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Abstract. This paper presents the cooperation between two searchers at the origin to seek for a random walk moving target on the line. Any information of the target position is not available to the searchers all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using numerical example.

Mathematics Subject Classification: 37A50, 60K30, 90B40.

Keywords: Search theory, Linear search, Random walk. 1.Introduction The prime focus of searching for a randomly moving particle on the real line is to
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Recently, Mohamed et al. [15] studied this problem when the target moves on one of n-intersected real lines in which any information of the target position is not available to the searchers all the time. Mohamed et al. formulate a search model and find the conditions under which the expected value of the first meeting time between one of the searchers and the target is finite. Furthermore, they showed the existence of the optimal search plan that minimizes the expected value of the first meeting time and found it. More recently, El-Hadidy [16] considered a search problem for a d-dimensional Brownian target that moves randomly on d-space. He found the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite. In addition, he showed the existence of the optimal search plan that minimizes the expected value of this first meeting time. A comprehensive discussion of many aspects of search problem is found in El-Hadidy et al. [18-30]. Finding a Random walk moving target inside a cylinder has numerous applications in physics. One of the famous search methods, is the coordinated linear search method which consider two unit-speed searchers starting at the origin point seek for a random walk target. A target is assumed to move randomly on a line according to a

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