The Secretary Problem with a Selection Committee: Do Conformist Committees Hire Better Secretaries?

• 成果类型: Article
• 署名作者: Alpern, Steve; Baston, Vic
• 署名单位: University of Warwick; University of Southampton
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2015.2377
• 发表日期: 2017
• 页码: 1184-1197
• 关键词: games; Group decisions; voting; committees; Industrial Organization; firm objectives; organization and behavior; decision making; Secretary problem

摘要

This paper analyzes a variation of the secretary problem in which two selectors with different fields of interest each want to appoint one of the n candidates with as much expertise as possible in their field. Selectors simultaneously vote to accept or reject: Unanimous decisions are respected, and candidates with a split decision are hired with probability p. Each candidate arrives with expertise x and y in the two fields, uniformly and independently distributed on [0; 1] and observable to both selectors. If a candidate with expertise pair (x, y) is hired by unanimous decision, the payoffs to the selectors are simply x and y. However, to model the level of conformity in the firm, we deduct a positive consensus cost c from the utility of a selector who has rejected a candidate who is nevertheless hired. We show(Theorem 1) that each stage game has a unique equilibrium in which there are two thresholds, z < nu; and say selector I accepts candidate (x,y) if x > nu or x > z and y > nu. We show that for sufficiently large p and c, decisions are unanimous, and that as the number n of candidates goes to infinity, the equilibrium value of the game goes to the golden mean. We show that as the consensus cost c increases from 0, this hurts the selectors (Theorem 4) but helps the firm (Theorem 6), whose utility from hiring candidate (x,y) is a weighted average of x and y. Thus a little conformity is good for the firm.