We study two-sided many-to-one matching markets with transferable utilities, e.g., labor and rental housing markets, in which money can exchange hands between agents, subject to distributional constraints on the set of feasible allocations. In such markets, we establish the efficiency of equilibrium arrangements, specified by an assignment and transfers between agents on the two sides of the market, and study the conditions on the distributional constraints and agent preferences under which equilibria exist. To this end, we first consider the setting when the number of institutions (e.g., firms in a labor market) is one and show that equilibrium arrangements exist irrespective of the nature of the constraint structure or the agents' preferences. However, equilibrium arrangements may not exist in markets with multiple institutions even when agents on each side have linear (or additively separable) preferences over agents on the other side. Thus, for markets with linear preferences, we study sufficient conditions on the constraint structure that guarantee the existence of equilibria using linear programming duality. Our linear programming approach not only generalizes that of Shapley and Shubik (1971) in the one-to-one matching setting to the many-to-one matching setting under distributional constraints but also provides a method to compute market equilibria efficiently.

翻译：我们研究了与可转让公用事业(例如劳动力和租赁住房市场)的双向多对一匹配市场,在这种市场中,资金可以在代理人之间交换手头,但须视一套可行的分配办法的分配限制而定;在这种市场中,我们通过市场两侧的代理人之间的转让和转让,确定均衡安排的效率,研究分配限制的条件和代理商的偏好,根据这些条件存在平衡;为此,我们首先考虑机构的数目(例如劳动力市场中的公司)是一体,并表明不论制约结构的性质或代理人的偏好,均势安排是存在的。然而,即使双方的代理人对另一方的代理人有线性(或连锁的)偏好,我们也可以在多个机构的市场上作出平衡安排。因此,对于有线性偏好市场的市场,我们研究关于保证存在平衡的制约结构的充分条件,利用线性规划双重性双重性。我们的线性方案编制方法不仅概括了Shapley和Shubaik(1971年)的平衡安排办法,而且还在一比一比一比一的市场制约下,为多种市场之间的平衡提供了一种高效率的对比。