Cooperate or Compete: Coalition Formation in Congestion Games

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 co-operating 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. The major findings are: a) the grand coalition of all players is stable only in certain scenarios; b) interestingly, in more realistic scenarios, the grand coalition is not stable, but other partitions (mostly the ones with only one non-singleton group) are stable or none of the partitions are stable. When none are stable, there is a possibility of cyclic behaviour. Basically the players cycle through different collaborative arrangements constantly in pursuit of better selfish outcomes. In essence, this research discovers the stable partitions when the resources are congestible and the coordination efforts carry a price.