This paper studies many-to-one assignment markets, or matching markets with wages. Although it is well-known that the core of this model is non-empty, the structure of the core has not been fully investigated. To the known dissimilarities with the one-to-one assignment game, we add that the bargaining set does not coincide with the core and the kernel may not be included in the core. Besides, not all extreme core allocations can be obtained by means of a lexicographic maximization or a lexicographic minimization procedure, as it is the case in the one-to-one assignment game. The maximum and minimum competitive salaries are characterized in two ways: axiomatically and by means of easily verifiable properties of an associated directed graph. Regarding the remaining extreme core allocations of the many-to-one assignment game, we propose a lexicographic procedure that, for each order on the set of workers, sequentially maximizes or minimizes each worker's competitive salary. This procedure provides all extreme vectors of competitive salaries, that is all extreme core allocations.

翻译：本文研究多对一分配市场，即带有工资的匹配市场。尽管该模型的核心非空是众所周知的，但核心的结构尚未得到充分研究。针对其与一对一分配博弈已知的差异，我们补充指出：议价集与核心并不重合，且核可能不包含在核心内。此外，并非所有极端核心分配都能通过词典序最大化或最小化程序得到（而在一对一分配博弈中这是可行的）。本文从两个角度刻画最大和最小竞争性工资：公理化方法以及通过关联有向图的可验证性质。关于多对一分配博弈中剩余的极端核心分配，我们提出一种词典序程序：该程序针对工人集合的每种顺序，依次最大化或最小化每位工人的竞争性工资。该程序可给出所有竞争性工资的极端向量，即所有极端核心分配。