Effects of Competition in a Secretary Problem

Daniel Cownden () and David Steinsaltz ()
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Daniel Cownden: School of Biology, University of St Andrews, St Andrews KY16 9TS, United Kingdom
David Steinsaltz: Department of Statistics, University of Oxford, Oxford OX1 3TG, United Kingdom

Operations Research, 2014, vol. 62, issue 1, 104-113

Abstract: 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.

Keywords: secretary problem; game theory; sequential decision analysis (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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