Graphical Congestion Games

  • Vittorio Bilò
  • Angelo Fanelli
  • Michele Flammini
  • Luca Moscardelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5385)


We consider congestion games with linear latency functions in which each player is aware only of a subset of all the other players. This is modeled by means of a social knowledge graph G in which nodes represent players and there is an edge from i to j if i knows j. Under the assumption that the payoff of each player is affected only by the strategies of the adjacent ones, we first give a complete characterization of the games possessing pure Nash equilibria. We then investigate the impact of the limited knowledge of the players on the performance of the game. More precisely, given a bound on the maximum degree of G, for the convergent cases we provide tight lower and upper bounds on the price of stability and asymptotically tight bounds on the price of anarchy. All the results are then extended to load balancing games.


Algorithmic Game Theory Nash Equilibrium Price of Anarchy Price of Stability Congestion Games Social Knowledge 


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  1. 1.
    Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proc. of STOC, pp. 57–66. ACM Press, New York (2005)Google Scholar
  2. 2.
    Beier, R., Czumaj, A., Krysta, P., Vocking, B.: Computing Equilibria for Congestion Games with (Im)perfect Information. In: Proc. of SODA, pp. 746–755. ACM Press, New York (2004)Google Scholar
  3. 3.
    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. LNCS, vol. 4051, pp. 311–322. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proc. of STOC, pp. 67–73. ACM Press, New York (2005)Google Scholar
  5. 5.
    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
  6. 6.
    Fabrikant, A., Papadimitriou, C.H., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proc. of STOC, pp. 604–612. ACM Press, New York (2004)Google Scholar
  7. 7.
    Facchini, G., van Megan, F., Borm, P., Tijs, S.: Congestion Models and Weighted Bayesian Potential Games. Theory and Decision 42, 193–206 (1997)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Gairing, M., Monien, B., Tiemann, K.: Selfish Routing with Incomplete Information. In: Proc. of SPAA, pp. 203–212. ACM Press, New York (2005)Google Scholar
  9. 9.
    Garg, D., Narahari, Y.: Price of Anarchy of Network Routing Games with Incomplete Information. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 1066–1075. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Georgiou, C., Pavlides, T., Philippou, A.: Network Uncertainty in Selfish Routing. In: Proc. of IPDPS. Computer Society (2006)Google Scholar
  11. 11.
    Harsanyi, J.C.: Games with Incomplete Information Played by Bayesian Players, I, II, III. Management Science 14, 159–182, 320–332, 468–502 (1967)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Harsanyi, J.C.: Games with Randomly Disturbed Payoffs. International Journal on Game Theory 21, 1–23 (1973)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Koutsoupias, E., Panagopoulou, P.N., Spirakis, P.G.: Selfish Load Balancing Under Partial Knowledge. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 609–620. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Kearns, M.J., Littman, M.L., Singh, S.P.: Graphical Models for Game Theory. In: Proc. of UAI, pp. 253–260. Morgan Kaufmann, San Francisco (2001)Google Scholar
  15. 15.
    Monderer, D., Shapley, L.S.: Potential Games. Games and Economic Behavior 14, 124–143 (1996)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Nash, J.: Equilibrium Points in n-person Games. Proceedings of the National Academy of Sciences 36, 48–49 (1950)Google Scholar
  17. 17.
    Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. International Journal of Game Theory 2, 65–67 (1973)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vittorio Bilò
    • 1
  • Angelo Fanelli
    • 2
  • Michele Flammini
    • 2
  • Luca Moscardelli
    • 2
    • 3
  1. 1.Dipartimento di MatematicaUniversity of Salento, Provinciale Lecce-ArnesanoLecceItaly
  2. 2.Dipartimento di InformaticaUniversity of L’Aquila, Loc. Vetoio, CoppitoL’AquilaItaly
  3. 3.Dipartimento di Informatica ed Applicazioni “R. M. Capocelli”University of SalernoFisciano (SA)Italy

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