Coalition Formation and Price of Anarchy in Cournot Oligopolies
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.
- 1.Airiau, S.: Lecture Notes in Coalitional Games. In: 11th European Agent Systems Summer School, EASSS 2009 (2009), http://staff.science.uva.nl/~stephane/Teaching/EASSS09/notes-coopGT-easss09.pdf
- 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
- 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.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.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
- 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.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
- 12.Harberger, A.: Monopoly and resource allocation. Amer. Econ. Review 44, 77–87 (1954)Google Scholar
- 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.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
- 17.Mas-Colell, A., Green, J., Whinston, M.D.: Microeconomic Theory. Oxford University Press, Oxford (1995)Google Scholar
- 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
- 23.Young, H.: Strategic Learning and Its Limits. Oxford University Press, Oxford (2004)Google Scholar