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A Survey of Uniqueness Results for Selfish Routing

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Book cover Network Control and Optimization (NET-COOP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 4465))

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Abstract

We consider the problem of selfish or competitive routing over a network with flow-dependent costs which is shared by a finite number of users, each wishing to minimize the total cost of its own flow. The Nash Equilibrium is well known to exist for this problem under mild convexity assumptions on the cost function of each user. However, uniqueness requires further conditions, either on the user cost functions or on the network topology. We briefly survey here existing results that pertain to the uniqueness issue. We further consider the mixed Nash-Wardrop problem and propose a common framework that allows a unified treatment of this problem.

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Authors and Affiliations

  1. Department of Electrical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel

    Nahum Shimkin

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  1. Nahum Shimkin
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Tijani Chahed Bruno Tuffin

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© 2007 Springer-Verlag Berlin Heidelberg

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Shimkin, N. (2007). A Survey of Uniqueness Results for Selfish Routing. In: Chahed, T., Tuffin, B. (eds) Network Control and Optimization. NET-COOP 2007. Lecture Notes in Computer Science, vol 4465. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72709-5_4

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  • DOI: https://doi.org/10.1007/978-3-540-72709-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72708-8

  • Online ISBN: 978-3-540-72709-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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