Advertisement

A New Model for Selfish Routing

  • Thomas Lücking
  • Marios Mavronicolas
  • Burkhard Monien
  • Manuel Rode
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2996)

Abstract

In this work, we introduce and study a new model for selfish routing over non-cooperative networks that combines features from the two such best studied models, namely the KP model and the Wardrop model in an interesting way.

We consider a set of nusers, each using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links. In a Nash equilibrium, no user can increase its Individual Cost by unilaterally deviating from its strategy. To evaluate the performance of such Nash equilibria, we introduce Quadratic Social Cost as a certain sum of Individual Costs – namely, the sum of the expectations of the squares of the incurred link latencies. This definition is unlike the KP model, where Maximum Social Cost has been defined as the maximum of Individual Costs.

We analyse the impact of our modeling assumptions on the computation of Quadratic Social Cost, on the structure of worst-case Nash equilibria, and on bounds on the Quadratic Coordination Ratio.

Keywords

Nash Equilibrium Mixed Strategy Pure Strategy Link Capacity Social Optimum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation Schemes for Scheduling. In: Proc. of SODA 1997, pp. 493–500 (1997)Google Scholar
  2. 2.
    Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-Optimal Network Design with Selfish Agents. In: Proc. of STOC 2003, pp. 511–520 (2003)Google Scholar
  3. 3.
    Beckmann, M.J.: On the Theory of Traffic Flow in Networks. Traffic Quart. 21, 109–116 (1967)Google Scholar
  4. 4.
    Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)Google Scholar
  5. 5.
    Braess, D.: Über ein Paradoxen aus der Verkehrsplanung. Unternehmensforschung 12, 258–268 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chandra, A.K., Wong, C.K.: Worst-case Analysis of a Placement Algorithm Related to Storage Allocation. SICOMP 4, 249–263 (1975)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Competitive Routing in Networks with Polynomial Costs. IEEE Transactions on Automatic Control 47, 92–96 (2002)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Cody, R.A., Coffman Jr., E.G.: Record Allocation for Minimizing Expected Retrieval Costs on Crum-Like Storage Devices. JACM 23, 103–115 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Czumaj, A., Vöcking, B.: Tight Bounds for Worst-Case Equilibria. In: Proc. of SODA 2002, pp. 413–420 (2002)Google Scholar
  10. 10.
    Czumaj, A., Krysta, P., Vöcking, B.: Selfish Traffic Allocation for Server Farms. In: Proc. of STOC 2002, pp. 287–296 (2002)Google Scholar
  11. 11.
    Dafermos, S.C., Sparrow, F.T.: The Traffic Assignment Problem for a General Network. Journal of Research of the National Bureau of Standards, Series B 73B, 91–118 (1969)MathSciNetGoogle Scholar
  12. 12.
    Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence Time to Nash Equilibria. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 502–513. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a Network Creation Game. In: Proc. of PODC 2003, pp. 347–351 (2003)Google Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Spirakis, P.: The Structure and Complexity of Extreme Nash Equilibria (2003) (submitted for publication)Google Scholar
  18. 18.
    Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate Equilibria and Ball Fusion. In: Proc. of SIROCCO 2002, pp. 223–235 (2002)Google Scholar
  19. 19.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    Leung, J.Y.T., Wei, W.D.: Tighter Bounds on a Heuristic for a Partition Problem. Information Processing Letters 56, 51–57 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Lücking, T., Mavronicolas, M., Monien, B., Rode, M., Spirakis, P., Vrto, I.: Which is the Worst-case Nash equilibrium? In: Rovan, B., Vojtas, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 551–561. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  22. 22.
    Mavronicolas, M., Spirakis, P.: The Price of Selfish Routing. In: Proc. of STOC 2001, pp. 510–519 (2001)Google Scholar
  23. 23.
    Nash, J.F.: Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences 36, 48–49 (1950)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Nash, J.F.: Non-cooperative Games. Annals of Mathematics 54(2), 286–295 (1951)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  26. 26.
    Papadimitriou, C.H.: Algorithms, Games and the Internet. In: Proc. of STOC 2001, pp. 749–753 (2001)Google Scholar
  27. 27.
    Roughgarden, T.: The Price of Anarchy is Independent of the Network Topology. In: Proc. of STOC 2002, pp. 428–437 (2002)Google Scholar
  28. 28.
    Roughgarden, T.: Selfish Routing, Ph. D. Thesis, Department of Computer Science, Cornell University (May 2002)Google Scholar
  29. 29.
    Roughgarden, T., Tardos, É.: How Bad is Selfish Routing? JACM 49, 236–259 (2002)CrossRefMathSciNetGoogle Scholar
  30. 30.
    Wardrop, J.G.: Some Theoretical Aspects of Road Traffic Research. In: Proceedings of the of the Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1952)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Lücking
    • 1
  • Marios Mavronicolas
    • 2
  • Burkhard Monien
    • 1
  • Manuel Rode
    • 1
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Department of Computer ScienceUniversity of CyprusNicosiaCyprus

Personalised recommendations