The Search Allocation Game

Abstract

Abstract Koopman first discussed a search problem to find an optimal distribution of searching resource for effective search. Since then, search theory has been a major theme in operations research. A search game named “search allocation game (SAG)” is one of the search game models with targets and searchers. 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. In this paper, we survey past researches on the search problems including the SAG and show some methodologies to solve the SAG. Further, we mention many extensions and practical applications of the model. Different from other models of the search game, the SAG is more compatible with formulations in general optimization problems such as linear/nonlinear programming problem, convex analysis, dynamic programming problem, or variational problem. Therefore, we can use the basics of such mathematical programming methodologies so that the SAG is comparatively easy for us to approach and apply to many practical search problems. Here, we first review the history of search problems surrounding the SAG, after Koopman. In the following sections, we describe basic models of the SAG with a stationary target and then with a moving target. We show optimal strategies of players in the SAGs and take some extensions of it, for example, datum search game on a continuous two‐dimensional space, the SAG with false contacts, consideration for attributes of searching resource, the SAG with energy supply strategy of target and others.