Cooperate or Compete: Coalition Formation in Congestion Games
Riya Sultana, Veeraruna Kavitha
TL;DR
This work analyzes coalition formation in atomic congestion games where cooperation yields reduced congestion losses but incurs a coordination cost $\beta$. It formulates a partition-form game in which each coalition's worth, $\nu_{\mathcal{C}}^{\mathcal{P}}(\boldsymbol{\phi})$, depends on the partition and the NE of the induced non-cooperative game, with multiple NE complicating anticipation. The authors introduce pessimal anticipation for blocking and derive stability conditions across congestion regimes, showing that grand coalitions are not universally stable and that realistic settings often favor partitions with a single non-singleton group or even no coordination. Numerical analyses illustrate how stability intervals in $\beta$ depend on congestion strength and the distribution of link rewards. Overall, the paper contributes a rigorous framework for understanding when cooperation improves system performance in congestible routing and when coordination costs preclude stable coalitions.
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.