A GAME THEORETIC MODEL OF A SUBMARINE BARRIER TO DETECT TRANSISTOR SUBMARINES
Interim research memo.
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA OPERATIONS EVALUATION GROUP
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This memorandum formulates and solves a barrier submarine-transitor submarine conflict as a two-person game. When described as a game, the conflict becomes a problem of obtaining distributions along the barrier of the locations of 1 transit lanes and 2 locations of the barrier submarine for which on the average a game theoretic optimum probability of detection by the barrier submarine is to be obtained. The game theoretic optimum or minimax solution gives if it exists at the least one distribution for the transit lanes having the property that, if the barrier submarine behaves optimally, no other distribution of lanes can decrease the probability of detection. In addition, the solution will give if it exists at least one distribution of barrier submarine positions, such that no other barrier submarine distribution will increase the probability of detecting an optimal transitor. Optimal solutions are derived in the appendix for games in which the barrier submarine detection equipment has 1 a definite range law and 2 a trapezoidal lateral range probability of detection law. The geometric method used there can be extended to other detection laws with an attendant increase in mathematical difficulties.
- Undersea and Antisubmarine Warfare