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.
투자관리와 재고관리에서 흔히 나타나는 상대순위에 의한 최적 중단 문제(Secretary Problem)의 일반화를 위하여 2가지 모형 -One -person Secretary Problem 과 Secretary game- 제안 되었다.
One-person Secretary Problem 에서 (1) 응모자는 고용주의 고용요청을 거부할 수 있고, (2) 고용주는 지나간 응모자에 대해서도 고용요청을 할 수 있다는 가정하에, 최고의 응모자를 선택할 확률을 최대화 하는 전략을 찾는 일반적인 순환식을 보였고, 응모자가 고용을 수락하는 확률이 일정한 경우와 geometric 인 두 경우에 대해 논했다.
Secretary game 에서는 가정 (1)만 고려하되, 전체 p명중 r명 이상이 동의하여야만 응모자를 고용할 수 있다고 가정하여, Nash-Equilibrium전략을 찾는 순환식을 보이고, (p,r)=(2,1)인 예를 들었다.
