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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
Stable URL: http://www.jstor.org/stable/27595891
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Weakest Link Marked Stopping Problem
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Abstract

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.

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