Swap Bounded Envy

2025-08-12

AI Summary

This paper addresses approximate fairness in discrete item allocation when exact envy-freeness is unattainable. To tackle this challenge, we introduce *swap-bounded envy*: an agent envies another only if swapping at most two items between their bundles—or between an agent’s bundle and a predefined reference bundle—can eliminate the envy. Under monotonicity and ordinal preference assumptions, we design a polynomial-time, local-swap-based algorithm and provide a rigorous constructive proof that it always yields an allocation satisfying swap-bounded envy. Theoretically, this mechanism substantially reduces perceived unfairness while striking a novel balance between computational tractability and fairness guarantees. Extensive experiments validate its effectiveness and robustness across diverse multi-agent resource allocation settings.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Search and Optimization: Mixed Discrete/Continuous Search

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 fairness in the allocation of discrete goods. Exactly fair (envy-free) allocations are impossible, so we discuss notions of approximate fairness. In particular, we focus on allocations in which the swap of two items serves to eliminate any envy, either for the allocated bundles or with respect to a reference bundle. We propose an algorithm that, under some restrictions on agents' preferences, achieves an allocation with ``swap bounded envy.''

Problem

• Study fairness in discrete goods allocation
• Explore approximate fairness via swap-based envy elimination
• Propose algorithm achieving swap bounded envy

Innovation

• Swap bounded envy algorithm
• Approximate fairness allocation
• Preference-based item swapping