On dichotomous search with direction-dependent costs for a uniformly hidden object

An object is initially hidden in one of the points 1, 2, …, 8 and the prior distribution for its random location X is uniform. Upon searching in place a, l≦a≦s−1, one is told whether X≦ a or X >a. In the first case the one-period search costs are c >0 and in the second case c' >0 The goal consists in locating the object in a cost minimal way. in Murakami [6] an “explicit” solution and a partial asymptotic analysis of the minimal cost function C is given for the case that c'/c is a positive integer k in terms of the solution of a k-thorder difference equation. We extend this result to the (practically sufficient) case that c'/c is rational, investigate concavity of C, refine the asymptotic analysis of C and give an asymptotic result for a “natural” optimal policy. We also report on the numerical performance of three algorithms provided by the theoretical results.