Optimal Expected Rank in a Two-Sided Secretary Problem
Kimmo Eriksson, Jonas Sjöstrand, Pontus Strimling
Operations Research · 2007 · Volume 55 · Issue 5
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
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