ON SOME STOCHASTIC TACTICAL ANTISUBMARINE GAMES.
Systems research memo.,
NORTHWESTERN UNIV EVANSTON ILL TECHNOLOGICAL INST
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In this paper some mathematical models are developed of tactical problems which arise in Antisubmarine Warfare. Specifically, the authors consider a game of pursuit between a hunter-killer force, player 1, and a possible submarine, player 2. The game consists of a sequence of moves and it terminates when player 2 is caught or evades player 1. When the players move they observe the actual tactical configuration of the forces state and each player chooses a tactical plan from a finite collection. This joint choice of tactical plans determines an immediate payoff and a transition probability distribution over the states. Hence an expected payoff function is defined. Formally this game is a Terminating Stochastic Game and Shapley demonstrated the existence of a value and optimal strategies solution. An iterative technique is proposed to approximate the solution to within desired accuracy. Each iteration of the technique is obtained by solving a set of linear programs.