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On some stocxastic tactical antisubmarine games

Author

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  • A. Charnes
  • R. G. Schroeder

Abstract

Mathematical models of tactical problems in Hntisubmarine Warfare (ASW) are developed. Specifically, a game of pursuit between a hunter‐killer force. player 1, and a possible submarine, player 2 is considered. The game consists of a sequence of moves and terminates when player 2 is tcaught or evades player 1. When the players move they observe the actual tactical configuration of the forces (state) and each player choosa‐s 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 (TSG). Shapley demonstrated the existence of a value and optimal strategies (solution), An iterative technique to approximate the solution to within desired accuracy is proposed. Each iteration of the technique is obtained by solving a set of linear programs. To introduce more realism into the game several variations of the TSG are also considered. One variation is a finite TSG and linear programming techniques are employed to find the solution.

Suggested Citation

  • A. Charnes & R. G. Schroeder, 1967. "On some stocxastic tactical antisubmarine games," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(3), pages 291-311.
    • Handle: RePEc:wly:navlog:v:14:y:1967:i:3:p:291-311
    DOI: 10.1002/nav.3800140303
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