The Price of Anarchy for Selfish Ring Routing Is Two

  • Xujin Chen
  • Benjamin Doerr
  • Xiaodong Hu
  • Weidong Ma
  • Rob van Stee
  • Carola Winzen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)


We analyze the network congestion game with atomic players, asymmetric strategies, and the maximum latency among all players as social cost. This important social cost function is much less understood than the average latency. We show that the price of anarchy is at most two, when the network is a ring and the link latencies are linear. Our bound is tight. This is the first sharp bound for the maximum latency objective.


Nash Equilibrium Latency Function Maximum Latency Congestion Game Linear Latency 
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  1. 1.
    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
  2. 2.
    Mavronicolas, M., Spirakis, P.G.: The price of selfish routing. In: Proc. of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001), pp. 510–519 (2001)Google Scholar
  3. 3.
    Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Czumaj, A.: Selfish routing on the internet. In: Leung, J. (ed.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press (2004)Google Scholar
  5. 5.
    Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibira. Internat. J. Game Theory 2(1), 65–67 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Roughgarden, T.: The price of anarchy is independent of the network topology. In: ACM Symposium on Theory of Computing, pp. 428–437 (2002)Google Scholar
  7. 7.
    Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact Price of Anarchy for Polynomial Congestion Games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 218–229. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. of the 37th ACM Symposium on Theory of Computing (STOC 2005), pp. 67–73 (2005)Google Scholar
  9. 9.
    Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proc. of the 37th ACM Symposium on Theory of Computing (STOC 2005), pp. 57–66 (2005)Google Scholar
  10. 10.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: The price of anarchy for restricted parallel links. Parallel Process. Lett. 16(1), 117–132 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lin, H., Roughgarden, T., Tardos, É., Walkover, A.: Stronger bounds on Braess’s paradox and the maximum latency of selfish routing (2011) (manuscript)
  12. 12.
    GLORIAD: Global ring network for advanced applications development,
  13. 13.
    Anshelevich, E., Zhang, L.: Path decomposition under a new cost measure with applications to optical network design. ACM T. Algorithms 4(1) (2008)Google Scholar
  14. 14.
    Blum, A., Kalai, A., Kleinberg, J.M.: Admission Control to Minimize Rejections. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 155–164. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Cheng, C.T.: Improved approximation algorithms for the demand routing and slotting problem with unit demands on rings. SIAM J. Discrete Math. 17(3), 384–402 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Schrijver, A., Seymour, P.D., Winkler, P.: The ring loading problem. SIAM J. Discrete Math. 11(1), 1–14 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Wang, B.F.: Linear time algorithms for the ring loading problem with demand splitting. J. Algorithms 54(1), 45–57 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: 45th Symposium on Foundations of Computer Science (FOCS 2004), pp. 295–304 (2004)Google Scholar
  19. 19.
    Chen, B., Chen, X., Hu, X.: The price of atomic selfish ring routing. J. Comb. Optim. 19(3), 258–278 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Chen, B., Chen, X., Hu, J., Hu, X.: Stability vs. optimality in selfish ring routing (2011) (submitted),
  21. 21.
    Chen, X., Doerr, B., Hu, X., Ma, W., van Stee, R., Winzen, C.: The price of anarchy for selfish ring routing is two. CoRR abs/1210.0230 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xujin Chen
    • 1
  • Benjamin Doerr
    • 2
  • Xiaodong Hu
    • 1
  • Weidong Ma
    • 1
  • Rob van Stee
    • 2
  • Carola Winzen
    • 2
  1. 1.Institute of Applied Mathematics, AMSSChinese Academy of SciencesBeijingChina
  2. 2.Max Planck Institute for InformaticsSaarbrückenGermany

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