The Asymptotic Behavior of the Price of Anarchy
This paper examines the behavior of the price of anarchy as a function 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 question: 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.
R. Colini-Baldeschi and M. Scarsini are members of GNAMPA-INdAM. R. Cominetti and P. Mertikopoulos gratefully acknowledge the support and hospitality of LUISS during a visit in which this research was initiated. R. Cominetti’s research is also supported by FONDECYT 1130564 and Núcleo Milenio ICM/FIC RC130003 “Información y Coordinación en Redes”. P. Mertikopoulos was partially supported by the French National Research Agency (ANR) project ORACLESS (ANR– 16– CE33–0004– 01) and the ECOS/CONICYT Grant C15E03. He gratefully acknowledges the support and hospitality of FONDECYT 1130564 and Núcleo Milenio “Información y Coordinación en Redes”. The authors also gratefully acknowledge financial support from the PGMO grant HEAVY.NET.
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