Fairness in Repeated Matching: A Maximin Perspective

2025-10-06

AI Summary

This paper studies long-term fairness optimization in multi-round repeated matching, focusing on the worst-off agent. It introduces two fairness notions: “anytime optimality” (guaranteeing utility for the most disadvantaged agent in each round) and “global optimality” (maximizing the cumulative utility of the worst-off agent across all rounds). As the problem is NP-hard, the authors characterize structural properties of Pareto-optimal matchings and establish a novel theoretical framework for fair matching. They design algorithms with both theoretical guarantees and practical applicability: a constant-factor approximation algorithm, a fixed-parameter tractable exact algorithm, and identify polynomial-time solvable special cases—e.g., sequential single-peaked preferences. Experimental results demonstrate effective trade-offs between fairness and efficiency. The proposed methods provide deployable computational tools for dynamic resource allocation under fairness constraints.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.

Problem

• Maximizes utility for least advantaged agents in repeated matching
• Addresses computational intractability of optimal sequential matchings
• Develops approximation algorithms for fair multi-round allocations

Innovation

• Maximin utility optimization for repeated matching
• Approximation algorithms for computationally intractable problems
• Fixed-parameter tractable algorithms for special cases