Search allocation game

This paper deals with a two-person zero-sum game called search allocation game (SAG), where a searcher allocates his searching resources in a search space to detect a target while the target takes a path running across the space to evade the searcher. We consider the discrete SAG and the continuous SAG defined on the discrete search space and the continuous one, respectively. In a general way, we prove an existence theorem of equilibrium points for both the SAGs and elucidate that an equilibrium of the continuous SAG is given by a convergence point of equilibria of the discrete SAG. After then we develop a method to solve a large size of the discrete problem with specific feasibility conditions. As one of numerical examples, we take so-called flaming datum search game, which is adequate to demonstrate the convergence theorem.