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 following question: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain a positive distance 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) and inflow patterns, the price of anarchy does converge to 1 in both heavy and light traffic, irrespective of the network topology and the number of O/D pairs in the network. We also examine the rate of convergence of the price of anarchy, and we show that it follows a power law whose degree can be computed explicitly when the network’s cost functions are polynomials.

When is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic / Colini Baldeschi, Riccardo; Cominetti, Roberto; Mertikopoulos, Panayotis; Scarsini, Marco. - In: OPERATIONS RESEARCH. - ISSN 0030-364X. - 68:2(2020), pp. 411-434. [10.1287/opre.2019.1894]

When is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic

Colini-Baldeschi, Riccardo;Scarsini, Marco
2020

Abstract

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 following question: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain a positive distance 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) and inflow patterns, the price of anarchy does converge to 1 in both heavy and light traffic, irrespective of the network topology and the number of O/D pairs in the network. We also examine the rate of convergence of the price of anarchy, and we show that it follows a power law whose degree can be computed explicitly when the network’s cost functions are polynomials.
nonatomic congestion games, price of anarchy, light traffic, heavy traffic, regular variation
When is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic / Colini Baldeschi, Riccardo; Cominetti, Roberto; Mertikopoulos, Panayotis; Scarsini, Marco. - In: OPERATIONS RESEARCH. - ISSN 0030-364X. - 68:2(2020), pp. 411-434. [10.1287/opre.2019.1894]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/193296
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