A search game with incomplete information on detective capability of searcher

This paper deals with a so-called search allocation games (SAG), which a searcher distributes search resources, such as detection sensors and search time, into a search space to detect a target and the target moves to evade the detection. Although there have been many published papers on the SAG, they almost dealt with complete information games. In this paper, we consider private information of the searcher about the detection effectiveness of the search resource and discuss a two-person zero-sum incomplete information SAG with the detection probability of the target as payoff. We derive its Bayesian equilibrium to evaluate the value of the incomplete information.