We study a fair division setting in which participants are to be fairly distributed among teams, where not only do the teams have preferences over the participants as in the canonical fair division setting, but the participants also have preferences over the teams. We focus on guaranteeing envy-freeness up to one participant (EF1) for the teams together with a stability condition for both sides. We show that an allocation satisfying EF1, swap stability, and individual stability always exists and can be computed in polynomial time, even when teams may have positive or negative values for participants. When teams have nonnegative values for participants, we prove that an EF1 and Pareto optimal allocation exists and, if the valuations are binary, can be found in polynomial time. We also show that an EF1 and justified envy-free allocation does not necessarily exist, and deciding whether such an allocation exists is computationally difficult.

翻译：本文研究一种公平分配场景，其中参与者需被公平分配至多个团队。与经典公平分配设定不同，该场景不仅团队对参与者存在偏好，参与者对团队也存在偏好。我们重点关注在保证团队满足"除一人外无嫉妒"（EF1）性质的同时，实现双方稳定性条件。研究表明，即使团队对参与者可能持有正值或负值估值，同时满足EF1、交换稳定性与个体稳定性的分配方案始终存在，且可在多项式时间内计算得出。当团队对参与者持有非负估值时，我们证明存在同时满足EF1与帕累托最优的分配方案；若估值为二元形式，则可在多项式时间内找到该方案。此外，我们证明同时满足EF1与正当无嫉妒性质的分配方案未必存在，且判定此类方案是否存在是计算困难的。