Equilibrium and Potential in Coalitional Congestion Games

TL;DR

This paper investigates conditions under which coalitional congestion games retain the potential game property and have pure Nash equilibria, extending the classical congestion game framework to cooperative settings.

Contribution

It identifies specific conditions that ensure coalitional congestion games are potential games with pure Nash equilibria, addressing a key gap in the literature.

Findings

Conditions for potentiality in coalitional congestion games

Existence of pure Nash equilibria under certain coalition structures

Extension of congestion game theory to cooperative scenarios

Abstract

The model of congestion games is widely used to analyze games related to traffic and communication. A central property of these games is that they are potential games and hence posses a pure Nash equilibrium. In reality it is often the case that some players cooperatively decide on their joint action in order to maximize the coalition's total utility. This is by modeled by Coalitional Congestion Games. Typical settings include truck drivers who work for the same shipping company, or routers that belong to the same ISP. The formation of coalitions will typically imply that the resulting coalitional congestion game will no longer posses a pure Nash equilibrium. In this paper we provide conditions under which such games are potential games and posses a pure Nash equilibrium.