Robust search policies against an intelligent evader

Abstract

In a classical search model, an object is hidden in one of many cells. Knowing the probability that the object is in each cell, a searcher wishes to find it. Each search in a cell incurs a cost and will discover the object with some probability, with both the cost and discovery probability dependent on the cell. This paper revisits this search problem with an intelligent evader who decides where to hide in order to evade the search. We make two contributions to the literature. First, we show how to compute a randomized policy for the searcher to minimize the expected cost until discovering the evader. Second, if the search has to stop at some point, with the deadline unannounced in advance, we show how the searcher can sequentially allocate each search to simultaneously maximize the probability of discovering the evader by an arbitrary deadline. In the case where the search cost is identical for all cells, our analysis shows that the latter policy is more robust.