ASYMPTOTIC THEORY OF SELECTION BY RELATIVE RANK WITH LOW COST
Sigeiti Moriguti · Journal of the Operations Research Society of Japan · 1993
Selection from among n objects by relative rank with no recall - the "secretary problem" - in the asymptotic case when n → ∞ is considered, assuming that k, the cost ratio, is 0(1/n), i.e. K=k ・ n is a finite constant. Starting from the special case of K=0, the situation changes smoothly as K grows and eventually approaches the "medium cost" case. Thus, the ratio of expected cost of observation to the expected rank goes smoothly from 0 to 1 as K goes from 0 to ∞.