On Bidimensional Congestion Games

  • Vittorio Bilò
  • Michele Flammini
  • Vasco Gallotti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)


We introduce multidimensional congestion games, that is, congestion games whose set of players can be partitioned into k + 1 clusters C 0,C 1,…,C k . Players in C 0 have full information about all the other participants in the game, while players in C i , for any 1 ≤ i ≤ k, have full information only about the members of C 0 ∪ C i and are unaware of all the other ones. This model has at least two interesting applications: (i) it is a special case of graphical congestion games in which the game’s social knowledge graph is undirected and has independence number equal to k, and (ii) it models scenarios in which players may be of different types and the level of competition that each player experiences on a resource depends on the player’s type and on the types of the other players sharing the resource. We focus on the case in which k = 2 and the cost function associated with each resource is linear and show bounds on the prices of anarchy and stability for two different social functions.


Full Information Social Function Social Optimum Congestion Game Pure Nash Equilibrium 
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.
    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
  2. 2.
    Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The Price of Stability for Network Design with Fair Cost Allocation. SIAM Journal of Computing 38(4), 1602–1623 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 57–66. ACM Press (2005)Google Scholar
  4. 4.
    Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted Congestion Games: Price of Anarchy, Universal Worst-Case Examples, and Tightness. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part II. LNCS, vol. 6347, pp. 17–28. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Bilò, V.: A Unifying Tool for Bounding the Quality of Non-Cooperative Solutions in Weighted Congestion Games. CoRR abs/1110.5439 (2011)Google Scholar
  6. 6.
    Bilò, V., Fanelli, A., Flammini, M., Moscardelli, L.: Graphical Congestion Games. Algorithmica 61(2), 274–297 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight Bounds for Selfish and Greedy Load Balancing. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part I. LNCS, vol. 4051, pp. 311–322. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 67–73. ACM Press (2005)Google Scholar
  9. 9.
    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
  10. 10.
    Christodoulou, G., Koutsoupias, E., Spirakis, P.G.: On the Performance of Approximate Equilibria in Congestion Games. Algorithmica 61(1), 116–140 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Fotakis, D., Gkatzelis, V., Kaporis, A.C., Spirakis, P.G.: The Impact of Social Ignorance on Weighted Congestion Games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 316–327. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish Unsplittable Flows. Theoretical Computer Science 348, 226–239 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Harks, T., Klimm, M.: On the Existence of Pure Nash Equilibria in Weighted Congestion Games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010, Part I. LNCS, vol. 6198, pp. 79–89. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Harks, T., Klimm, M., Möhring, R.H.: Characterizing the Existence of Potential Functions in Weighted Congestion Games. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 97–108. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. International Journal of Game Theory 2, 65–67 (1973)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vittorio Bilò
    • 1
  • Michele Flammini
    • 2
  • Vasco Gallotti
    • 2
  1. 1.Dipartimento di Matematica e Fisica “Ennio De Giorgi”Università del SalentoLecceItaly
  2. 2.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversità di L’AquilaL’AquilaItaly

Personalised recommendations