Advertisement

Efficient Convergence to Pure Nash Equilibria in Weighted Network Congestion Games

  • Panagiota N. Panagopoulou
  • Paul G. Spirakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

In large-scale or evolving networks, such as the Internet, there is no authority possible to enforce a centralized traffic management. In such situations, Game Theory and the concepts of Nash equilibria and Congestion Games [8] are a suitable framework for analyzing the equilibrium effects of selfish routes selection to network delays.

We focus here on layered networks where selfish users select paths to route their loads (represented by arbitrary integer weights). We assume that individual link delays are equal to the total load of the link. We focus on the algorithm suggested in [2], i.e. a potential-based method for finding pure Nash equilibria (PNE) in such networks. A superficial analysis of this algorithm gives an upper bound on its time which is polynomial in n (the number of users) and the sum of their weights. This bound can be exponential in n when some weights are superpolynomial. We provide strong experimental evidence that this algorithm actually converges to a PNE in strong polynomial time in n (independent of the weights values). In addition we propose an initial allocation of users to paths that dramatically accelerates this algorithm, compared to an arbitrary initial allocation. A by-product of our research is the discovery of a weighted potential function when link delays are exponential to their loads. This asserts the existence of PNE for these delay functions and extends the result of [2].

Keywords

Nash Equilibrium Pure Strategy Layered Network Delay Function 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fabrikant, A., Papadimitriou, C., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proc. of the 36th ACM Symp. on Theory of Computing, (STOC 2004) (2004)Google Scholar
  2. 2.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish Unsplittable Flows. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 593–605. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: 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
  4. 4.
    Mehlhorn, K., Näher, S.: LEDA – A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  5. 5.
    Milchtaich, I.: Congestion Games with Player-Specific Payoff Functions. Games and Economic Behavior 13, 111–124 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Monderer, D., Shapley, L.: Potential Games. Games and Economic Behavior 14, 124–143 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Nash, J.F.: Equilibrium Points in N-person Games. Proc. of National Academy of Sciences 36, 48–49 (1950)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Rosenthal, R.W.: A Class of Games Poseessing Pure-Strategy Nash Equilibria. International Journal of Game Theory 2, 65–67 (1973)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Panagiota N. Panagopoulou
    • 1
    • 2
  • Paul G. Spirakis
    • 1
    • 2
  1. 1.Computer Technology InstitutePatrasGreece
  2. 2.Computer Engineering and Informatics DepartmentPatras UniversityGreece

Personalised recommendations