Computational Economics

, Volume 28, Issue 3, pp 251–275 | Cite as

On the Computation of Stability in Multiple Coalition Formation Games

  • M Elena Sáiz
  • Eligius M. T Hendrix
  • Niels J Olieman


In non-cooperative models of coalition formation, players have to decide whether or not to participate in a coalition (alliance). Game theoretic analyses of the formation of alliances in games with externalities, stress the difficulties in designing self-enforcing treaties because of free-riding. The presence of a strong free-rider incentive prevents most alliances of being stable and/or effective. This paper focuses on computing stability in a game on multiple coalition formation with membership rules and different transfer schemes. A new mathematical programming notation for game theory concepts is outlined. To compute stability, the new notation is used for implementation into computer coding. Implementation and computation aspects are discussed. Numerical illustration of the algorithm shows that stability varies with the applied membership rules and transfer schemes. An application of coalition formation to International Environmental Agreements (lEAs) is provided.


Environment Game theory Coalition formation Stability Implementation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altamirano-Cabrera, J.-C. and Finus, M. (2004). Permit Trading and Stability of International Climate Agreements.forthcoming to Journal of Applied Economics.Google Scholar
  2. Bloch, F. (1995). Endogenous Structures of Association in Oligopolies. Rand J. Econ., 26, 537–556.CrossRefGoogle Scholar
  3. Bloch, F. (1996). Sequential Formation of Coalitions with Fixed Payoff Division and Externalities. Games Econ. Behav., 14, 90–123.CrossRefGoogle Scholar
  4. Bosello, F., Buchner, B., Carraro, C. and Raggi, D. (2004). Can Equity Enhance Efficiency? Some Lessons from ClimateNegotitations. C. Carraro and V. Fragnelli (eds.), Game Practice and the Environment, Edward Elgar, Cheltenham, UK.Google Scholar
  5. Bosello, F., Carraro, C. and Buchner, B. (2003). Equity, Development, and Climate Change Control. Journal of theEuropean Economic Association, 1(2–3):601–611(11).CrossRefGoogle Scholar
  6. Botteon, M. and Carraro, C. (1997). Burden-Sharing and Coalition Stability in Environmental Negotiations with Asymmetric Countries Carraro, C. (ed), International Environmental Negotiations: Strategic Policy Issues, E. Elgar: Cheltenham,ch. 3, 26–55.Google Scholar
  7. Carraro, C.(2003). The Structure of International Agreements on Climate Change. International Environmental Agreements onClimate Change, Kluwer Academic Publishers, Dordrecht, 1999. Carraro, C. and Marchiori, C. Stable Coalitions.Carraro, C. (ed), The Endogenous Formation of Economic Coalitions, E. Elgar: Cheltenham.Google Scholar
  8. D'Aspremont, C.A., Jacquemin, A., Gabszewicz, J.J. and Weymark, J. (1983). On the Stability of Collusive Price Leadership.Canadian Journal of Economics, 16, 17–25.CrossRefGoogle Scholar
  9. Dellink, R.B., Altamirano, J.-C., Finus, M., van Ierland, E.C., Ruijs, A. and Weikard, H.P. (2003). Empirical BackgroundPaper of the STACO Model,mimeo, Wageningen University. Google Scholar
  10. Eyckmans and J. Finus, M. (2003)(a) Coalition Formation in a Global Warming Game: How the Design of Protocols Affects theSuccess of Environmental Treaty-Making. vol. CLIMNEG WP, 56.Google Scholar
  11. Eyckmans, J. and Finus, M. (2003)(b). New Roads to International Environmental Agreements: The Case of Global Warming. FEEMWorking Paper No. 88.2003.Google Scholar
  12. Finus, M., van Ierland, E.C. and Dellink, R.B. (2006). Stability of Climate Coalitions in a Cartel Formation Game. Notadi Lavoro 61.2003, FEEM; forthcoming in Economics of Governance.Google Scholar
  13. Finus, M., Altamirano, J.-C. and van Ierland, E.C. (2005). The effect of membership rules and voting schemes on the success ofinternational climate agreements. Public Choice, 125, 97–127.CrossRefGoogle Scholar
  14. Finus, M., S´iz, M.E. and Hendrix, E.M.T. (2004). An Empirical Test of New Develpments in Coalition Theory for theDesign of International Environmental Agreements. Submitted to Environmental& Resource Economics.Google Scholar
  15. Morasch, K. (2000). Strategic alliances as Stackelberg cartels — concept and equilibrium alliance structure.International Journal of Industrial Organization, 18(2):257–282.CrossRefGoogle Scholar
  16. Nordhaus, W.D. (1994). Managing the Global Commons. Ed. MIT Press, Cambridge, MA.Google Scholar
  17. Olieman, N.J. and Hendrix, E.M.T. (2006). Stability likelihood of coalitions in a two-stage cartel game: An estimationmethod. Forthcoming in European Journal of Operational Research.Google Scholar
  18. Ray, D. and Vohra, R. (1997). Equilibrium Binding Agreements. Journal of Economic Theory, 73, 30–78.CrossRefGoogle Scholar
  19. Ray, D. and Vohra, R.A. (1999). Theory of Endogenous Coalition Structures. Games and Economic Behavior,26, 286–336.CrossRefGoogle Scholar
  20. S´iz, M.E., Olieman, N.J., and Hendrix, E.M.T., and Finus, M. (2004). Determination of Stable Structures in aMultiple Coalition Game. Mansholt Working Papers, Discussion Paper n.12.Google Scholar
  21. Thoron, S. (2000). Market organization: Noncooperative models of coalition formation. Interaction and Market Structure, D.Delli Gatti, M. Gallegati and A. Kirman Editors, Springer-Verlag, 207–223.Google Scholar
  22. Yi, S.-S. and H. Shin (1995). Endogenous Formation of Coalitions in Oligopoly Dartmouth College Department of Economics WPNo. 95–2.Google Scholar
  23. Yi, S.-S. (1996). Endogenous Formation of Customs Unions under Imperfect Competition: Open Regionalism Is Good. J.Internat. Econ., 41, 151–175.Google Scholar
  24. Yi, S.-S. (1997). Stable Coalition Structures with Externalities. Games and Economic Behavior, 20, 201–237.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • M Elena Sáiz
    • 1
  • Eligius M. T Hendrix
    • 1
  • Niels J Olieman
    • 1
  1. 1.Operations Research and Logistics GroupWageningen UniversityWageningenThe Netherlands

Personalised recommendations