We consider a general multi-principal multi-agent contracting game in a complete-information supply-chain setting and determine coordinating equilibrium transfer schedules in closed form. The resulting contracts manage to align incentives for decentralized decision-making and achieve first-best channel solutions. We allow for multidimensional actions and arbitrary payoff externalities between all members of the supply chain. For the coordinating contracts to exist it suffices that all payoff

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... ctions are continuous on the compact action sets in a general sense that accommodates discrete action sets. Our approach unifies and generalizes a significant portion of the extant supply-chain literature. It can be applied to a very large class of many-to-many supply-chain settings.