A Search Game with a Strategy of Energy Supply for Target

Abstract

This paper deals with a two-person zero-sum game called the search allocation game (SAG). A searcher distributes his searching resources in a search space to detect a target while the target moves around in the search space to evade the searcher. The target movement is subject to energy constraints, which means that the target spends some energy to move and he cannot move to other places on exhaustion of his energy. However, the target can supply his energy at the risk of letting himself more likely to be detected by the searcher. A strategy of the searcher is a distribution of his searching resources and a target strategy is to select a path running in the search space and make a decision of energy supply. We propose two linear programming formulations to solve the SAG with energy supply. We also analyze some characteristics of optimal strategies by some numerical examples.