Control in Hedonic Games

TL;DR

This paper explores how an external actor can influence coalition formation in hedonic games by adding or removing agents to achieve specific control goals, providing a comprehensive complexity analysis.

Contribution

It introduces the study of control problems in hedonic games, analyzing their computational complexity across various stability notions and control actions.

Findings

Complete complexity classifications for control problems in hedonic games.

Control problems vary in complexity depending on preferences and stability concepts.

New insights into how external actions can shape coalition structures.

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.