Price of anarchy for parallel link networks with generalized mean objective
Kleer,Pieter
Kleer,Pieter
Abstract
The price of anarchy is the most well-known measure for quantifying the inefficiency of equilibrium flows in traffic networks and routing games. In this work, we give unifying price of anarchy bounds for atomic and non-atomic parallel link routing games with polynomial cost functions under various cost objectives including the arithmetic mean, geometric mean and worst-case cost objective. We do this through the study of the generalized p-mean as cost objective, and obtain upper bounds on the price of anarchy in terms of this parameter p. Our bounds unify existing results from the literature, and, in particular, give alternative proofs for price of anarchy results in parallel link routing games with polynomial cost functions under the geometric mean objective obtained by Vinci et al. (ACM Trans Econ Comput 10(2):41, 2022). We recover those simply as a limiting case. To the best of our knowledge, these are the first price of anarchy bounds that capture multiple cost objectives simultaneously in a closed-form expression.
Description
Publisher Copyright: © 2022, The Author(s).
Date
2023-03
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
Organizational Units
Journal Issue
Keywords
Nash equilibrium, wardrop flow, price of anarchy, generalized mean, parallel link networks
Citation
Kleer, P 2023, 'Price of anarchy for parallel link networks with generalized mean objective', OR Spectrum, vol. 45, no. 1, pp. 27-55. https://doi.org/10.1007/s00291-022-00696-7