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Price of anarchy for parallel link networks with generalized mean objective

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  • Pieter Kleer

    (Tilburg University)

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.

Suggested Citation

  • Pieter Kleer, 2023. "Price of anarchy for parallel link networks with generalized mean objective," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 27-55, March.
    • Handle: RePEc:spr:orspec:v:45:y:2023:i:1:d:10.1007_s00291-022-00696-7
    DOI: 10.1007/s00291-022-00696-7
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    References listed on IDEAS

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    1. Thanasis Lianeas & Evdokia Nikolova & Nicolas E. Stier-Moses, 2019. "Risk-Averse Selfish Routing," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 38-57, February.
    2. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    3. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    4. Harks, Tobias & Schröder, Marc & Vermeulen, Dries, 2019. "Toll caps in privatized road networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 947-956.
    5. Pradeep Dubey, 1986. "Inefficiency of Nash Equilibria," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 1-8, February.
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