Asymptotic theory of selection by relative rank with low cost

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=kën 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 •.