论文标题
激励秘书问题中的隐藏类型
Incentivizing Hidden Types in Secretary Problem
论文作者
论文摘要
我们研究了$ n $ sop申请人之间的游戏，这些申请者遇到了费用$ c $（相对于工作价值），以在面试中揭示其类型，并试图最大程度地提高雇用最好的可能性。我们定义了一个完整的学习均衡，并证明了它的存在，独特性和最佳性。在均衡中，管理员接受当前最佳申请人$ n $，概率$ c $，如果$ n <n^*$，则概率为1，如果$ n \ ge n^*$对于阈值$ n^*$独立于$ c $。与无需成本的情况相反，成功的概率收敛到$ 1/\ mathrm {e} \ aS $ n $的0.37 $倾向于无限，而成功的概率衰减如$ n^{ - c} $。
We study a game between $N$ job applicants who incur a cost $c$ (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best. We define a full learning equilibrium and prove its existence, uniqueness, and optimality. In equilibrium, the administrator accepts the current best applicant $n$ with probability $c$ if $n<n^*$ and with probability 1 if $n\ge n^*$ for a threshold $n^*$ independent of $c$. In contrast to the case without cost, where the success probability converges to $1/\mathrm{e}\approx 0.37$ as $N$ tends to infinity, with cost the success probability decays like $N^{-c}$.
