Hide-and-search Game with the Risk Criterion

In this paper, a hide-and-search game with the risk criterion is investigated. The target space consists of n discrete regions and each region is characterized by the searching cost, the detection rate per unit searching effort and the reward when the target is detected. At the beginning of the game, a target selects a region so as to maximize the expected risk of the search and hides himself in it. On the other hand, a searcher searches the target allocating his available total searching cost among regions so as to minimize the expected risk of the search. We formulate this search situation as a two-person zero-sum game and derive optimal strategies.