Exact Price of Anarchy for Polynomial Congestion Games

  • Sebastian Aland
  • Dominic Dumrauf
  • Martin Gairing
  • Burkhard Monien
  • Florian Schoppmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3884)

Abstract

We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions. The given values also hold for weighted and unweighted network congestion games.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 57–66 (2005)Google Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press (1956)Google Scholar
  4. 4.
    Christodoulou, G., Koutsoupias, E.: On The Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 67–73 (2005)Google Scholar
  6. 6.
    Czumaj, A., Krysta, P., Vöcking, B.: Selfish Traffic Allocation for Server Farms. In: Proc. of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 287–296 (2002)Google Scholar
  7. 7.
    Czumaj, A., Vöcking, B.: Tight Bounds for Worst-Case Equilibria. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 413–420 (2002); Also accepted to Journal of Algorithms as Special Issue of SODA 2002 Google Scholar
  8. 8.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish Unsplittable Flows. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 593–605. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 161–175. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: Computing Nash Equilibria for Scheduling on Restricted Parallel Links. In: Proc. of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), pp. 613–622 (2004)Google Scholar
  11. 11.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: The Price of Anarchy for Polynomial Social Cost. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 574–585. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: Nash Equilibria in Discrete Routing Games with Convex Latency Functions. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 645–657. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Gairing, M., Lücking, T., Monien, B., Tiemann, K.: Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 51–65. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Gairing, M., Monien, B., Tiemann, K.: Selfish Routing with Incomplete Information. In: Proc. of the 17th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA 2005), pp. 203–212 (2005)Google Scholar
  15. 15.
    Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate Equilibria and Ball Fusion. Theory of Computing Systems 36(6), 683–693 (2003)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    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
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, Oxford (1995)MATHGoogle Scholar
  19. 19.
    McKelvey, R.D., McLennan, A.: Computation of Equilibria in Finite Games. Handbook of Computational Economics (1996)Google Scholar
  20. 20.
    Milchtaich, I.: Congestion Games with Player-Specific Payoff Functions. Games and Economic Behavior 13(1), 111–124 (1996)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Monderer, D., Shapley, L.S.: Potential Games. Games and Economic Behavior 14(1), 124–143 (1996)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Nash, J.F.: Equilibrium Points in n-Person Games. Proc. of the National Academy of Sciences of the United States of America 36, 48–49 (1950)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Nash, J.F.: Non-Cooperative Games. Annals of Mathematics 54(2), 286–295 (1951)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Papadimitriou, C.H.: Algorithms, Games, and the Internet. In: Proc. of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001), pp. 749–753 (2001)Google Scholar
  25. 25.
    Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. Int. Journal of Game Theory 2, 65–67 (1973)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Roughgarden, T.: How Unfair is Optimal Routing. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 203–204 (2002)Google Scholar
  27. 27.
    Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press, Cambridge (2005)MATHGoogle Scholar
  28. 28.
    Roughgarden, T., Tardos, É.: How Bad Is Selfish Routing? Journal of the ACM 49(2), 236–259 (2002)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    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 (1952)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sebastian Aland
    • 1
  • Dominic Dumrauf
    • 1
  • Martin Gairing
    • 1
  • Burkhard Monien
    • 1
  • Florian Schoppmann
    • 1
  1. 1.Department of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany

Personalised recommendations