Stable partitions in additively separable hedonic games

TL;DR

This paper advances understanding of stable partitions in additively separable hedonic games by providing efficient algorithms for some stability concepts and proving NP-hardness for others, highlighting the computational complexity landscape.

Contribution

It introduces a polynomial-time algorithm for contractually individually stable partitions and proves NP-hardness for core existence and related stability checks.

Findings

Polynomial-time algorithm for contractually individually stable partition

NP-hardness of core and strict core existence

coNP-completeness of verifying grand coalition stability

Abstract

An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. In this paper, we solve various open problems concerning the computational complexity of stable partitions in additively separable hedonic games. First, we propose a polynomial-time algorithm to compute a contractually individually stable partition. This contrasts with previous results such as the NP-hardness of computing individually stable or Nash stable partitions. Secondly, we prove that checking whether the core or the strict core exists is NP-hard in the strong sense even if the preferences of the players are symmetric. Finally, it is shown that verifying whether a partition consisting of the grand coalition is contractually strict core stable or Pareto optimal is coNP-complete.