Individual Rationality in Constrained Hedonic Games: Additively Separable and Fractional Preferences

2026-03-23

AI Summary

This study investigates the existence of individually rational coalition partitions in hedonic games where the number of coalitions is exactly \(k\) and coalition sizes are constrained. Focusing on additively separable and fractional preference models, the work employs graph-theoretic modeling, combinatorial optimization, and computational complexity analysis—leveraging the structure of preference graphs—to systematically delineate the boundary between tractable and intractable instances. The research establishes a complete complexity landscape for the existence of individually rational outcomes under strong constraints, identifies several non-trivial yet efficiently solvable cases, and determines precise infeasibility thresholds, thereby providing foundational theoretical insights into stable coalition formation in resource- or size-constrained environments.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Preferences

Application Category

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

Abstract

Hedonic games are an archetypal problem in coalition formation, where a set of selfish agents want to partition themselves into stable coalitions. In this work, we focus on two natural constraints on the possible outcomes. First, we require that exactly k coalitions are created. Then, loosely following the model of Bilò et al. (AAAI 2022), we assume that each of the k coalitions is additionally associated with a lower and upper bound on its size. The notion of stability that we study is that of individual rationality (IR), which requires that no agent strictly prefers to be alone compared to being in his or her coalition. Although IR is trivially satisfiable even in the most general models of hedonic games, the complexity picture of deciding whether an IR allocation exists, considering the above constraints, is unexpectedly rich. We reveal that tractable fragments of this computational problem require surprisingly nontrivial arguments, even if we restrict ourselves to additively separable and fractional hedonic games. Our tractability results, achieved by exploiting the structure of the underlying preference graph, are also complemented by their intractability counterparts, painting a fairly complete picture of the tractability landscape of this problem.

Problem

• Hedonic Games
• Individual Rationality
• Coalition Formation
• Additively Separable Preferences
• Fractional Preferences

Innovation

• constrained hedonic games
• individual rationality
• coalition formation
• computational complexity
• additively separable preferences