Values on regular games under Kirchhoff's laws
AbstractThe 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 InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 58 (2009)
Issue (Month): 3 (November)
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Web page: http://www.elsevier.com/locate/inca/505565
Regular set system Communication situation Regular game Shapley value Kirchhoff's laws;
Other versions of this item:
- Fabien Lange & Michel Grabisch, 2006. "Values on regular games under Kirchhoff's laws," Cahiers de la Maison des Sciences Economiques b06087, Université Panthéon-Sorbonne (Paris 1).
- Fabien Lange & Michel Grabisch, 2006. "Values on regular games under Kirchhoff’s laws," Working Paper Series 0807, Óbuda University, Keleti Faculty of Business and Management, revised Nov 2008.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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