Bounding the inefficiency of equilibria in nonatomic congestion games

Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a “best possible” outcome. We study a nonatomic version of the congestion games defined by Rosenthal [Int. J. Game Theory 2 (1973) 65], and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players—games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing games.