Abstract
In this work, we consider an interesting variant of the well-studied KP model [18] for selfish routing that reflects some influence from the much older Wardrop model [31]. In the new model, user traffics are still unsplittable, while social cost is now the expectation of the sum, over all links, of a certain polynomial evaluated at the total latency incurred by all users choosing the link; we call it polynomial social cost. The polynomials that we consider have non-negative coefficients. We are interested in evaluating Nash equilibria in this model, and we use the Price of Anarchy as our evaluation measure. We prove the Fully Mixed Nash Equilibrium Conjecture for identical users and two links, and establish an approximate version of the conjecture for arbitrary many links. Moreover, we give upper bounds on the Price of Anarchy.
This work has been partially supported by the DFG-Sonderforschungsbereich 376 Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen, by the EU within the 6th Framework Programme under contract 001907 “Dynamically Evolving, Large Scale Information Systems” (DELIS), by research funds at University of Cyprus, and by the VEGA grant No. 2/3164/23.
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Gairing, M., Lücking, T., Mavronicolas, M., Monien, B. (2004). The Price of Anarchy for Polynomial Social Cost. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_44
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