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Values on regular games under Kirchhoff's laws

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  • Fabien Lange

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, Keleti Faculty of Economics - Budapest Tech)

  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

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

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00496553.

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Date of creation: Nov 2009
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Publication status: Published, Mathematical Social Sciences, 2009, 58, 3, 322-340
Handle: RePEc:hal:cesptp:halshs-00496553

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00496553
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Related research

Keywords: Regular set system; communication situation; regular game; Shapley value; Kirchhoff's laws.;

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References

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  1. 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.
  2. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the Shapley value: a new approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00178916, HAL.
  3. Hwang, Yan-An & Liao, Yu-Hsien, 2008. "Potential approach and characterizations of a Shapley value in multi-choice games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 56(3), pages 321-335, November.
  4. repec:hal:journl:halshs-00178916 is not listed on IDEAS
  5. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 513, Cowles Foundation for Research in Economics, Yale University.
  6. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, Springer, vol. 21(3), pages 249-66.
  7. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 471R, Cowles Foundation for Research in Economics, Yale University.
  8. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, Elsevier, vol. 37(1), pages 79-95, January.
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Citations

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Cited by:
  1. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
  2. Michel Grabisch & Peter Sudhölter, 2014. "The positive core for games with precedence constraints," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 14036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Average tree solutions and the distribution of Harsanyi dividends," MPRA Paper 17909, University Library of Munich, Germany.
  4. 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.
  5. Selcuk, O. & Talman, A.J.J., 2013. "Games With General Coalitional Structure," Discussion Paper, Tilburg University, Center for Economic Research 2013-002, Tilburg University, Center for Economic Research.
  6. Aoi Honda & Michel Grabisch, 2008. "An axiomatization of entropy of capacities on set systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00281598, HAL.
  7. Michel Grabisch, 2010. "Ensuring the boundedness of the core of games with restricted cooperation," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 10093, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  8. repec:hal:cesptp:hal-00803233 is not listed on IDEAS

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