Control in Hedonic Games

2026-02-18

AI Summary

This study investigates the computational complexity of controlling coalition formation in hedonic games through external manipulation by adding or deleting agents. Focusing on three natural objectives—preventing a specific agent from being isolated, ensuring a given pair of agents belong to the same coalition, and enforcing the grand coalition—the work systematically characterizes the complexity landscape of six control problems under friend-oriented and additively separable preference models. By integrating computational complexity theory with multiple stability notions—including individual rationality, individual stability, Nash stability, and core stability—the paper provides a complete classification of tractability across different combinations of preference structures and stability criteria, delineating precisely which scenarios are solvable in polynomial time and which are NP-hard, thereby filling a significant theoretical gap in the literature on hedonic game control.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

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
• Social Networks and Social Media: Computational social science

Abstract

We initiate the study of control in hedonic games, where an external actor influences coalition formation by adding or deleting agents. We consider three basic control goals (1) enforcing that an agent is not alone (NA); (2) enforcing that a pair of agents is in the same coalition (PA); (3) enforcing that all agents are in the same grand coalition (GR), combined with two control actions: adding agents (AddAg) or deleting agents (DelAg). We analyze these problems for friend-oriented and additive preferences under individual rationality, individual stability, Nash stability, and core stability. We provide a complete computational complexity classification for control in hedonic games.

Problem

• hedonic games
• control
• coalition formation
• computational complexity
• stability

Innovation

• hedonic games
• control
• computational complexity
• coalition formation
• stability