A multi-stage search allocation game with the payoff of detection probability

This paper deals with a multi-stage two-person zero-sum game called the multi-stage search allocation game (MSSAG), in which a searcher and an evader participate. The searcher distributes his searching resources in a discrete search space to detect the evader, while the evader moves under an energy constraint to evade the searcher. At each stage of the search, the searcher is informed of the evader’s position and his moving energy, and the evader knows the rest of the searcher’s budget, by which the searcher allocates searching resources. A payoff of the game is the probability of detecting the evader during the search. There have been few search games that have dealt with the MSSAG. We formulate the problem as a dynamic programming problem. Then, we solve the game to obtain a closed form of equilibrium point, and to investigate the properties of the solution theoretically and numerically.