2015 Volume 58 Issue 4 Pages 353-375
This paper deals with a two-person zero-sum search game, in which a searcher distributes search resource to detect a target and the target moves to evade the searcher. The game includes private information of an initial position of the target and a detection probability of the target as payoff. The searcher estimates the initial position with a probability distribution. We model the problem as an incomplete-information game, and propose a convex programming formulation and a linear programming one to derive an optimal distribution of search resource of the searcher and an optimal target strategy of selecting paths. However, the number of paths exponentially increases as the number of time points becomes larger. To cope with the combinatorial explosion, we propose a new approach using Markov movement strategy of the target. By some numerical examples, we analyze players' optimal strategies and evaluate the value of information of the target initial position.
