In an industry where firms compete via supply functions the set of market outcomes that can arise is large. If decreasing supply functions are ruled out, the set of equilibrium outcomes reduces somewhat, but it remains large: any price between the competitive price and the Cournot price can be sustained by a supply function equilibrium. In sharp contrast, this multiplicity disappears when firms take into account the gains they can attain by coordinating their actions: if the number of firms is above a threshold we identify (e.g., three if demand is linear), then the Cournot equilibrium is the unique outcome that can be sustained by a coalition-proof supply function equilibrium
