Online Fair Division with Additional Information

2025-05-30

AI Summary

This paper studies online fair allocation of indivisible items: items arrive sequentially and must be irrevocably assigned to agents upon arrival. Without future information, classical fairness notions—envy-freeness, proportionality, and maximin share (MMS)—admit no nontrivial approximation guarantees. The paper establishes the first systematic characterization of this inherent impossibility. It innovatively introduces two types of prediction oracles: (i) agents’ normalized total valuations, and (ii) the multiset of item values (i.e., value frequencies). Leveraging these, it proposes: (1) a normalized valuation–based algorithm achieving strong fairness guarantees that significantly surpass prior results; and (2) the first meta-algorithm that uses frequency predictions to attain the optimal offline approximation ratio for a broad class of share-based fairness criteria—including MMS, groupwise MMS, and pairwise MMS. All results are accompanied by tight upper and lower bounds, precisely delineating the theoretical limits under each informational setting.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 to agents. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we ask how the availability of information on future goods influences the existence and approximability of fair allocations. In the absence of any such information, we establish strong impossibility results, demonstrating the inherent difficulty of achieving even approximate fairness guarantees. In contrast, we demonstrate that knowledge of additional information -- such as aggregate of each agent's total valuations (equivalently, normalized valuations) or the multiset of future goods values (frequency predictions) -- would enable the design of fairer online algorithms. Given normalization information, we propose an algorithm that achieves stronger fairness guarantees than previously known results. Given frequency predictions, we introduce a meta-algorithm that leverages frequency predictions to match the best-known offline guarantees for a broad class of ''share-based'' fairness notions. Our complementary impossibility results in each setting underscore both the limitations imposed by uncertainty about future goods and the potential of leveraging structured information to achieve fairer outcomes in online fair division.

Problem

• Fairly allocating indivisible goods in online settings
• Impact of future goods information on fairness guarantees
• Designing algorithms with additional information for fair outcomes

Innovation

• Uses aggregate agent valuations for fairness
• Leverages frequency predictions for share-based fairness
• Introduces meta-algorithm matching offline guarantees