Social Optimality and Cooperation in Nonatomic Congestion games

Igal Milchtaich

Journal of Economic Theory 114 (), 56–87


Congestion externalities may result in nonoptimal equilibria. For these to occur, it suffices that facilities differ in their fixed utilities or costs. As this paper shows, the only case in which equilibria are always socially optimal, regardless of the fixed components, in that in which the costs increase logarithmically with the size of the set of users. Therefore, achieving a socially optimal choice of facilities generally requires some form of external intervention or cooperation. For heterogeneous populations (in which the fixed utilities or costs vary across users as well as across facilities), this raises the question of utility or cost sharing. The sharing rule proposed in this paper is the Harsanyi transferable-utility value of the game—which is based on the users’ marginal contributions to the bargaining power of coalitions.

JEL classification

C71, C72, D62


Congestion; Cooperation; Nonatomic games; Social optimality; Cost sharing; Harsanyi TU value; Potential