A SEARCH ALLOCATION GAME WITH AN INTERDICTOR

Abstract

Our theory on search games in this paper could be applied to anti-smuggling operations on the sea, with the process of detection of smugglers (targets) by surveillance airplanes (searchers) and the capture of them by patrol boats. In almost all models of search games, they involve two main players: searchers and targets. In this paper, we propose a new search game model with the dispatch of a patrol boat as an interdictor by the searcher to capture the detected target. The searcher allocates some search resources to detect the target while deploying an interdictor for dispatch after the detection and the target moves on the sea to evade the searcher. In the paper, we develop a DC programming formulation to derive an equilibrium point in a general way and a linear programming formulation that can be applied to a speci(cid:12)c situation. At the equilibrium point, we obtain an optimal waiting point for the interdictor, an optimal allocation of search resources and an optimal movement plan of the target. We analyze those rational strategies of players by computational examples.