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題名 雙人決策秘書問題的研究
A Variation of Two Decision Makers in a Secretary Problem作者 周冠群
Chou, Guan-Chun貢獻者 余清祥
Jack Yue, C.
周冠群
Chou, Guan-Chun關鍵詞 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日期 2000 上傳時間 18-Apr-2016 16:31:56 (UTC+8) 摘要 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.參考文獻 [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. 描述 碩士
國立政治大學
應用數學系
84751006資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001744 資料類型 thesis dc.contributor.advisor 余清祥 zh_TW dc.contributor.advisor Jack Yue, C. en_US dc.contributor.author (Authors) 周冠群 zh_TW dc.contributor.author (Authors) Chou, Guan-Chun en_US dc.creator (作者) 周冠群 zh_TW dc.creator (作者) Chou, Guan-Chun en_US dc.date (日期) 2000 en_US dc.date.accessioned 18-Apr-2016 16:31:56 (UTC+8) - dc.date.available 18-Apr-2016 16:31:56 (UTC+8) - dc.date.issued (上傳時間) 18-Apr-2016 16:31:56 (UTC+8) - dc.identifier (Other Identifiers) A2002001744 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85502 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 84751006 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 封面頁 證明書 致謝詞 論文摘要 目錄 第一章 前言 第二章 雙人決策的秘書問題 第一節 最佳策略 第二節 獲勝機率 第三章 決策者雙方獲勝機率之平衡 第一節 後決策者能預知下一位應徵者的薪資要求 第二節 最佳策略與k值極大的狀況 第三節 後決策者已知所有的資訊 第四章 結論與未來研究方向 第一節 比較與推論 第二節 未來研究方向 參考文獻 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001744 en_US dc.subject (關鍵詞) 秘書問題 zh_TW dc.subject (關鍵詞) 雙人決策者 zh_TW dc.subject (關鍵詞) 完整訊息 zh_TW dc.subject (關鍵詞) 預知下一步 zh_TW dc.subject (關鍵詞) Secretary problem en_US dc.subject (關鍵詞) Two decision makers en_US dc.subject (關鍵詞) Full informtion en_US dc.subject (關鍵詞) One-step look-ahead en_US dc.subject (關鍵詞) Clairvoyant en_US dc.title (題名) 雙人決策秘書問題的研究 zh_TW dc.title (題名) A Variation of Two Decision Makers in a Secretary Problem en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [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. zh_TW
