Values on regular games under Kirchhoff’s laws
AbstractIn cooperative game theory, the Shapley value is a central notion defining a rational way to share the total worth of a game among players. In this paper, we address a general framework leading to applications to games with communication graphs, where the set of feasible coalitions forms a poset where all maximal chains have the same length. We first show that previous definitions and axiomatizations of the Shapley value proprosed by Faigle and Kern, and Bilbao and Edelman still work. Our main contribution is then to propose a new axiomatization avoiding the hierarchical strength axiom of Faigle and Kern, and considering a new way to define the symmetry among players. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the classical efficiency axiom correspond actually to the two Kirchhoff’s laws in the resistor circuit associated to the Hasse diagram of feasible coalitions. We finally work out a weak form of the monotonicity axiom which is satisfied by the proposed value.
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Bibliographic InfoPaper provided by Óbuda University, Keleti Faculty of Business and Management in its series Working Paper Series with number 0807.
Length: 23 pages
Date of creation: 2006
Date of revision: Nov 2008
Regular set systems; regular games; Shapley value; probabilistic efficient values; regular values; Kirchhoff’s laws.;
Other versions of this item:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-12-01 (All new papers)
- NEP-CDM-2008-12-01 (Collective Decision-Making)
- NEP-GTH-2008-12-01 (Game Theory)
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