Mechanism Design for Fair Division: Allocating Divisible Items without Payments

We revisit the classic problem of fair division from a mechanism design perspective, using Proportional Fairness as a benchmark. In particular, we aim to allocate a collection of divisible items to a set of agents while incentivizing the agents to be truthful in reporting their valuations. For the very large class of homo-geneous valuations, we design a truthful mechanism that provides every agent with at least a 1/e â\u89\u88 0.368 fraction of her Proportionally Fair valuation. To complement this result, we show that no truthful mecha-nism can guarantee more than a 0.5 fraction, even for the restricted class of additive linear valuations. We also propose another mechanism for additive linear valuations that works really well when every item is highly demanded. To guarantee truthfulness, our mechanisms discard a carefully chosen fraction of the al-located resources; we conclude by uncovering interesting connections between our mechanisms and known mechanisms that use money instead