Effects of Competition in a Secretary Problem

Journal article

In a novel multiplayer extension of the famous secretary problem, multiple players seek to employ secretaries from a common labour pool. Secretaries do not accept being put on hold, always accept job offers immediately, and leave the labour pool once rejected by a single player. All players have an identical preference for secretaries, and all players seek to optimize the probability of obtaining the best of all n secretaries. We find that in the Nash equilibrium, as the number, N, of players searching the labour pool grows, the optimal strategy converges to a simple function of N. For the two-player case we also compute how much players can gain through cooperation and how the optimal strategy changes under a payoff structure that promotes spite. © 2014 INFORMS.

Authors: Cownden, D; Steinsaltz, D

• Publication status: Published
• Journal: OPERATIONS RESEARCH
• Volume: 62
• Issue: 1
• Pages: 104-113
• Publication date: 2014-01-01
• DOI: 10.1287/opre.2013.1233
• EISSN: 1526-5463
• ISSN: 0030-364X
• Language: English
• Keywords: Secretary problem; Sequential decision analysis; Game theory