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The gamma-core and coalition formation

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  • Parkash Chander

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Abstract

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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Bibliographic Info

Article provided by Springer 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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Related research

Keywords: C71; C72; D62; Core; Strategic games; Nash equilibrium; Coalition formation;

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References

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  1. Moulin, Herve, 1987. "Egalitarian-Equivalent Cost Sharing of a Public Good," Econometrica, Econometric Society, vol. 55(4), pages 963-76, July.
  2. Joseph Farrell and Garth Saloner., 1988. "Coordination through Committees and Markets," Economics Working Papers 8864, University of California at Berkeley.
  3. Belleflamme, Paul, 2000. "Stable Coalition Structures with Open Membership and Asymmetric Firms," Games and Economic Behavior, Elsevier, vol. 30(1), pages 1-21, January.
  4. Barrett, Scott, 1994. "Self-Enforcing International Environmental Agreements," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 878-94, Supplemen.
  5. Carraro, Carlo & Siniscalco, Domenico, 1991. "Strategies for the International Protection of the Environment," CEPR Discussion Papers 568, C.E.P.R. Discussion Papers.
  6. Carsten Helm, 2001. "On the existence of a cooperative solution for a coalitional game with externalities," International Journal of Game Theory, Springer, vol. 30(1), pages 141-146.
  7. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627.
  8. Parkash Chander, 1998. "International Treaties on Global Pollution: A Dynamic Time-Path Analysis," Economics Working Paper Archive 400, The Johns Hopkins University,Department of Economics.
  9. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
  10. Herbert E. Scarf, 1970. "On the Existence of a Cooperative Solution for a General Class of N-Person Games," Cowles Foundation Discussion Papers 293, Cowles Foundation for Research in Economics, Yale University.
  11. CHANDER, Parkash & TULKENS, Henry, 1995. "The Core of an Economy with Multilateral Environmental Externalities," CORE Discussion Papers 1995050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Debraj Ray & Rajiv Vohra, 1996. "A Theory of Endogenous Coalition Structure," Papers 0068, Boston University - Industry Studies Programme.
  13. Chander, P. & Tulkens, H., . "A core-theoretic solution for the design of cooperative agreements on transfrontier pollution," CORE Discussion Papers RP -1158, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. 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).
  15. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, vol. 38(1), pages 66-72, January.
  16. Chander, Parkash, 1993. "Dynamic Procedures and Incentives in Public Good Economies," Econometrica, Econometric Society, vol. 61(6), pages 1341-54, November.
  17. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August.
  18. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  19. DIAMANTOUDI, Effrosyni & XUE, Licun, 2002. "Coalitions, agreements and efficiency," CORE Discussion Papers 2002047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  20. Roberts, Donald John, 1974. "The Lindahl solution for economies with public goods," Journal of Public Economics, Elsevier, vol. 3(1), pages 23-42, February.
  21. Yi, Sang-Seung, 1997. "Stable Coalition Structures with Externalities," Games and Economic Behavior, Elsevier, vol. 20(2), pages 201-237, August.
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Citations

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Cited by:
  1. Kumoi, Yuki & Matsubayashi, Nobuo, 2014. "Vertical integration with endogenous contract leadership: Stability and fair profit allocation," European Journal of Operational Research, Elsevier, vol. 238(1), pages 221-232.
  2. Dritan Osmani & Richard S.J. Tol, 2008. "Evolution in time of Farsightedly Stable Coalitions: An Application of FUND," Working Papers FNU-162, Research unit Sustainability and Global Change, Hamburg University, revised May 2008.
  3. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.
  4. Zahur, Nahim Bin, 2014. "Farsighted Fuzzy Coalitions in an Economy with Multilateral Negative Externalities," 2014 Conference (58th), February 4-7, 2014, Port Maquarie, Australia 165807, Australian Agricultural and Resource Economics Society.
  5. Beard, Rodney & Mallawaarachchi, Thilak, 2011. "Are international environmental agreements stable ex-post?," MPRA Paper 34303, University Library of Munich, Germany.
  6. Olivier Bos & Béatrice Roussillon & Paul Schweinzer, 2013. "Agreeing on Efficient Emissions Reduction," CESifo Working Paper Series 4345, CESifo Group Munich.
  7. Calvo, Emilio & Rubio, Santiago J., 2013. "Dynamic Models of International Environmental Agreements: A Differential Game Approach," International Review of Environmental and Resource Economics, now publishers, vol. 6(4), pages 289-339, April.
  8. Brennan Platt, 2009. "Spoilers, blocking coalitions, and the core," Social Choice and Welfare, Springer, vol. 33(3), pages 361-381, September.
  9. CHANDER, Parkash & TULKENS, Henry, 2011. "The kyoto Protocol, the Copenhagen Accord, the Cancun Agreements, and beyond: an economic and game theoretical exploration and interpretation," CORE Discussion Papers 2011051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Dritan Osmani, . "A note on optimal transfer schemes, stable coalition for environmental protection and joint maximization assumption," Working Papers FNU-176, Research unit Sustainability and Global Change, Hamburg University.
  11. Rabia Nessah & Kristiaan Kerstens, 2008. "Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets," Working Papers 2008-ECO-13, IESEG School of Management.
  12. Odd Godal & Bjart Holtsmark, 2010. "International emissions trading with endogenous taxes," Discussion Papers 626,, Research Department of Statistics Norway.

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