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Optimal Expected Rank in a Two-Sided Secretary Problem

Kimmo Eriksson, Jonas Sjöstrand () and Pontus Strimling ()
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Jonas Sjöstrand: Department of Mathematics and Physics, Mälardalen University, SE-721 23 Västerås, Sweden
Pontus Strimling: Department of Mathematics and Physics, Mälardalen University, SE-721 23 Västerås, Sweden

Operations Research, 2007, vol. 55, issue 5, 921-931

Abstract: In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.

Keywords: games/group decisions; strategic secretary problem; dynamic programming/optimal control; optimal stopping (search for similar items in EconPapers)
Date: 2007
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