Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Price of Anarchy

2005; Koutsoupias
  • George Christodoulou
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_299

Keywords and Synonyms

Coordination ratio      

Problem Definition

The Price of Anarchy, captures the lack of coordination in systems where users are selfish and may have conflicted interests. It was first proposed by Koutsoupias and Papadimitriou in [9], where the term coordination ratio was used instead, but later Papadimitriou in [12] coined the term Price of Anarchy, that finally prevailed in the literature.

Roughly, the Price of Anarchy is the system cost (e. g. makespan, average latency) of the worst-case Nash Equilibrium over the optimal system cost, that would be achieved if the players were forced to coordinate. Although it was originally defined in order to analyze a simple load-balancing game, it was soon applied to numerous variants and to more general games. The family of (weighted) congestion games [11,13] is a nice abstract form to describe most of the alternative settings.

The Price of Anarchy may vary, depending on the
  • equilibirium solution concept (e. g. pure, mixed,...


Nash Equilibrium Mixed Strategy Pure Strategy Strategy Profile 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.
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Recommended Reading

  1. 1.
    Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. In: 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), pp. 218–229. Springer, Marseille (2006)Google Scholar
  2. 2.
    Awerbuch, B., Azar, Y., Epstein A.: Large the price of routing unsplittable flow. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 57–66. ACM, Baltimore (2005)Google Scholar
  3. 3.
    Awerbuch, B., Azar, Y., Richter, Y., Tsur, D.: Tradeoffs in worst-case equilibria. In: Approximation and Online Algorithms, 1st International Workshop (WAOA), pp. 41–52. Springer, Budapest (2003)Google Scholar
  4. 4.
    Christodoulou, G., Koutsoupias, E.: On the price of anarchy and stability of correlated equilibria of linear congestion games. In: Algorithms – ESA 2005, 13th Annual European Symposium, pp. 59–70. Springer, Palma de Mallorca (2005)CrossRefGoogle Scholar
  5. 5.
    Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 67–73. ACM, Baltimore (2005)Google Scholar
  6. 6.
    Cominetti, R., Correa, J.R., Moses, N.E.S.: Network games with atomic players. In: Automata, Languages and Programming, 33rd International Colloquium (ICALP), pp. 525–536. Springer, Venice (2006)CrossRefGoogle Scholar
  7. 7.
    Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 413–420. ACM/SIAM, San Fransisco (2002)Google Scholar
  8. 8.
    Koutsoupias, E., Mavronicolas, M., Spirakis, P.G.: Approximate equilibria and ball fusion. Theor. Comput. Syst. 36, 683–693 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Proc. of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS), pp. 404–413. Springer, Trier (1999)Google Scholar
  10. 10.
    Mavronicolas, M., Spirakis, P.G.: The price of selfish routing. In: Proc. on 33rd Annual ACM Symposium on Theory of Computing (STOC), pp. 510–519. ACM, Heraklion (2001)Google Scholar
  11. 11.
    Monderer, D., Shapley, L.: Potential games. Games Econ. Behav. 14, 124–143 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Papadimitriou, C.H.: Algorithms, games, and the internet. In: Proc. on 33rd Annual ACM Symposium on Theory of Computing (STOC), pp. 749–753. ACM, Heraklion (2001)Google Scholar
  13. 13.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theor. 2, 65–67 (1973)zbMATHCrossRefGoogle Scholar
  14. 14.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49, 236–259 (2002)Google Scholar
  15. 15.
    Roughgarden, T., Tardos, E.: Bounding the inefficiency of equilibria in nonatomic congestion games. Games Econ. Behav. 47, 389–403 (2004)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • George Christodoulou
    • 1
  1. 1.Max-Planck-Institute for Computer ScienceSaarbrueckenGermany