Equilibrium and potential in coalitional congestion games

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. JEL classification: C72

On existence of equilibrium under social coalition structures

“…For a number x, |x| denotes its absolute value, and x denotes the greatest integer smaller than or equal to x. 8 For other related studies on congestion games, seeHayrapetyan et al (2006),Holzman and Law-Yone (1997),Kuniavsky et al (2014), Milchtaich (1996. For applications of RSGs, seeMilinski (1979),Quint and Shubik (1994).…”