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The gamma-core and coalition formation

  • Parkash Chander

    ()

This paper reinterprets the gamma-core (Chander and Tulkens (1995, 1997)) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. It is assumed that coalitions can freely merge or break apart, are farsighted (that is, it is the final and not the immediate payoffs that matter to the coalitions) and a coalition may deviate if and only if it stands to gain from it. It is then shown that subsequent to a deviation by a coalition, the nonmembers will have incentives to break apart into singletons, as is assumed in the definition of the gamma-characteristic function, and that the grand coalition is the only stable coalition structure.

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File URL: http://hdl.handle.net/10.1007/s00182-006-0067-9
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Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 35 (2007)
Issue (Month): 4 (April)
Pages: 539-556

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Handle: RePEc:spr:jogath:v:35:y:2007:i:4:p:539-556
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  1. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
  2. CHANDER, Parkash & TULKENS, Henry, 1994. "A Core-Theoretic Solution for the Design of Cooperative Agreements on Transfrontier Pollution," CORE Discussion Papers 1994048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. D. K. Foley, 1967. "Lindahl's Solution and the Core of an Economy with Public Goods," Working papers 3, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Farrell, Joseph & Saloner, Garth, 1987. "Coordination Through Committees and Markets," Department of Economics, Working Paper Series qt5sn4b6v4, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  5. Carsten Helm, 2001. "On the existence of a cooperative solution for a coalitional game with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 141-146.
  6. Yi, Sang-Seung, 1997. "Stable Coalition Structures with Externalities," Games and Economic Behavior, Elsevier, vol. 20(2), pages 201-237, August.
  7. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  8. Roberts, Donald John, 1974. "The Lindahl solution for economies with public goods," Journal of Public Economics, Elsevier, vol. 3(1), pages 23-42, February.
  9. CHANDER, Parkash, 1998. "International treaties on global pollution: a dynamic time-path analysis," CORE Discussion Papers 1998054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Chander, P. & Tulkens, H., . "The core of an economy with multilateral environmental externalities," CORE Discussion Papers RP 1276, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Moulin, Herve, 1987. "Egalitarian-Equivalent Cost Sharing of a Public Good," Econometrica, Econometric Society, vol. 55(4), pages 963-76, July.
  12. DIAMANTOUDI, Effrosyni & XUE, Licun, 2002. "Coalitions, agreements and efficiency," CORE Discussion Papers 2002047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
  14. Carraro, Carlo & Siniscalco, Domenico, 1993. "Strategies for the international protection of the environment," Journal of Public Economics, Elsevier, vol. 52(3), pages 309-328, October.
  15. TULKENS, Henry, 1997. "Cooperation vs. free riding in international environmental affairs: two approaches," CORE Discussion Papers 1997052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
  17. Ray, D. & Vohra, R., 1993. "Equilibrium Binding Agreements," Papers 21, Boston University - Department of Economics.
  18. Belleflamme, Paul, 2000. "Stable Coalition Structures with Open Membership and Asymmetric Firms," Games and Economic Behavior, Elsevier, vol. 30(1), pages 1-21, January.
  19. Chander, Parkash, 1993. "Dynamic Procedures and Incentives in Public Good Economies," Econometrica, Econometric Society, vol. 61(6), pages 1341-54, November.
  20. Barrett, Scott, 1994. "Self-Enforcing International Environmental Agreements," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 878-94, Supplemen.
  21. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August.
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