Hedonic Games with Graph-restricted Communication

TL;DR

This paper explores the complexity of stable coalition formations in hedonic games constrained by graph structures, introducing new algorithms and stability concepts, with efficient solutions on specific graph types but hardness results in general cases.

Contribution

It provides an efficient algorithm for finding individually stable partitions on acyclic graphs and introduces in-neighbor stability, analyzing its computational complexity across different graph structures.

Findings

Efficient algorithm for individually stable partitions on acyclic graphs

Polynomial-time solution for in-neighbor stability on paths

NP-hardness results for trees and PLS-hardness for symmetric games

Abstract

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the complexity of finding stable outcomes in such games, for several notions of stability. In particular, we provide an efficient algorithm that finds an individually stable partition for an arbitrary hedonic game on an acyclic graph. We also introduce a new stability concept -in-neighbor stability- which is tailored for our setting. We show that the problem of finding an in-neighbor stable outcome admits a polynomial-time algorithm if the underlying graph is a path, but is NP-hard for arbitrary trees even for additively separable hedonic games; for symmetric additively separable games we obtain a PLS-hardness result.