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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aigner, M.: Combinatorial Theory. Springer, Heidelberg (1979)
Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near-optimal network design with selfish agents. In: Proc. of the 35th Annual ACM Symp. on Theory of Computing, pp. 511–520 (2003)
Awerbuch, B., Azar, Y., Richter, Y., Tsur, D.: Tradeoffs in worst-case equilibria. In: Solis-Oba, R., Jansen, K. (eds.) WAOA 2003. LNCS, vol. 2909, pp. 41–52. Springer, Heidelberg (2004)
Beckmann, M.J.: On the theory of traffic flow in networks. Traffic Quart 21, 109–116 (1967)
Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press (1956)
Braess, D.: Über ein Paradoxon der Verkehrsplanung. Unternehmensforschung 12, 258–268 (1968)
Czumaj, A.: Selfish routing on the internet. In: Leung, J. (ed.) To appear as a chapter in Handbook of Scheduling: Algorithms, Models, and Performance Analysis, CRC Press, Boca Raton (2004)
Czumaj, A., Krysta, P., Vöcking, B.: Selfish traffic allocation for server farms. In: Proc. of the 34th Annual ACM Symp. on Theory of Computing, pp. 287–296 (2002)
Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. In: Proc. of the 13th Annual ACM-SIAM Symp. on Discrete Algorithms, pp. 413–420 (2002)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proc. of the 22nd Annual Symp. on Principles of Distributed Computing, pp. 347–351 (2003)
Feldmann, R., Gairing, M., Lücking, T., Monien, B., Rode, M.: Nashification and the coordination ratio for a selfish routing game. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 514–526. Springer, Heidelberg (2003)
Feldmann, R., Gairing, M., Lücking, T., Monien, B., Rode, M.: Selfish routing in non-cooperative networks: A survey. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 21–45. Springer, Heidelberg (2003)
Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: The structure and complexity of Nash equilibria for a selfish routing game. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 123–134. Springer, Heidelberg (2002)
Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: Nash equilibria in discrete routing games with convex latency functions. In: Proc. of the 31st Int. Colloq. on Automata, Languages, and Programming (2004) (to appear)
Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Spirakis, P.: Extreme nash equilibria. In: Blundo, C., Laneve, C. (eds.) ICTCS 2003. LNCS, vol. 2841, pp. 1–20. Springer, Heidelberg (2003) Accepted to Theoretical Computer Science
Koutsoupias, E.: Selfish task allocation. Bulletin of the EATCS 81, 79–88 (2003)
Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate equilibria and ball fusion. Theory of Computing Systems 36(6), 683–693 (2003)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Kumar, V.S.A., Marathe, M.V.: Improved results for stackelberg scheduling strategies. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 776–787. Springer, Heidelberg (2002)
Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A new model for selfish routing. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 547–558. Springer, Heidelberg (2004)
Lücking, T., Mavronicolas, M., Monien, B., Rode, M., Spirakis, P., Vrto, I.: Which is the Worst-case Nash Equilibrium? In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 551–561. Springer, Heidelberg (2003)
Mavronicolas, M., Spirakis, P.: The price of selfish routing. In: Proc. of the 33rd Annual ACM Symp. on Theory of Computing, pp. 510–519 (2001)
Milchtaich, I.: Congestion games with player-specific payoff functions. Games and economic behavior 13, 111–124 (1996)
Nash, J.: Non-cooperative games. Annals of Mathematics 54(2), 286–295 (1951)
Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. Int. Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T.: Designing networks for selfish users is hard. In: Proc. of the 42nd Annual Symp. on Foundations of Computer Science, pp. 472–481 (2001)
Roughgarden, T.: Stackelberg scheduling strategies. In: Proc. of the 33rd Annual ACM Symp. on the Theory of Computing, pp. 104–113 (2001)
Roughgarden, T.: The price of anarchy is independent of the network topology. In: Proc. of the 34th Annual ACM Symp. on the Theory of Computing, pp. 428–437 (2002)
Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)
Vazirani, V.: Approximation Algorithms. Springer, Heidelberg (2001)
Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proc. of the Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1956)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-540-28629-5_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22823-3
Online ISBN: 978-3-540-28629-5
eBook Packages: Springer Book Archive