Multilateral funding for global environmental protection, such as biodiversity conservation, requires donor participation. When are donors willing to participate? We examine a game-theoretic model of multilateral funding for environmental projects in developing countries. Donors must first decide whether to participate in a multilateral institution. They do so in anticipation of a bargaining outcome that depends on their participation decisions. The multilateral institution then bargains with a recipient over the distribution of gains from project implementation. We find that the donors' and the recipient's vulnerability to negative environmental externalities have diverging effects on their participation behavior. As donors' vulnerability to negative externalities increases, their bargaining power decreases and fewer donors participate. But as the recipient's vulnerability increases, more donors participate because their bargaining power grows. These findings can illuminate bargaining over multilateral climate finance and inform the design of international institutions.