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The collective value: a new solution for games with coalition structures

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  • Yoshio Kamijo

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Abstract

In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented. Copyright Sociedad de Estadística e Investigación Operativa 2013

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File URL: http://hdl.handle.net/10.1007/s11750-011-0191-y
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Bibliographic Info

Article provided by Springer in its journal TOP.

Volume (Year): 21 (2013)
Issue (Month): 3 (October)
Pages: 572-589

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Handle: RePEc:spr:topjnl:v:21:y:2013:i:3:p:572-589

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Related research

Keywords: Coalition structure; Two-step Shapley value; Weighted Shapley value; Coalition-size weights; Axiomatization; Implementation; 91-02; 91A12;

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References

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  1. René van den Brink & Gerard van der Laan, 2001. "A Class of Consistent Share Functions for Games in Coalition Structure," Tinbergen Institute Discussion Papers 01-044/1, Tinbergen Institute.
  2. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
  3. Kamijo, Yoshio, 2008. "Implementation of weighted values in hierarchical and horizontal cooperation structures," Mathematical Social Sciences, Elsevier, Elsevier, vol. 56(3), pages 336-349, November.
  4. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
  5. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
  6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 589-614, May.
  7. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, Elsevier, vol. 31(3), pages 171-182, June.
  8. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
  9. Vidal-Puga, Juan & Bergantinos, Gustavo, 2003. "An implementation of the Owen value," Games and Economic Behavior, Elsevier, vol. 44(2), pages 412-427, August.
  10. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 1047-64, July.
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Cited by:
  1. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2011. "Two Values for Transferable Utility Games with Coalition and Graph Structure," Tinbergen Institute Discussion Papers 11-164/1, Tinbergen Institute.
  2. Gérard Hamiache, 2012. "A Matrix Approach to TU Games with Coalition and Communication Structures," Social Choice and Welfare, Springer, Springer, vol. 38(1), pages 85-100, January.

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