Fair Division via Resource Augmentation

A research team from multiple institutions including Hannaneh Akrami, Amos Fiat, and six other authors has published groundbreaking work on algorithmic fairness, introducing the formal concept of 'resource augmentation' for maximin share (MMS) allocation of indivisible goods. Their paper, 'Fair Division via Resource Augmentation,' addresses a fundamental problem in multi-agent AI systems: how many additional copies of resources are needed to guarantee each agent receives at least their fair share according to MMS criteria. The research establishes that for general monotone valuations, an exact MMS allocation can be guaranteed using at most Θ(m/e) total copies, where m represents the number of goods, and proves this bound is tight even for XOS valuations—a significant advancement in fair division theory.

The technical contributions reveal important separations between valuation classes: additive valuations require at most min{n-2, ⌊m/3⌋(1+o(1))} distinct copies, while submodular valuations may need n-1 copies, establishing a clear computational hierarchy. The team also demonstrates practical approximation tradeoffs, showing that ⌊n/2⌋ copies suffice for a 6/7-approximation to original MMS, and ⌊n/3⌋ copies achieve a 4/5-approximation—both improvements over best-known guarantees without copies. By connecting MMS with copies to the 1-out-of-d MMS framework, the research provides the first impossibility results for that relaxed notion while creating translation mechanisms between fairness frameworks. These mathematical foundations enable more equitable AI systems for resource allocation in cloud computing, task assignment, and multi-agent coordination.