Core concepts for share vectors
A value mapping for cooperative games with transferable utilities is a mapping that assigns to every game a set of vectors each representing a distribution of the payoffs. A value mapping is efficient if to every game it assigns a set of vectors which components all sum up to the worth that can be obtained by all players cooperating together. An approach to efficiently allocate the worth of the `grand coalition' is using share mappings which assign to every game a set of share vectors being vectors which components sum up to one. Every component of a share vector is the corresponding players' share in the total payoff that is to be distributed among the players. In this paper we discuss a class of share mappings containing the (Shapley) share-core, the Banzhaf share-core and the Large Banzhaf share-core, and provide characterizations of this class of share mappings.
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Volume (Year): 18 (2001)
Issue (Month): 4 ()
|Note:||Received: 9 August 1999/Accepted: 25 April 2000|
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References listed on IDEAS
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- Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
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- Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
- van den Brink, J.R. & van der Laan, G., 1999. "Potentials and Reduced Games for Share Functions," Discussion Paper 1999-41, Tilburg University, Center for Economic Research.
- Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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