Equilibria in load balancing games



A Nash equilibrium (NE) in a multi-agent game is a strategy profile that is resilient to unilateral deviations. A strong Nash equilibrium (SE) is one that is stable against coordinated deviations of any coalition. We show that, in the load balancing games, NEs approximate SEs in the sense that the benefit of each member of any coalition from coordinated deviations is well limited. Furthermore, we show that an easily recognizable special subset of NEs exhibit even better approximation of SEs.


Nash equilibrium load balancing approximation 

2000 MR Subject Classification

91B50 68M20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Andelman, N., Feldman, M., Mansour, Y. Strong price of anarchy. In: Proceeding of 18th Annual ACM-SIAM Symposium on Discrete Algorithms, 2007, 189–198Google Scholar
  2. [2]
    Aumann, R. Acceptable Points in General Cooperative n-Person Games. In: Contributions to the Theory of Games IV, Annals of Mathematics 40, ed. by R.D. Luce, A.W. Tucker, 1959, 287–324Google Scholar
  3. [3]
    Feldman, M., Tamir, T. Approximate Strong Equilibrium in Job Scheduling Games. To appear in: Journal of Artificial Intelligence ResearchGoogle Scholar
  4. [4]
    Fotakis, D., Kontogiannis, S., Mavronicolas, M., Spiraklis, P. The structure and complexity of Nash equilibria for a selfish routing game. In: Proceedings of the 29th International Colloquium on Automata, Languages and Programming, 2002, 510–519Google Scholar
  5. [5]
    Graham, R. Bounds on multiprocessing timing anomalies. SIAM J. Applied Mathematics, 17: 263–269 (1969)Google Scholar
  6. [6]
    Korte, B., Vygen, J. Combinatorial Optimization: Theory and Algorithms, 4th ed. Springer, 2008Google Scholar
  7. [7]
    Monien, B., Schroeder, U.-P., editors. Proceedings of the 1st International Symposium on Algorithmic Game Theory, Vol 4997 of Lecture Notes in Computer Science. Springer, 2008Google Scholar
  8. [8]
    Wolfram Research. Mathematica: Technical and Scientific Software. http://www.wolfram.com/

Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Qufu Normal UniversityShandongChina
  2. 2.Warwick Business SchoolUniversity of WarwickWarwickUK

Personalised recommendations