Metric Hedonic Games on the Line

2026-02-05

AI Summary

This study investigates a class of hedonic games based on linear metric distances, where agents possess type values and the cost of a coalition is determined by the disparity among members’ types—such as maximum, average, or threshold distance—making it applicable to scenarios like team formation in sports or clustering along political spectra. By introducing a novel variant of this model and analyzing both swap and jump stability, the work systematically examines the existence of stable coalition structures, the Price of Anarchy (PoA), the Price of Stability (PoS), and the impact of constraints on the number of coalitions. The main contributions establish that stable outcomes always exist and reveal that their social efficiency critically depends on the specific cost function and structural constraints, yielding rich and often counterintuitive trade-offs between stability and efficiency.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Hedonic games are fundamental models for investigating the formation of coalitions among a set of strategic agents, where every agent has a certain utility for every possible coalition of agents it can be part of. To avoid the intractability of defining exponentially many utilities for all possible coalitions, many variants with succinct representations of the agents'utility functions have been devised and analyzed, e.g., modified fractional hedonic games by Monaco et al. [JAAMAS 2020]. We extend this by studying a novel succinct variant that is related to modified fractional hedonic games. In our model, each agent has a fixed type-value and an agent's cost for some given coalition is based on the differences between its value and those of the other members of its coalition. This allows to model natural situations like athletes forming training groups with similar performance levels or voters that partition themselves along a political spectrum. In particular, we investigate natural variants where an agent's cost is defined by distance thresholds, or by the maximum or average value difference to the other agents in its coalition. For these settings, we study the existence of stable coalition structures, their properties, and their quality in terms of the price of anarchy and the price of stability. Further, we investigate the impact of limiting the maximum number of coalitions. Despite the simple setting with metric distances on a line, we uncover a rich landscape of models, partially with counter-intuitive behavior. Also, our focus on both swap stability and jump stability allows us to study the influence of fixing the number and the size of the coalitions. Overall, we find that stable coalition structures always exist but that their properties and quality can vary widely.

Problem

• Hedonic Games
• Metric Space
• Coalition Formation
• Stability
• Price of Anarchy

Innovation

• Metric Hedonic Games
• Coalition Formation
• Stability Analysis
• Price of Anarchy
• Succinct Utility Representation