Worst-Case Equilibria

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)


In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.


Nash Equilibrium Pure Strategy Initial Load Social Optimum Identical Link 
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.
    B. Braden, D. Clark, J. Crowcroft, B. Davie, S. Deering, D. Estrin, S. Floyd, V. Jacobson, G. Minshall, C. Partridge, L. Peterson, K. Ramakrishnan, S. Shenker, J. Wroclawski, and L. Zhang. Recommendations on Queue Management and Congestion Avoidance in the Internet, April 1998.
  2. 2.
    Y. Cho and S. Sahni. Bounds for list schedules on uniform processors. SIAM Journal on Computing, 9(1):91–103, 1980.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Floyd and K. Fall. Router Mechanisms to Support End-to-End Congestion Control. Technical report, Lawrence Berkeley National Laboratory, February 1997.Google Scholar
  4. 4.
    G. R. Grimmet and D. R. Stirzaker. Probability and Random Processes, 2nd ed.. Oxford University Press, 1992.Google Scholar
  5. 5.
    Y. Korilis and A. Lazar. On the existence of equilibria in noncooperative optimal flow control. Journal of the ACM 42(3):584–613, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Y. Korilis, A. Lazar, A. Orda. Architecting noncooperative networks. IEEE J. Selected Areas of Comm., 13, 7, 1995.Google Scholar
  7. 7.
    R. La, V. Anantharam. Optimal routing control: Game theoretic approach. Proc. 1997 CDC Conf. Google Scholar
  8. 8.
    G. Owen. Game Theory, 3rd ed.. Academic Press, 1995.Google Scholar
  9. 9.
    K. Park, M. Sitharam, S. Chen. Quality of service provision in noncooperative network environments. Manuscript, Purdue Univ., 1998.Google Scholar
  10. 10.
    C. H. Papadimitriou, M. Yannakakis. On complexity as bounded rationality. In Proceedings of the Twenty-Sixth Annual ACM Symposium on the Theory of Computing. pages 726–733, Montreal, Quebec, Canada, 23–25 May 1994.Google Scholar
  11. 11.
    S. J. Shenker. Making greed work in networks: a game-theoretic analysis of switch service disciplines. IEEE/ACM Transactions on Networking, 3(6):819–831, Dec.1995.Google Scholar
  12. 12.
    S. Shenker, D. Clark, D. Estrin, and S. Herzog. Pricing in Computer Network: Reshaping the Research Agenda. Communications Policy, 20(1), 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Univ of CaliforniaLos Angeles
  2. 2.Univ of CaliforniaBerkeley

Personalised recommendations