  In the "secretary problem", well-known in the theory of optimal stopping, an
employer is about to interview a maximum of N secretaries about which she has
no prior information. Chow et al. proved that with an optimal strategy the
expected rank of the chosen secretary tends to approximately 3.87.
  We study a two-sided game-theoretic version of this optimal stopping problem,
where men search for a woman to marry at the same time as women search for a
man to marry. We find that in the unique subgame perfect equilibrium, the
expected rank grows as the square root of N and that, surprisingly, the leading
coefficient is exactly 1. We also discuss some possible variations.
