Coalition Formation and Price of Anarchy in Cournot Oligopolies

  • Nicole Immorlica
  • Evangelos Markakis
  • Georgios Piliouras
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6484)


Non-cooperative game theory purports that economic agents behave with little regard towards the negative externalities they impose on each other. Such behaviors generally lead to inefficient outcomes where the social welfare is bounded away from its optimal value. However, in practice, self-interested individuals explore the possibility of circumventing such negative externalities by forming coalitions. What sort of coalitions should we expect to arise? How do they affect the social welfare?

We study these questions in the setting of Cournot markets, one of the most prevalent models of firm competition. Our model of coalition formation has two dynamic aspects. First, agents choose strategically how to update the current coalition partition. Furthermore, coalitions compete repeatedly between themselves trying to minimize their long-term regret. We prove tight bounds on the social welfare, which are significantly higher than that of the Nash equilibria of the original game. Furthermore, this improvement in performance is robust across different supply-demand curves and depends only on the size of the market.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Airiau, S.: Lecture Notes in Coalitional Games. In: 11th European Agent Systems Summer School, EASSS 2009 (2009),
  2. 2.
    Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 189–198 (2007)Google Scholar
  3. 3.
    Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning and Games. Cambridge University Press, Cambridge (2006)MATHCrossRefGoogle Scholar
  4. 4.
    Chalkiadakis, G.: A Bayesian Approach to Multiagent Reinforcement Learning and Coalition Formation under Uncertainty. PhD thesis, Department of Computer Science, University of Toronto, Canada (2007)Google Scholar
  5. 5.
    Chalkiadakis, G., Elkind, E., Polukarov, M., Jennings, N.R.: The price of democracy in coalition formation. In: International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 401–408 (2009)Google Scholar
  6. 6.
    Cournot, A.A.: Recherches sur les Principes Mathématiques de la Théorie des Richesses. Hatchette, Paris (1838); English translation: Researches into the Mathematical Principles of the Theory of Wealth. Macmillan, New York (1897)Google Scholar
  7. 7.
    Cramton, P., Palfrey, T.: Cartel enforcement with uncertainty about costs. International Economic Review 31(1), 17–47 (1990)MATHCrossRefGoogle Scholar
  8. 8.
    Dieckmann, T., Schwalbe, U.: Dynamic Coalition Formation and the Core (1998); Economics Department Working Paper Series, Department of Economics, National University of Ireland - MaynoothGoogle Scholar
  9. 9.
    Even-Dar, E., Mansour, Y., Nadav, U.: On the convergence of regret minimization dynamics in concave games. In: ACM Symposium on Theory of Computing, STOC (2009)Google Scholar
  10. 10.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic congestion games among coalitions. ACM Trans. Algorithms 4(4), 1–27 (2008)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Guo, X., Yang, H.: The price of anarchy of cournot oligopoly. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 246–257. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Harberger, A.: Monopoly and resource allocation. Amer. Econ. Review 44, 77–87 (1954)Google Scholar
  13. 13.
    Hart, S., Kurz, M.: Endogenous formation of coalitions. Econometrica 51, 1047–1064 (1983)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Hayrapetyan, A., Tardos, É., Wexler, T.: The effect of collusion in congestion games. In: ACM Symposium on Theory of Computing (STOC), pp. 89–98 (2006)Google Scholar
  15. 15.
    Kluberg, J., Perakis, G.: Generalized quantity competition for multiple products and loss of efficiency. In: 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 930–936 (2008)Google Scholar
  16. 16.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Computer Science Review 3(2), 65–69 (2009)CrossRefGoogle Scholar
  17. 17.
    Mas-Colell, A., Green, J., Whinston, M.D.: Microeconomic Theory. Oxford University Press, Oxford (1995)Google Scholar
  18. 18.
    Nadav, U., Piliouras, G.: No regret learning in oligopolies: Cournot vs bertrand. In: 3rd International Symposium on Algorithmic Game Theory, SAGT (2010)Google Scholar
  19. 19.
    Ray, D.: A Game-Theoretic Perspective on Coalition Formation. Oxford Univ. Press, Oxford (2007)MATHCrossRefGoogle Scholar
  20. 20.
    Ray, D., Vohra, R.: Equilibrium binding agreements. Journal of Economic Theory 73, 30–78 (1997)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Suetens, S., Potters, J.: Bertrand colludes more than Cournot. Experimental Economics 10, 71–77 (2007)MATHCrossRefGoogle Scholar
  23. 23.
    Young, H.: Strategic Learning and Its Limits. Oxford University Press, Oxford (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nicole Immorlica
    • 1
  • Evangelos Markakis
    • 2
  • Georgios Piliouras
    • 3
    • 4
  1. 1.Dept. of EECSNorthwestern UniversityEvanstonUSA
  2. 2.Dept of InformaticsAthens Univ. of Economics and BusinessAthensGreece
  3. 3.Dept. of EEGeorgia Institute of TechnologyAtlantaUSA
  4. 4.Dept. of EconomicsJohn Hopkins UniversityBaltimoreUSA

Personalised recommendations