In the celebrated stable-matching problem, there are two sets of agents M and W, and the members of M only have preferences over the members of W and vice versa. It is usually assumed that each member of M and W is a single entity. However, there are many cases in which each member of M or W represents a team that consists of several individuals with common interests. For example, students may need to be matched to professors for their final projects, but each project is carried out by a team of students. Thus, the students first form teams, and the matching is between teams of students and professors. When a team is considered as an agent from M or W, it needs to have a preference order that represents it. A voting rule is a natural mechanism for aggregating the preferences of the team members into a single preference order. In this paper, we investigate the problem of strategic voting in the context of stable-matching of teams. Specifically, we assume that members of each team use the Borda rule for generating the preference order of the team. Then, the Gale-Shapley algorithm is used for finding a stable-matching, where the set M is the proposing side. We show that the single-voter manipulation problem can be solved in polynomial time, both when the team is from M and when it is from W. We show that the coalitional manipulation problem is computationally hard, but it can be solved approximately both when the team is from M and when it is from W.

翻译：在著名的稳定匹配问题中，存在两个代理人集合M和W，M中的成员仅对W中的成员有偏好，反之亦然。通常假设M和W的每个成员均为单一实体。然而在许多情况下，M或W的每个成员代表一个由若干具有共同利益的个体组成的团队。例如，学生需要与教授匹配以完成最终项目，但每个项目由学生团队执行。因此，学生首先组成团队，匹配发生在学生团队与教授之间。当团队被视为M或W中的代理人时，需要具有代表其偏好的偏好序。投票规则是将团队成员偏好聚合为单一偏好序的自然机制。本文研究团队稳定匹配背景下的策略投票问题。具体而言，我们假设每个团队成员使用博达规则生成团队的偏好序，然后采用盖尔-沙普利算法（以M为提议方）寻找稳定匹配。我们证明：无论团队来自M还是W，单投票者操纵问题均可在多项式时间内求解；联盟操纵问题在计算上是困难的，但无论团队来自M还是W均可近似求解。