优先阻塞者：一般约束下匹配中的福利与激励

中文摘要 AI 辅助

机构经常面临比单一容量更复杂的约束。保护一个无法被容纳的学生的优先权，可能会阻塞一个符合条件但优先级较低的学生。我们引入了COP-and-Choose，这是一个累积报价过程后接一个选择步骤的机制，并证明其贪心版本（跳过此类阻塞者）不会让任何学生比任何公平匹配或背包延迟接受（KDA）更差。贪心是保持这一保证的唯一一致性规则。在每所学校的可替代性和规模单调性条件下，贪心是防策略操纵的，并且在防策略操纵机制中是帕累托无支配的。如果其中任一条件在某所学校失败，那么增加一个容量为一的学校就会产生一个市场，在该市场中，对于每一种提议顺序，贪心都是可操纵的，并且没有防策略操纵机制能弱帕累托支配它。在一个具有模拟偏好的三资源难民重新安置校准中，19%至33%的家庭相对于KDA有所获益，且没有家庭受损，而21%至83%的家庭强烈嫉妒另一个家庭。

英文摘要

Institutions often face constraints richer than a single capacity. Protecting the priority of a student who cannot be accommodated may then block a lower-priority student who fits. We introduce COP-and-Choose, a cumulative offer process followed by a choice step, and show that its greedy version, which skips such blockers, leaves no student worse off than any fair matching or Knapsack Deferred Acceptance (KDA). Greedy is the unique consistent rule preserving this guarantee. With substitutability and size monotonicity at every school, greedy is strategy-proof and Pareto-undominated among strategy-proof mechanisms. If either fails at a school, one additional capacity-one school yields a market where, under every proposal order, greedy is manipulable and no strategy-proof mechanism weakly Pareto dominates it. In a three-resource refugee-resettlement calibration with simulated preferences, 19--33 percent of families gain relative to KDA and none lose, while 21--83 percent strongly envy another family.

发表机构

• Université de Montréal（蒙特利尔大学）
• Washington University in St. Louis（华盛顿大学圣路易斯分校）
• Durham University Business School（杜伦大学商学院）
• Özyeğin University（奥兹耶金大学）

机构由 AI 辅助整理，请以论文原文为准。