信息的双刃剑：学校选择中揭示与隐藏的抽签
The Double-Edged Sword of Information: Revealed versus Hidden Lotteries in School Choice
- University of California, San Diego（加州大学圣地亚哥分校）
- Toyota Technological Institute at Chicago（芝加哥丰田技术研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究放宽学生同质偏好假设，在贝叶斯纳什均衡模型下分析学校选择中揭示抽签号对匹配率和社会福利的影响，发现其效果取决于偏好异质性且存在非单调效应，揭示政策具有复杂权衡。
AI中文摘要：
在学校选择中，当偏好同一所学校的学生人数超过可用座位数时，匹配机制通常使用抽签号来打破平局。关于向学生揭示抽签号的影响，理论和实证研究兴趣日益增长。实践中，近年来纽约市公立学校开始向学生揭示抽签号以提高透明度。先前文献的理论发现也表明，在延迟接受算法下，揭示抽签号严格提高了匹配数量。然而，这些理论结果基于一个过度简化的假设，即所有学生对学校有相同的偏好排序。在本工作中，我们放宽了这一假设，允许学生具有异质性的偏好排序。在一个学生策略构成贝叶斯纳什均衡的博弈论模型下，我们刻画了揭示抽签号可能改善或恶化匹配结果的情形，匹配结果通过匹配率和社会福利两个指标来衡量。我们进一步考虑了揭示抽签的部分信息，并展示了学生可获得信息量中的非单调效应。这些结果共同说明了抽签揭示政策引发的复杂权衡。
英文摘要：
In school choice, a lottery number is often used by the matching mechanism to break ties when there are more students who prefer the same school than the number of seats available. There has been growing theoretical and empirical interest in understanding the impact of revealing the lottery number to students. In practice, in recent years, the NYC Public Schools started revealing the lottery number to students to improve transparency. Theoretical findings from prior literature also suggest that revealing the lottery number strictly improves the number of matches under the deferred acceptance algorithm. However, these theoretical results are based on the over-simplifying assumption that all students share the same preference ranking for schools. In this work, we relax this assumption and allow students to have heterogeneous preference rankings. Under a game-theoretic model where student strategies form a Bayesian Nash equilibrium, we characterize scenarios where revealing the lottery number can either improve or worsen the matching outcome, measured by two metrics of match rate and social welfare. We further consider revealing partial information about the lottery, and demonstrate non-monotonic effects in the amount of information available to students. These results together illustrate complex tradeoffs induced by the lottery revealing policy.
