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A Weakest Link Marked Stopping Problem
Steven A. Lippman, Sheldon M. Ross and Sridhar Seshadri
Journal of Applied Probability
Vol. 44, No. 4 (Dec., 2007), pp. 843-851
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/27595891
Page Count: 9
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We consider a model in which we have k items to be sold. Potential buyers make offers in a sequential fashion. Once made, the offer is either rejected or marked for acceptance. Once k items have been marked, the items are then sold to the buyers whose offers were marked, but at a price equal to the minimum of the k marked offers. Assuming that the successive offers are independent and identically distributed according to a specified distribution and that there is a fixed cost incurred whenever an offer is rejected, we determine structural results about the optimal policy, present computational approaches for finding the optimal policy, and give some heuristic policies.
Journal of Applied Probability © 2007 Applied Probability Trust