A SECRETARY PROBLEM WITH UNCERTAIN EMPLOYMENT WHEN THE NUMBER OF OFFERS IS RESTRICTED

Abstract

We consider the so-called secretary problem, in which an offer may be declined by each applicant with a fixed known probability q (= 1 - p, 0 &le; q < 1) and the number of offering chances are at most m (&ge; 1). The optimal strategy of this problem is derived and some asymptotic results are presented. Furthermore we briefly consider the case in which the acceptance probability depends on the number m of offering chances.