We consider an allocation problem of multiple types of objects to agents, where each type of object has multiple copies (e.g., multiple seats in a school), each agent is endowed with an object, and some distributional constraints are imposed on the allocation (e.g., minimum/maximum quotas). We develop two mechanisms that are strategyproof, feasible (they always satisfy distributional constraints), and individually rational, assuming the distributional constraints are represented by an M-convex set. One mechanism, based on Top Trading Cycles, is Pareto efficient; the other, which belongs to the mechanism class specified by Kojima et al. [1], satisfies a relaxed fairness requirement. The class of distributional constraints we consider contains many situations raised from realistic matching problems, including individual minimum/maximum quotas, regional maximum quotas, type-specific quotas, and distance constraints. Finally, we experimentally evaluate the performance of these mechanisms by a computer simulation.

我们考虑多种类型的对象到代理的分配问题，其中每种类型的对象都有多个副本（例如，学校中的多个座位），每个代理被赋予一个对象，并且对分配施加一些分布约束（例如，最小/最大配额）。我们开发了两种机制，它们是策略证明的、可行的（它们总是满足分布约束）和个体理性的，假设分布约束由 M-凸集表示。一种基于顶级交易周期的机制是帕累托有效的；另一个属于Kojima等人指定的机制类。[1]，满足宽松的公平要求。我们考虑的分布约束类别包含许多从现实匹配问题中提出的情况，包括个人最小/最大配额，区域最大配额、特定类型配额和距离限制。最后，我们通过计算机模拟实验评估这些机制的性能。