Abstract
In the classical model of games with transferable utility one assumes that each subgroup of players can form and cooperate to obtain its value. However, we can think that in some situations this assumption is not realistic, that is, not all coalitions are feasible. This suggests that it is necessary to raise the whole question of generalizing the concept of transferable utility game, and therefore to introduce new solution concepts. In this paper we define games on matroids and extend theτ-value as a compromise value for these games.
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References
Bilbao J.M. and Edelman P.H. (2000). The Shapley value on convex geometries.Discrete Applied Mathematics 103, 33–40.
Bilbao J.M., Driessen T.S.H., Jiménez-Losada A. and Lebrón E. (2001). The Shapley value for games on matroids: The static model.Mathematical Methods of Operations Research 53, 333–348.
Driessen T.S.H. and Tijs S.H. (1983). Theτ-value, the nucleolus and the core for a subclass of games.Methods of Operations Research 46, 395–406.
Driessen T.S.H. and Tijs S.H. (1985). Theτ-value, the core and semiconvex games.International Journal of Game Theory 14, 229–247.
Faigle U. and Kern W. (1992). The Shapley value for cooperative games under precedence constraints.International Journal of Game Theory 21, 249–266.
Tijs S.H. (1981). Bounds for the core and theτ-value. In: Moeschlin O. and Pallaschke D. (eds.),Game Theory and Mathematical Economics. North-Holland.
Tijs S.H. (1987). An axiomatization of theτ-value.Mathematical Social Sciences 12, 9–20.
Tijs S.H. and Otten G.-J. (1993). Compromise values in cooperative game theory.Top 1, 1–51.
Welsh D.J.A. (1995). Matroids: Fundamental Concepts. In: Graham R., Grötschel M. and Lovász L. (eds.),Handbook of Combinatorics. Elsevier Science B.V., 481–526.
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This work has been partially supported by the Spanish Ministery of Science and Technology under grant SEC2000-1243.
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Bilbao, J.M., Jiménez-Losada, A., Lebrón, E. et al. Theτ-value for games on matroids. Top 10, 67–81 (2002). https://doi.org/10.1007/BF02578941
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DOI: https://doi.org/10.1007/BF02578941