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International Symposium on Algorithmic Game Theory

SAGT 2017: Algorithmic Game Theory pp 147–159Cite as

Reconciling Selfish Routing with Social Good

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10504))

Abstract

Selfish routing is a central problem in algorithmic game theory, with one of the principal applications being that of routing in road networks. Inspired by the emergence of routing technologies and autonomous driving, we revisit selfish routing and consider three possible outcomes of it: (i) \(\theta \)-Positive Nash Equilibrium flow, where every path that has non-zero flow on all of its edges has cost no greater than \(\theta \) times the cost of any other path, (ii) \(\theta \)-Used Nash Equilibrium flow, where every used path that appears in the path flow decomposition has cost no greater than \(\theta \) times the cost of any other path, and (iii) \(\theta \)-Envy Free flow, where every path that appears in the path flow decomposition has cost no greater than \(\theta \) times the cost of any other path in the path flow decomposition. We first examine the relations of these outcomes among each other and then measure their possible impact on the network’s performance. Right after, we examine the computational complexity of finding such flows of minimum social cost and give a range for \(\theta \) for which this task is easy and a range of \(\theta \) for which this task is NP-hard for the concepts of \(\theta \)-Used Nash Equilibrium flow and \(\theta \)-Envy Free flow. Finally, we propose strategies which, in a worst-case approach, can be used by a central planner in order to provide good \(\theta \)-flows.

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Notes

  1. 1.

    The concept of fairness in selfish routing has been considered in the past, with the two main approaches defining fairness as: (1) the ratio of the maximum path delay in a given flow to the average delay under Nash equilibrium [20] and (2) the ratio of the maximum path delay to the minimum path delay in a given flow [11].

  2. 2.

    In the literature, PNE is typically used for abbreviating Pure Nash Equilibrium, but we always use it to denote Positive Nash Equilibrium, as defined here.

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Acknowledgements

This work was supported in part by NSF grant numbers CCF-1216103, CCF-1350823 and CCF-1331863. Part of the research was performed while a subset of the authors were at the Simons Institute in Berkeley, CA in Fall 2015.

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Authors and Affiliations

  1. The University of Texas at Austin, Austin, USA

    Soumya Basu, Ger Yang, Thanasis Lianeas, Evdokia Nikolova & Yitao Chen

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  1. Soumya Basu
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  2. Ger Yang
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  3. Thanasis Lianeas
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  4. Evdokia Nikolova
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  5. Yitao Chen
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Correspondence to Soumya Basu .

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Editors and Affiliations

  1. University of Salento, Lecce, Italy

    Vittorio Bilò

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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Basu, S., Yang, G., Lianeas, T., Nikolova, E., Chen, Y. (2017). Reconciling Selfish Routing with Social Good. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-66700-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66699-0

  • Online ISBN: 978-3-319-66700-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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