An effective innovation effort for ‘global challenges’ must be multilateral, because the outcomes will be globally shared, highly uncertain, and very large-scale. At present we lack a framework for organizing such multilateral collaboration. Global challenges relate to the consumption of ‘common-pool’ or ‘common property’ resources. It is often held that such resources involve a ‘tragedy of the commons’ for which the proposed solutions are usually full state control or privatization. However, the late Elinor Ostrom argued that the state/market approach to the commons is flawed conceptually and empirically. In multiple studies she showed that resources are often managed collectively through negotiation and collaboration among ‘polycentric’ agents. This paper aims to outline the conceptual approach, to suggest that it can be scaled up to the world level as an approach to the global challenges, and to propose an agenda for research on major innovation challenges involved.