On the Nash Stability in the Hedonic Coalition Formation Games

TL;DR

This paper investigates conditions under which a Nash-stable partition exists in hedonic coalition formation games, introducing the Nash-stable core and showing how relaxed utility sharing can ensure stability.

Contribution

It defines the Nash-stable core and analyzes conditions for its non-emptiness, linking utility sharing methods to stability in hedonic games.

Findings

Relaxed efficiency in utility sharing promotes Nash stability.

Conditions for a non-empty Nash-stable core are characterized.

Theoretical framework for stability in hedonic coalition games.

Abstract

This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the definition of the Nash-stable core. We study the conditions for having a non-empty Nash-stable core. More precisely, we show how relaxed efficiency in utility sharing method allows to ensure a non-empty Nash-stable core.