the Pontrjagin approach yields an explicit formula for the sets of initial states which the pursuer can capture in at most (i.e. in the worst case) a given number of stages. An explicit formula can also be deduced when the pursuer aims at minimizing the duration of the games.

Performance evaluations of different dynamic games strategies arc presented, achieved within realistic environment (via a high level of realism in computer simulation), which illustrate the interest of games techniques for various applications in the tactical domain, and suggest some deeper exploration.

This research was sponsored by Direction des Recherches, Etudes et Techniques, FRANCE