Fair Allocation of Indivisible Goods to Asymmetric Agents

We study fair allocation of indivisible goods to agents with unequal entitlements. Our emphasis is on the case where the goods are indivisible and agents have unequal entitlements. This problem is a generalization of the work by Procaccia and Wang [14] wherein the agents are assumed to be symmetric. We show that, in some cases with n agents, no allocation can guarantee better than 1/n approximation of a fair allocation when the entitlements are not necessarily equal. Furthermore, we devise a simple algorithm that ensures a 1/n approximation guarantee.