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| Title: | 雙人決策秘書問題的研究
A Variation of Two Decision Makers in a Secretary Problem |
| Authors: | 周冠群
Chou, Guan-Chun |
| Contributors: | 余清祥
Jack Yue, C.
周冠群
Chou, Guan-Chun |
| Keywords: | 秘書問題
雙人決策者
完整訊息
預知下一步
Secretary problem
Two decision makers
Full informtion
One-step look-ahead
Clairvoyant |
| Date: | 2000 |
| Issue Date: | 2016-04-18 16:31:56 (UTC+8) |
| Abstract: | Chen, Rosenberg和Shepp（1997）的“雙人決策者的秘書問題“（A Secretary Problem with Two Decision Makers），探討在完整訊息（Full Information）與選擇次序不變的情況下，具有優先選擇權的決策者佔有較大優勢。這裡所謂的優勢意指在雙方最終選擇的大小為勝負條件所產生獲勝機率的比較。而本篇文章主要是延伸此一探討，意即在若不變動兩者選擇的次序，但賦予後選擇決策者較多資訊的條件下，能否平衡雙方的優劣勢。我們首先討論後決策者擁有預知下一步（One-step look-ahead）資訊能力的條件下，雙方優勢的改變；隨之若是在後決策者能預知完全資訊的情況下，是否能平衡雙方的優劣勢。而事實上，即便在後決策者擁有所有資訊的條件，仍無法完全改變此一情況；更進一步而言，先選擇決策者甚至在不知道後決策者已掌握了所有資訊的情況下，仍可佔有獲勝機率大於後決策者的優勢。這裡我們將提供理論與理論上的數值結果。
Chen, Rosenberg, and Shepp (1997) considered a variation of the "secretary problem" in which the salary demands of a group of applicants are from a known and continuous distribution (i.e., full information case) and these applicants are interviewed sequentially by two managers, say, I and II. For every applicant. Manager I has the right to interview and hire him/her first. If Manager I rejects the applicant, Manager II can interview him/her. No recall is allowed when the applicant is rejected by both managers, and neither manager can interview and hire another applicant once he/she has hired an applicant. The manager who chooses the applicants with the lower salary wins the game. Chen et al. shows that manager I has bigger winning chance than manager II in the full information case. |
| Reference: | [1] Berry, D. A., Chen, R. W. and Rosenberg, B. (1997). “A secretary problem”, Technical Report.
[2] Chen, R. W., Rosenberg, B. and Shepp, L. A. (1997). “A secretary problem with two decision makers”, Technical Report.
[3] Chow, Y. S., Robbins, H., Moriguti, S., and Samuels, S. M. (1964). “Optimal selection based on relative rank (the “secretary problem”)”, Israel Journal of Mathematics 2, 81-90.
[4] Ferguson, T. S. (1989). “Who solved the secretary problem?”, Statistical Science 4, 282-289
[5] Frank, A. Q. and Samuels, S. M. (1980). “On an optimal stopping problem of Gusein-Zade”, Stochastic Processes and their Application 10, 299-311.
[6] Gardner, M. (1960). “Mathematical games”, Scientific American 202, 135, 178.
[7] Gilbert, J. and Mosteller, F. (1966). “Recognizing the maximum of a sequence”, Journal of American Statistical Association 61, 35-73.
[8] Samuels, S. M. (1981). “Minimax stopping rules when the underlying distribution is uniform”, Journal of American Statistical Association 76, 188-197.
[9] Samuels, S. M. (1991). “Secretary problems” In Handbook of Sequential Analysis (B. K. Ghosh and P. K. Sen, eds.). Dekker, New York.
[10] Smith, M. H. and Deely, J. J. (1975). “A secretary problem with finite memory”, Journal of American Statistical Association 70, 357-361. |
| Description: | 碩士
國立政治大學
應用數學系
84751006 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#A2002001744 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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