A Generalization of the Multi-Stage Search Allocation Game

Abstract

This chapter deals with a multistage two-person zero-sum game called multistage search allocation game (MSSAG), in which a searcher and a target participate. The searcher distributes his searching resource in a search space to detect the target and the target moves under an energy constraint to evade the searcher. At the beginning of each stage, the searcher is informed of the target’s position and of his moving energy, and the target knows the amount of the searcher’s resource used so far. The game ends when the searcher detects the target. The payoff of the game is the probability of detecting the target during the search. There have been few search games on the MSSAG. We started the discussion on the MSSAG in a previous paper, where we assumed an exponential function for the detection probability of the target. In this chapter, we introduce a general function for the detection probability, aiming at more applicability. We first formulate the problem as a dynamic program. Then, by convex analysis, we propose a general method to solve the problem, and elucidate some general properties of optimal solutions.