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The price of Anarchy in series-parallel network congestion games

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Abstract

We study the inefficiency of pure Nash equilibria in symmetric network congestion games defined over series-parallel networks with affine edge delays. For arbitrary networks, Correa (Math Oper Res 44(4):1286–1303, 2019) proved a tight upper bound of 5/2 on the PoA. On the other hand, for extension-parallel networks, a subclass of series-parallel networks, Fotakis (Theory Comput Syst 47:113–136, 2010) proved that the PoA is 4/3. He also showed that this bound is not valid for series-parallel networks by providing a simple construction with PoA 15/11. Our main result is that for series-parallel networks the PoA cannot be larger than 2, which improves on the bound of 5/2 valid for arbitrary networks. We also construct a class of instances with a lower bound on the PoA that asymptotically approaches 27/19, which improves on the lower bound of 15/11.

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Acknowledgements

We thank the reviewers for their detailed comments and suggestions, that greatly improved the presentation of the paper. We also thank the Associate Editor for suggesting a construction that inspired the derivation of our lower bound on the PoA.

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  1. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, USA

    Bainian Hao & Carla Michini

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  1. Bainian Hao
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  2. Carla Michini
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Correspondence to Bainian Hao.

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Hao, B., Michini, C. The price of Anarchy in series-parallel network congestion games. Math. Program. 203, 499–529 (2024). https://doi.org/10.1007/s10107-022-01803-w

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