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A Two-Step Shapley Value For Cooperative Games With Coalition Structures

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  • YOSHIO KAMIJO

    ()
    (Faculty of Political Science and Economics, Waseda University, 1-6-1, Nishiwaseda, Shunjuku-ku, Tokyo, Japan)

Abstract

In this paper, we study cooperative games with coalition structures. We show that a solution concept that applies the Shapley value to games among and within coalitions and in which the pure surplus that the coalition obtains is allocated among the intra-coalition members in an egalitarian way, is axiomatized by modified axioms on null players and symmetric players and the usual three axioms: efficiency, additivity and coalitional symmetry. In addition to the original definition, we give two expressions of this solution concept. One is an average of modified marginal contributions and the other is the weighted Shapley value of a game with restricted communication.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 11 (2009)
Issue (Month): 02 ()
Pages: 207-214

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Handle: RePEc:wsi:igtrxx:v:11:y:2009:i:02:p:207-214

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Related research

Keywords: Cooperative game; coalition structure; two-step Shapley value; JEL Classification: C71;

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Cited by:
  1. Michael Jones & Jennifer Wilson, 2013. "Two-step coalition values for multichoice games," Computational Statistics, Springer, vol. 77(1), pages 65-99, February.
  2. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
  3. Rene van den Brink & Anna Khmelnitskaya & Gerard van der Laan, 2011. "An Efficient and Fair Solution for Communication Graph Games," Tinbergen Institute Discussion Papers 11-052/1, Tinbergen Institute.
  4. Rene van den Brink & Anna Khmelnitskaya & Gerard van der Laan, 2011. "An Owen-Type Value for Games with Two-Level Communication Structures," Tinbergen Institute Discussion Papers 11-089/1, Tinbergen Institute.
  5. Gérard Hamiache, 2012. "A Matrix Approach to TU Games with Coalition and Communication Structures," Social Choice and Welfare, Springer, vol. 38(1), pages 85-100, January.
  6. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions," Economics Letters, Elsevier, vol. 117(1), pages 263-267.
  7. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(3), pages 572-589, October.
  8. Juan Vidal-Puga, 2005. "The Harsanyi paradox and the 'right to talk' in bargaining among coalitions," Game Theory and Information 0501005, EconWPA.
  9. Rene van den Brink & Anna Khmelnitskaya & Gerard van der Laan, 2011. "An Owen-Type Value for Games with Two-Level Communication Structures," Tinbergen Institute Discussion Papers 11-089/1, Tinbergen Institute.
  10. Kongo, Takumi, 2011. "Value of games with two-layered hypergraphs," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 114-119, September.
  11. Takumi Kongo, 2010. "Difference between the position value and the Myerson value is due to the existence of coalition structures," International Journal of Game Theory, Springer, vol. 39(4), pages 669-675, October.

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