We consider a multilateral matching market, where two or more agents can engage in a joint venture via multilateral contracts. Possible joint ventures are exogenously given. We study four stability concepts: stability, weak setwise stability, strong group stability, and setwise stability. We characterize the structure of possible joint ventures that guarantee the efficiency and existence of outcomes satisfying these stability concepts under general preference profiles. Specifically, we show that any stable outcome, weakly setwise stable outcome, and setwise stable outcome are efficient for any preference profile if and only if the structure of possible joint ventures satisfies a condition called the acyclicity. We also show that the acyclicity is a necessary and sufficient condition for the existence of a stable outcome and strongly group stable outcome for any preference profile. Moreover, we show that a weaker condition called the no-crossing property is a necessary and sufficient condition for the existence of a weakly setwise stable outcome and setwise stable outcome for any preference profile.

我们考虑多边匹配市场，其中两个或多个代理可以通过多边合同参与合资企业。可能的合资企业是外生的。我们研究四个稳定性概念：稳定性、弱集合稳定性、强群稳定性和集合稳定性。我们描述了可能的合资企业的结构，这些合资企业保证了在一般偏好配置下满足这些稳定性概念的结果的效率和存在。具体而言，我们表明，当且仅当可能的合资企业的结构满足称为非循环性的条件时，任何稳定结果、弱设定稳定结果和设定稳定结果对任何偏好配置都是有效的。我们还表明，对于任何偏好配置文件，非循环性是存在稳定结果和强组稳定结果的必要和充分条件。此外，我们表明，称为无交叉属性的较弱条件是存在弱设定稳定结果和任何偏好配置文件的设定稳定结果的必要和充分条件。