Three-sided stable matching problem with two of them as cooperative partners

In this paper, three-sided stable matching problem is discussed, in which two sets, $$V_1$$V1 and $$V_2$$V2 are cooperative partners, and the agent of the other set U has a strict preference to the agents of set $$V_1$$V1 and set $$V_2$$V2 respectively. On the other side, the agents of set $$V_1$$V1 and set $$V_2$$V2 have a strict preference to the agent of set U . About this three-sided matching problem, this paper gives the definition of stable matching, proves that the problem must have a stable matching, and gives an algorithm that can obtain a stable matching.