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 extensions of the constrained equal awards, the constrained equal losses and the proportional rules. We show that the first two rules do not preserve certain essential properties and prove the conditions under which both rules do preserve those properties. We characterize the extension of the proportional rule as the only solution that satisfies individual equal treatment of equals. 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). Finally, we analyse a strategic game based on decentralized rationing problems in which agents can move freely across groups to submit their claims.