拟阵约束下具有无差异关系的顶级交易循环机制

中文摘要 AI 辅助

我们研究了在可能持有初始禀赋且可能对物品无差异的代理人之间重新分配不可分割物品的问题。每个代理人拥有自己的一组可接受物品，而拟阵约束规定了哪些物品组合的分配是可行的。该模型涵盖了房屋市场、无禀赋的新来者参与的房屋分配，以及每个学校在拟阵约束下的学生分配问题。针对这一模型，我们引入了顶级类别交易循环机制（TCTC），该机制将顶级交易循环机制（TTC）扩展到拟阵约束和弱偏好情形。当选择一个交易循环时，TCTC固定每个代理人的顶级无差异类别而非特定物品，并将类别内的选择推迟到最后。TCTC在弱偏好的完整域上满足个体理性、帕累托效率以及弱群体策略证明性，并且其运行时间为多项式时间。当偏好和报告为严格偏好时，TCTC满足强群体策略证明性。结合一个已知的不可能性结果，我们的定理确立了在逐学校约束下，个体理性、帕累托效率和策略证明性成立的最大域。

英文摘要

We study the reallocation of indivisible objects among agents who may hold initial endowments and may be indifferent between objects. Each agent has her own set of admissible objects, and a matroid constraint specifies which combinations of assigned objects are feasible. The model contains the housing market, house allocation with newcomers who hold no endowment, and the assignment of students to schools under matroidal constraints at each school. For this model, we introduce the top-class trading cycles mechanism (TCTC), which extends the top trading cycles mechanism (TTC) to matroid constraints and weak preferences. When a trading cycle is selected, TCTC fixes each agent's top indifference class rather than a specific object and postpones the choice within the class to the end. TCTC is individually rational, Pareto efficient, and weakly group-strategy-proof on the full domain of weak preferences, and it runs in polynomial time. When preferences and reports are strict, TCTC is strongly group-strategy-proof. Together with a known impossibility result, our theorem establishes a maximal domain of school-by-school constraints for individual rationality, Pareto efficiency, and strategy-proofness.

发表机构

• Chuo University（中央大学）

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