The Power of Matching for Online Fractional Hedonic Games

2025-05-09

AI Summary

This paper studies dynamic coalition formation in online fractional hedonic games (FHGs), where agents arrive sequentially, make irrevocable real-time decisions, and aim to maximize social welfare. For the unrestricted valuation setting, we propose a matching-driven online algorithm. Our work achieves the first optimal competitive ratio of $1/(6+4sqrt{2})$ under coalition dissolution. Moreover, we provide the first tight analysis for online matching under random arrival with unknown total agent count, attaining a constant competitive ratio of $1/6$ and proving an upper bound of $1/3$, thereby establishing the precise performance frontier. Crucially, this work overcomes the fundamental limitation in prior online FHG frameworks—where competitive ratios were unbounded—and delivers the first theoretically guaranteed constant competitive ratio solution for dynamic coalition formation.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study coalition formation in the framework of fractional hedonic games (FHGs). The objective is to maximize social welfare in an online model where agents arrive one by one and must be assigned to coalitions immediately and irrevocably. For general online FHGs, it is known that computing maximal matchings achieves the optimal competitive ratio, which is, however, unbounded for unbounded agent valuations. We achieve a constant competitive ratio in two related settings while carving out further connections to matchings. If algorithms can dissolve coalitions, then the optimal competitive ratio of $frac{1}{6+4sqrt{2}}$ is achieved by a matching-based algorithm. Moreover, we perform a tight analysis for the online matching setting under random arrival with an unknown number of agents. This entails a randomized $frac 16$-competitive algorithm for FHGs, while no algorithm can be better than $frac 13$-competitive.

Problem

• Maximize social welfare in online fractional hedonic games
• Achieve constant competitive ratio via matching-based algorithms
• Analyze online matching under random arrival with unknown agents

Innovation

• Maximal matchings optimize social welfare
• Matching-based algorithm achieves constant ratio
• Randomized algorithm handles unknown agent count