Skip to main content
SpringerLink
Log in

On the Performance of Approximate Equilibria in Congestion Games

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

We study the performance of approximate Nash equilibria for congestion games with polynomial latency functions. We consider how much the price of anarchy worsens and how much the price of stability improves as a function of the approximation factor ε. We give tight bounds for the price of anarchy of atomic and non-atomic congestion games and for the price of stability of non-atomic congestion games. For the price of stability of atomic congestion games we give non-tight bounds for linear latencies. Our results not only encompass and generalize the existing results of exact equilibria to ε-Nash equilibria, but they also provide a unified approach which reveals the common threads of the atomic and non-atomic price of anarchy results. By expanding the spectrum, we also cast the existing results in a new light.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. In: STACS, pp. 218–229 (2006)

  2. Albers, S.: On the value of coordination in network design. In: SODA, pp. 294–303 (2008)

  3. 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: FOCS, pp. 295–304 (2004)

  4. Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: STOC, pp. 57–66 (2005)

  5. Beckmann, M., McGuire, C.B., Winston, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)

    Google Scholar 

  6. Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. In: ICALP, pp. 311–322 (2006)

  7. Chen, X., Deng, X.: Settling the complexity of two-player Nash equilibrium. In: FOCS, pp. 261–272 (2006)

  8. Chen, H.-L., Roughgarden, T.: Network design with weighted players. In: SPAA, pp. 29–38 (2006)

  9. Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. In: SODA, pp. 169–178 (2007)

  10. Christodoulou, G., Koutsoupias, E.: On the price of anarchy and stability of correlated equilibria of linear congestion games. In: ESA, pp. 59–70 (2005)

  11. Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: STOC, pp. 67–73 (2005)

  12. Christodoulou, G., Koutsoupias, E., Spirakis, P.G.: On the performance of approximate equilibria in congestion games. In: CoRR (2008). 0804.3160

  13. Correa, J.R., Schulz, A.S., Stier Moses, N.E.: Selfish routing in capacitated networks. Math. Oper. Res. 29(4), 961–976 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Correa, J.R., Schulz, A.S., Stier Moses, N.E.: Fast, fair, and efficient flows in networks. Oper. Res. 55, 215–225 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dafermos, S.C., Sparrow, F.T.: The traffic assignment problem for a general network. J. Res. Natl. Bur. Stand. Ser. B 73B(2), 91–118 (1969)

    Article  MathSciNet  Google Scholar 

  16. Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a Nash equilibrium. In: STOC, pp. 71–78 (2006)

  17. Daskalakis, C., Mehta, A., Papadimitriou, C.H.: A note on approximate Nash equilibria. In: WINE (2006)

  18. Fiat, A., Kaplan, H., Levy, M., Olonetsky, S., Shabo, R.: On the price of stability for designing undirected networks with fair cost allocations. In: ICALP (1), pp. 608–618 (2006)

  19. Fabrikant, A., Papadimitriou, C., Talwar, K.: On the complexity of pure equilibria. In: STOC (2004)

  20. Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: STACS, pp. 404–413 (1999)

  21. Lipton, R.J., Markakis, E., Mehta, A.: Playing large games using simple strategies. In: EC, pp. 36–41 (2003)

  22. Milchtaich, I.: Congestion games with player-specific payoff functions. Games Econ. Behav. 13, 111–124 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  23. Monderer, D., Shapley, L.: Potential games. Games Econ. Behav. 14, 124–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  24. Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  25. Papadimitriou, C.H.: Algorithms, games, and the internet. In: STOC, pp. 749–753 (2001)

  26. Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65–67 (1973)

    Article  MATH  Google Scholar 

  27. Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)

    MathSciNet  Google Scholar 

  28. Roughgarden, T., Tardos, E.: Bounding the inefficiency of equilibria in nonatomic congestion games. Games Econ. Behav. 47(2), 389–403 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  29. Roughgarden, T.: Selfish routing. Ph.D. Thesis, Cornell University, May 2002

  30. Roughgarden, T.: How unfair is optimal routing? In: SODA, pp. 203–204 (2002)

  31. Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press, Cambridge (2005)

    Google Scholar 

  32. Skopalik, A., Vöcking, B.: Inapproximability of pure Nash equilibria. In: STOC, pp. 355–364 (2008)

  33. Tsaknakis, H., Spirakis, P.G.: An optimization approach for approximate Nash equilibria. In: WINE, pp. 47–56 (2007)

  34. Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proceedings of the Institute of Civil Engineers, Part II, vol. 1, pp. 325–378 (1952)

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Saarland, Saarbrücken, Germany

    George Christodoulou

  2. Department of Informatics, University of Athens, Athens, Greece

    Elias Koutsoupias

  3. Computer Engineering and Informatics Department, Patras University, Patras, Greece

    Paul G. Spirakis

Authors
  1. George Christodoulou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elias Koutsoupias
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paul G. Spirakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George Christodoulou.

Additional information

Part of the work has been done while G. Christodoulou was at the University of Liverpool.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Christodoulou, G., Koutsoupias, E. & Spirakis, P.G. On the Performance of Approximate Equilibria in Congestion Games. Algorithmica 61, 116–140 (2011). https://doi.org/10.1007/s00453-010-9449-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-010-9449-2

Keywords

Search

Navigation