Cooperate or Compete: Coalition Formation in Congestion Games

Abstract: This paper investigates the potential benefits of cooperation in scenarios where finitely many agents compete for shared resources, leading to congestion and thereby reduced rewards. By appropriate coordination the members of the cooperating group (a.k.a., coalition) can minimize the congestion losses due to inmates, while efficiently facing the competition from outsiders (coalitions indulge in a non-cooperative congestion game). The quest in this paper is to identify the stable partition of coalitions that are not challenged by a new coalition. In contrast to the traditional cooperative games, the worth of a coalition in our game also depends upon the arrangement of the opponents. Every arrangement leads to a partition and a corresponding congestion game; the resultant Nash equilibria (NEs) dictate the `worth'. The analysis is further complicated due to the presence of multiple NEs for each such game.