Congestion Games, Load Balancing, and Price of Anarchy

  • Anshul Kothari
  • Subhash Suri
  • Csaba D. Tóth
  • Yunhong Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3405)


Imagine a set of self-interested clients, each of whom must choose a server from a permissible set. A server’s latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. Many emerging Internet-centric applications such as peer-to-peer networks, multi-player online games and distributed computing platforms exhibit such interaction of self-interested users. This interaction is naturally modeled as a congestion game, which we call server matching. In this overview paper, we summarize results of our ongoing work on the analysis of the server matching game, and suggest some promising directions for future research.


Nash Equilibrium Load Balance Latency Function Optimal Match Congestion Game 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near-optimal network design with selfish agents. In: Proc. 35th STOC, pp. 511–520. ACM Press, New York (2003)Google Scholar
  2. 2.
    Awerbuch, A., Azar, A., Grove, E.F., Krishnan, P., Kao, M.Y., Vitter, J.S.: Load balancing in the L p norm. In: Proc. 36th FOCS, pp. 383–391. IEEE, Los Alamitos (1995)Google Scholar
  3. 3.
    Azar, Y., Naor, J., Rom, R.: The competitiveness of online assignments. Journal of Algorithms 18(2), 221–237 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Berkeley open infrastructure for network comp.,
  5. 5.
    Czumaj, A., Krysta, P., Vöcking, B.: Selfish traffic allocation for server farms. In: Proc. 34th SOTC, pp. 287–296. ACM Press, New York (2002)Google Scholar
  6. 6.
    Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. In: Proc. of 13th ACM-SIAM Sympos. Discrete Algorithms, pp. 413–420. ACM Press, New York (2002)Google Scholar
  7. 7.
    Edmonds, J., Karp, R.M.: Theoretical improvement in algorithmic efficiency for network flow problems. Journal of the ACM 19(2), 248–264 (1972)zbMATHCrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
  10. 10.
    Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proc. 22nd PODC, pp. 347–351. ACM Press, New York (2003)Google Scholar
  11. 11.
    Fotakis, D., Kontogiannis, S.C., Koutsoupias, E., Mavronicolas, M., Spirakis, P.G.: 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
  12. 12.
  13. 13.
  14. 14.
    Harvey, N.J.A., Ladner, R.E., Lovász, L., Tamir, T.: Semi-matchings for bipartite graphs and load balancing. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 294–306. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
  16. 16.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97 (1955)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Nisan, N., Ronen, A.: Computationally feasible VCG mechanisms. In: Proc. 2nd Conf. on EC, pp. 242–252. ACM Press, New York (2000)Google Scholar
  19. 19.
    Papadimitriou, C.: Algorithms, games, and the internet. In: Proc. 33rd Sympos. on Theory of Computing, pp. 749–753. ACM Press, New York (2001)Google Scholar
  20. 20.
  21. 21.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Roughgarden, T.: Selfish routing. PhD thesis, Cornell University (2002)Google Scholar
  23. 23.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49, 235–259 (2002)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Suri, S., Tóth, C.D., Zhou, Y.: Selfish load balancing and atomic congestion games. In: Proc. 16th SPAA, pp. 188–195. ACM Press, New York (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Anshul Kothari
    • 1
  • Subhash Suri
    • 1
  • Csaba D. Tóth
    • 1
  • Yunhong Zhou
    • 2
  1. 1.Computer Science Depart.University of CaliforniaSanta Barbara
  2. 2.HP LabsPalo AltoUSA

Personalised recommendations