Decentralized rationing problems and the proportional rule

Abstract

Decentralized rationing problems are those in which the resource is not directly assigned to agents, but first allocated to groups of agents and then divided among their members. Within this framework, we define the decentralized proportional rule. We characterize it as the only solution that satisfies equal treatment of equals, provided claims are rational numbers. Adding a continuity property the result is extended to the general domain of all decentralized rationing problems. Finally, we prove that the proportional rule is the only solution that assigns the same allocation regardless of whether the resource is distributed directly to agents or in a decentralized manner (with agents grouped).