We provide efficient, fair, and non-manipulable mechanisms for the multi-type resource allocation problems (MTRAs) and multiple assignment problems where agents have partial preferences over bundles consisting of multiple divisible items. We uncover a natural reduction from multiple assignment problems to MTRAs, which preserves the properties of MTRA mechanisms. We extend the well-known random priority (RP) and probabilistic serial (PS) mechanisms to MTRAs with partial preferences as multi-type PS (MPS) and multi-type RP (MRP) and propose a new mechanism, multi-type general dictatorship (MGD), which combines the ideas of MPS and MRP. We show that for the unrestricted domain of partial order preferences, unfortunately, no mechanism satisfies both sd-efficiency and sd-envy-freeness, even as they each satisfy different weaker notions of the desirable properties of efficiency, fairness, and non-manipulability we consider. Notwithstanding this impossibility result, our main message is positive: When agents' preferences are represented by acyclic CP-nets, MRP satisfies ex-post-efficiency, sd-strategyproofness, and upper invariance, while MPS satisfies sd-efficiency, sd-envy-freeness, ordinal fairness, and upper invariance, recovering the properties of RP and PS; the MGD satisfies sd-efficiency, equal treatment of equals, and decomposability under the unrestricted domain of partial preferences. We introduce a natural domain of bundle net preferences, which generalizes previously studied domain restrictions of partial preferences for multiple assignment problems and is incomparable to the domain of acyclic CP-nets. We show that MRP and MPS satisfy all properties of the RP and PS under bundle net preferences as well.

我们为多类型资源分配问题 (MTRA) 和多重分配问题提供高效、公平和不可操纵的机制，其中代理对由多个可分割项目组成的捆绑包有部分偏好。我们发现了从多重分配问题到 MTRA 的自然减少，这保留了 MTRA 机制的特性。我们将众所周知的随机优先级 (RP) 和概率串行 (PS) 机制扩展到具有部分偏好的 MTRA，如多类型 PS (MPS) 和多类型 RP (MRP)，并提出了一种新机制，多类型一般独裁(MGD)，它结合了 MPS 和 MRP 的思想。我们表明，对于偏序偏好的无限制域，不幸的是，没有任何机制可以同时满足 sd-efficiency 和 sd-envy-freeness，即使它们每个都满足我们考虑的效率、公平性和不可操纵性等理想属性的不同较弱概念。尽管存在这种不可能的结果，但我们的主要信息是积极的：当代理人的偏好由非循环 CP-nets 表示时，MRP 满足事后效率、sd-strategyproofness 和上不变性，而 MPS 满足 sd-efficiency、sd-envy-自由性、序数公平性和上不变性，恢复了RP和PS的性质；MGD 满足 sd-efficiency, equal treatment of equals, and decomposability under the unrestricted domain of partial preferences. 我们引入了 bundle net preferences 的自然域，它概括了先前研究的多重分配问题的部分偏好的域限制，并且与非循环 CP-nets 域无法比拟。