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Values on regular games under Kirchhoff's laws

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  • Lange, Fabien
  • Grabisch, Michel

Abstract

The Shapley value is a central notion defining a rational way to share the total worth of a cooperative game among players. We address a general framework leading to applications to games with communication graphs, where the feasible coalitions form a poset whose all maximal chains have the same length. Considering a new way to define the symmetry among players, we propose an axiomatization of the Shapley value of these games. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the efficiency axiom correspond to the two Kirchhoff's laws in the circuit associated to the Hasse diagram of feasible coalitions.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 3 (November)
Pages: 322-340

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:3:p:322-340

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Regular set system Communication situation Regular game Shapley value Kirchhoff's laws;

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References

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  1. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
  2. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471, Cowles Foundation for Research in Economics, Yale University.
  3. Hwang, Yan-An & Liao, Yu-Hsien, 2008. "Potential approach and characterizations of a Shapley value in multi-choice games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 321-335, November.
  4. repec:hal:cesptp:halshs-00178916 is not listed on IDEAS
  5. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
  6. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
  7. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Computational Statistics, Springer, vol. 65(1), pages 153-167, February.
  8. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
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Citations

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Cited by:
  1. Michel Grabisch & Peter Sudhölter, 2014. "The positive core for games with precedence constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020282, HAL.
  2. repec:hal:cesptp:hal-00803233 is not listed on IDEAS
  3. Honda, Aoi & Grabisch, Michel, 2008. "An axiomatization of entropy of capacities on set systems," European Journal of Operational Research, Elsevier, vol. 190(2), pages 526-538, October.
  4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Average tree solutions and the distribution of Harsanyi dividends," MPRA Paper 17909, University Library of Munich, Germany.
  5. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
  6. Michel Grabisch, 2010. "Ensuring the boundedness of the core of games with restricted cooperation," Documents de travail du Centre d'Economie de la Sorbonne 10093, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  7. Selcuk, O. & Talman, A.J.J., 2013. "Games With General Coalitional Structure," Discussion Paper 2013-002, Tilburg University, Center for Economic Research.
  8. Grabisch, Michel & Sudhölter, Peter, 2014. "The positive core for games with precedence constraints," Discussion Papers of Business and Economics 8/2014, Department of Business and Economics, University of Southern Denmark.

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