Abstract
Abstract : The game is a two-person zero-sum game. On each play, each player selects any point on a line of finite length. The payoff is a trapezoidal function of the separation between the two selected points; it is constant for separations from zero to R sub 1, changes linearly between R sub 1 and R sub 2, and is zero for separations greater than R sub 2. The derivation and proof of the solution are interesting due to the discontinuities in the slope of the payoff function. The solution includes the special cases of triangular (R sub 1 = 0) and rectangular (R sub 1 = R sub 2) payoff functions. The game is related to search theory in its applicability to the barrier problem. Uniform distribution along the barrier is not in general an optimal strategy for either the maximizer (detector) or the avoider (transitor). In selecting optimal strategies the detec or must have more information on the payoff function (lateral range curve) than is required by the transitor.
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