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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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
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