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A coalition formation value for games in partition function form

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  • Grabisch, Michel
  • Funaki, Yukihiko

Abstract

The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to allocate the worth of the grand coalition to each player, i.e., how to find an adequate solution concept, taking into account the whole process of coalition formation. We propose in this paper the original concepts of scenario-value, process-value and coalition formation value, which represent the average contribution of players in a scenario (a particular sequence of coalitions within a given coalition formation process), in a process (a sequence of partitions of the society), and in the whole (all processes being taken into account), respectively. We give also two axiomatizations of our coalition formation value.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 221 (2012)
Issue (Month): 1 ()
Pages: 175-185

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Handle: RePEc:eee:ejores:v:221:y:2012:i:1:p:175-185

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Game theory; Coalition formation; Games in partition function form; Shapley value;

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References

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  1. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer, vol. 28(2), pages 157-171.
  2. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
  3. Diamantoudi, Effrosyni & Xue, Licun, 2007. "Coalitions, agreements and efficiency," Journal of Economic Theory, Elsevier, vol. 136(1), pages 105-125, September.
  4. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
  5. Pham Do, K.H. & Norde, H.W., 2002. "The Shapley Value for Partition Function Form Games," Discussion Paper 2002-4, Tilburg University, Center for Economic Research.
  6. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer, vol. 20(2), pages 129-47.
    • Itzhak Gilboa & Ehud Lehrer, 1990. "Global Games," Discussion Papers 922, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions And Externalities In The Value," Economics Working Papers we057339, Universidad Carlos III, Departamento de Economía.
  8. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer, vol. 18(1), pages 37-44.
  9. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
  10. repec:hal:journl:hal-00457827 is not listed on IDEAS
  11. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
  12. repec:hal:cesptp:hal-00457827 is not listed on IDEAS
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Cited by:
  1. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00749950, HAL.
  2. Vincent Iehlé, 2014. "The lattice structure of the S-Lorenz core," Working Papers halshs-00846826, HAL.
  3. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
  4. repec:hal:journl:hal-00457827 is not listed on IDEAS

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