雙人決策秘書問題的研究

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.