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A weakest link marked stopping problem. (English) Zbl 1144.90028

Summary: 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.

MSC:

90C39 Dynamic programming
90C40 Markov and semi-Markov decision processes
60G40 Stopping times; optimal stopping problems; gambling theory
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