抄録
A version of the secretary problem is considered. The ranks of items,
whose values are independent, identically distributed random variables X1,X2, . . . ,Xn
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 [2]. The asymptotic behaviour of the solution
is also investigated.
