We develop VCG-like mechanisms for resource allocation environments where the players have concave utility functions, and the resource constraints can be represented through convex inequality constraints; multicommodity flow problems are a prime example. Unlike VCG mechanisms that require each player to communicate an entire utility function, our mechanisms only require each player to communicate a single scalar quantity. Despite the limited communication, we establish the existence of an efficient Nash equilibrium. Under some further assumptions, we also establish that all Nash equilibria are efficient. Our approach defines an entire family of resource allocation mechanisms; as a special case, we recover the class of mechanisms recently introduced by Yang and Hajek for a single resource.
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