On optimal stopping baswd on relative rank

Abstract

This thesis deals with a class of optimal stopping problems based on relative rank, usually called the Secretary Problem and can be applicable to investment decisions, inventory control and so on. To allow more realistic formulations of these original problems, this thesis suggests two extensions ; One-person Secretary Problem and Secretary Game. In the One-person Secretary Problem, we permit (1) the applicant the right to refuse an offer of employment with same probability and (2) the employer the attempt to recall a skipped applicant but with nonincreasing probability of acceptance. General formulae for finding the procedure which maximizes the probability of selecting the best are obtained as recursive equations. By backward induction, two special cases, constant probability of acceptance and geometric probability of acceptance, are discussed in detail. In the Secretary Game, we consider only (1). An applicant can be employed, if no less than r(1≤r≤p) players among a group of p players agree. General recursive formulae for Nash eguilibrium strategies are obtained and a simple case (p,r)=(2,1) is discussed.