本文中提及三種合謀協議。三個參賽者私下達成代理人協議即是由其中一位參賽者為三人的全權代表另兩人形同無意見者；三個參賽者私下達成合夥協議即是參賽者三人彼此為合作夥伴意見一致；三個參賽者私下達成層級式代理人協議即是參賽者三人中一位為第一代表，另一位為第二代表，第三人形同無意見者。一個成功的協議即是參與協議者所得之總利益因達成協議而增加。本文將陳述此二協議下的眾多結論。在加權過半數投票賽局中，每個最小獲益聯盟的參賽者人數多少跟合謀協議的結果有著某種程度的關聯。本文在此方面提出一些結論。 Three kinds of collusion agreements are presented here. Three Players making a proxy agreement means one of the three players acting as a proxy for the others. Three Players making an associated agreement means three players acting on the other's behalf. A new kind of agreements called hierarchy agreement is that there are three players i, j and k with i acting as a proxy for j and k and j acting as another proxy for k without i. A successful agreement means the very three players gaining more benefits from the agreement. Several results in these collusion agreements are obtained. In weighted majority voting games the number of players in every minimal winning coalition leads to different outcomes of collusion agreements.
