This paper considers the multilateral matching market, where two or more agents can make a contract on a joint venture multilaterally. The possible joint ventures are exogenously given, and the preference relation of each agent is represented by a quasilinear utility function consisting of the valuation on the joint venture and the monetary transfer. We investigate three stability concepts: the weak setwise stable outcome, the stable outcome, and the strongly group stable outcome. We show that if the structure of the possible joint ventures satisfies a condition called the acyclicity, then these three stability concepts are equivalent with each other, are efficient, and exist for any continuous valuation functions. We also show that the acyclicity is necessary to guarantee the equivalence and the efficiency of the stability concepts for any continuous and concave valuation functions. For the existence, the acyclicity is is a necessary condition for the stable and the strongly group stable outcomes. On the other hand, we need an additional condition to obtain a necessary condition for the existence of the weakly setwise stable outcome.