A new look at the role of players’ weights in the weighted Shapley value
everal new families of semivalues for weighted n-person transferable utility games are axiomatically constructed and discussed under increasing collections of axioms, where the weighted Shapley value arises as the resulting one member family. A more general approach to such weighted games defined in the form of two components, a weight vector λ and a classical TU-game v, is provided. The proposed axiomatizations are done both in terms of λ and v. Several new axioms related to the weight vector λ are discussed, including the so-called “amalgamating payoffs” axiom, which characterizes the value of a weighted game in terms of another game with a smaller number of players. They allow for a new look at the role of players’ weights in the context of the weighted Shapley value for the model of weighted games, giving new properties of it. Besides, another simple formula for the weighted Shapley value is found and examples illustrating some surprising behavior of it in the context of players’ weights are given. The paper contains a wide discussion of the results obtained.
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- Pierre Dehez, 2011. "Allocation of fixed costs: characterization of the (dual) weighted Shapley value," Working Papers of BETA 2011-03, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
- Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008.
"Dividends and Weighted Values in Games with Externalities,"
366, Barcelona Graduate School of Economics.
- Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2010. "Dividends and weighted values in games with externalities," International Journal of Game Theory, Springer, vol. 39(1), pages 177-184, March.
- Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008. "Dividends and Weighted Values in Games with Externalities," UFAE and IAE Working Papers 758.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Ines Macho-Stadler & David Perez-Castrillo & David Wettstein, 2009. "Dividends and Weighted Values in Games with Externalities," Working Papers 0906, Ben-Gurion University of the Negev, Department of Economics.
- Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
- Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer, vol. 35(3), pages 523-538, June.
- Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer, vol. 20(2), pages 183-90.
- repec:spr:compst:v:45:y:1997:i:1:p:109-118 is not listed on IDEAS
- Gómez-Rúa, María & Vidal-Puga, Juan, 2008.
"The axiomatic approach to three values in games with coalition structure,"
8904, University Library of Munich, Germany.
- Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
- Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
- Bergantinos, Gustavo & Lorenzo-Freire, Silvia, 2008. ""Optimistic" weighted Shapley rules in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 289-298, February.
- Guillaume Haeringer, 1998.
"A new weight scheme for the Shapley value,"
Game Theory and Information
- E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer, vol. 29(1), pages 1-9.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
- Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
- Valeri Vasil'Ev, 2007. "Weber Polyhedron And Weighted Shapley Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 139-150.
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