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The purpose of this paper is to make up for lacks of the past researches with respect to basic search models with continuous effort. We suppose a discrete search space composed of n boxes and an exponential·type detection function in each box. First an explicit solution is derived for a detection search game. Secondly we con­ sider an information search problem and propose a sequential method of constructing the optimal policy. Thirdly we consider a certainty search game in which the payoff function is given by the posterior uncertainty with respect to the position of player I (hider) and obtain the solution in the form of a solution of a certain simultaneous equa­ tions. Finally we consider a whereabouts search model and derive the same result as the discrete effort case.

SEARCH MODELS WITH CONTINUOUS EFFORT UNDER VARIOUS CRITERIA