A rank-based selection with cardinal payoffs and a cost of choice

Details A rank-based selection with cardinal payoffs and a cost of choice A rank-based selection with cardinal payoffs and a cost of choice

2008-12-18

arxiv.org/abs/0812.3483v1

Scientiae Mathematicae Japonicae 69(2), 285-293, 2009: e2009, 69-77

Mathematics

Optimization and Control

11 pages

Scientific paper

A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables $X_1,X_2,...,X_n$ from a uniform distribution on $[0; 1]$, are observed sequentially by the grader. He has to select exactly one item, when it appears, and receives a payoff which is a function of the unobserved realization of random variable assigned to the item diminished by some cost. The methods of analysis are based on the existence of an embedded Markov chain and use the technique of backward induction. The result is a generalization of the selection model considered by Bearden(2006). The asymptotic behaviour of the solution is also investigated.

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