Online Fair Division with Additional Information

TL;DR

This paper explores online fair division of indivisible goods, analyzing how different levels of future information impact achievable fairness guarantees, and introduces algorithms with robustness to prediction errors.

Contribution

It introduces new algorithms and impossibility results for online fair division under various informational assumptions, including normalization and frequency predictions, with learning-augmented robustness.

Findings

Impossibility results for approximate fairness without information.

Algorithms achieving improved fairness with normalization info.

Meta-algorithm matching offline fairness bounds with predictions.

Abstract

We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we investigate how access to future information changes what guarantees are achievable. Without any information, we prove strong impossibility results even for approximate fairness. With normalization information (agents' total values), we provide an algorithm that achieves stronger fairness guarantees than previously known results, and show matching impossibilities for stronger notions. With frequency predictions (value multisets without order), we design a meta-algorithm that lifts a broad class of offline ''share-based'' guarantees to the online setting, matching the best-known offline bounds. Finally, we provide learning-augmented variants of both models: under noisy totals or noisy frequency predictions, our guarantees are robust and degrade gracefully with the error parameters.