## 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.

Original language | English |
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Pages (from-to) | 411-434 |

Number of pages | 24 |

Journal | Operations Research |

Volume | 68 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2020 |

Externally published | Yes |

## Keywords

- Heavy traffic
- Light traffic
- Nonatomic congestion games
- Price of anarchy
- Regular variation