一类双边秘书问题的最优停止
Optimal stopping in a two-sided secretary problem
摘要：
在最优停止理论中著名的“秘书问题”中，雇主将要面试最多N个秘书，而她没有事先的信息。Chow等人证明，在最优策略下，所选秘书的期望排名趋于约3.87。我们研究了这个最优停止问题的双边博弈论版本，其中男性寻找一个女人结婚的同时，女性寻找一个男人结婚。我们发现，在唯一的子博弈完美均衡，预期的排名增长的平方根N，令人惊讶的是，首项系数正好是1。我们还讨论了一些可能的变化。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
