Competition yields efficiency in load balancing games

We study a nonatomic congestion game with NN parallel links, with each link under the control of a profit maximizing provider. Within this ‘load balancing game’, each provider has the freedom to set a price, or toll, for access to the link and seeks to maximize its own profit. Given prices, a Wardrop equilibrium among users is assumed, under which users all choose paths of minimal and identical effective cost. Within this model we have oligopolistic price competition   which, in equilibrium, gives rise to situations where neither providers nor users have incentives to adjust their prices or routes, respectively. In this context, we provide new results about the existence and efficiency of oligopolistic equilibria. Our main theorem shows that, when the number of providers is small, oligopolistic equilibria can be extremely inefficient; however as the number of providers NN grows, the oligopolistic equilibria become increasingly efficient (at a rate of 1/N1/N) and, as N→∞N→∞, the oligopolistic equilibrium matches the socially optimal allocation.