The asymptotic behavior of the price of anarchy

International audienceThis paper examines the behavior of the price of anarchy as a func- tion of the traffic inflow in nonatomic congestion games with multiple origin- destination (O/D) pairs. Empirical studies in real-world networks show that the price of anarchy is close to 1 in both light and heavy traffic, thus raising the ques- tion: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain bounded away from 1 for all values of the traffic inflow, even in simple three-link networks with a single O/D pair and smooth, convex costs. On the other hand, for a large class of cost functions (including all polynomials), the price of anarchy does converge to 1 in both heavy and light traffic conditions, and irrespective of the network topology and the number of O/D pairs in the network