学校选择问题中的有效匹配

中文摘要

学校选择中的稳定匹配未必是帕累托有效的，并可能使数千名学生处于本可避免的较差境地。若不存在任何匹配，能够使至少一名优先权被 μ 违反的学生处境改善，同时又不违反任何处境变差的学生的优先权，则称匹配 μ 为优先权中性的；这里，处境的改善或变差均相对于 μ 而言。若一个匹配既是优先权中性的，又是帕累托有效的，则称其为优先权有效的。我们证明，存在唯一的优先权有效匹配，且它帕累托支配每一个优先权中性匹配和每一个稳定匹配。此外，在选择该优先权有效匹配的机制中，如实申报是每位学生的最大最小最优策略。

Abstract

Stable matchings in school choice needn’t be Pareto efficient and can leave thousands of students worse off than necessary. Call a matching μ priority-neutral if no matching can make any student whose priority is violated by μ better off without violating the priority of some student who is made worse off. Call a matching priority-efficient if it is priority-neutral and Pareto efficient. We show that there is a unique priority-efficient matching and that it dominates every priority-neutral matching and every stable matching. Moreover, truth-telling is a maxmin optimal strategy for every student in the mechanism that selects the priority-efficient matching. (JEL C78, I21, I28)