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The secretary problem with a selection committee : do conformist committees hire better secretaries
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Alpern, Steve and Baston, V. J. (2017) The secretary problem with a selection committee : do conformist committees hire better secretaries. Management Science, 63 (4). 1184 -1197. doi:10.1287/mnsc.2015.2377 ISSN 0025-1909.
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Official URL: http://dx.doi.org/10.1287/mnsc.2015.2377
Abstract
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 < v, and say selector I accepts candidate (x, y) if x > v or x > z and y > v. 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.
Item Type: | Journal Article | ||||||||||
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Subjects: | H Social Sciences > HB Economic Theory H Social Sciences > HD Industries. Land use. Labor Q Science > QA Mathematics |
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Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
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Library of Congress Subject Headings (LCSH): | Game Theory, Conformity in the workplace , Organizational behavior , Manpower planning | ||||||||||
Journal or Publication Title: | Management Science | ||||||||||
Publisher: | Institute for Operations Research and the Management Sciences (I N F O R M S) | ||||||||||
ISSN: | 0025-1909 | ||||||||||
Official Date: | April 2017 | ||||||||||
Dates: |
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Volume: | 63 | ||||||||||
Number: | 4 | ||||||||||
Page Range: | 1184 -1197 | ||||||||||
DOI: | 10.1287/mnsc.2015.2377 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Date of first compliant deposit: | 5 February 2016 | ||||||||||
Date of first compliant Open Access: | 27 April 2017 | ||||||||||
Funder: | United States. Air Force. Office of Scientific Research (AFOSR) | ||||||||||
Grant number: | FA9550-14-1-0049 |
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