A Search Game Taking Account of Linear Effects and Linear Constraints of Searching Resource

Search theory has been a major theme in Operations Research. This paper deals with a twoperson zero-sum search game, called search allocation game (SAG), with a searcher and a target as players. In the SAG, the searcher distributes his searching resource in a search space to detect the target while the target moves to evade the searcher. Practical searching resource has a variety of properties on their effects and constraints. A flare fired by a drifting person in the water keeps its brightness within a limited range during some time. Namely, the flare has the property of long-distance effectiveness and temporal durability. There have been so far few researches focusing on the property of searching resource. From a general discussion about the property of searching resource, we notice that linear expressions of variables denoting the resource are crucial to formulate the SAG. In this paper, we propose two linear programming formulations to solve the SAG with linear expressions concerning the effect and the constraints of searching resource and to derive optimal strategies of the searcher and the target.