Abstract
Consideration of reference systems for semivalues leads us to a global representation of the action of a semivalue on a game. Using this representation, we show how to modify semivalues to take account of coalition structures on the player set. The players' allocations according to a semivalue, including a modified semivalue, can be computed by means of products of matrices obtained from the multilinear extension of the game.
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References
Carreras, F. and Magaña, A. (1994), The multilinear extension and the modified Banzhaf-Coleman index, Mathematical Social Sciences 28, 215–222.
Dragan, I. (1999), Potential and consistency for semivalues of finite cooperative TU games. International Journal of Mathematics, Game Theory and Algebra 9, 85–97.
Dubey, P., Neyman, A. and Weber, R.J. (1981), Value theory without efficiency. Mathematics of Operations Research 6, 122–128.
Hart, S. and Kurz, M. (1983), Endogenous Formation of Coalitions. Econometrica 51, 1047–1064.
Owen, G. (1972), Multilinear extensions ofgames. Management Science 18, 64–79.
Owen, G. (1977), Values ofgames with a priori unions, in: R. Henn and O. Moeschlin, eds., Essays in Mathematical Economics and Game Theory, Berlin: Springer.
Owen, G. (1981), Modification of the Banzhaf-Coleman index for games with a priori unions, in: M.J. Holler, ed., Power, Voting and Voting Power, Physica-Verlag.
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Amer, R., Miguel giménez, J. Modification of Semivalues for Games with Coalition Structures. Theory and Decision 54, 185–205 (2003). https://doi.org/10.1023/A:1027353528853
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DOI: https://doi.org/10.1023/A:1027353528853