Reduction and dynamic approach for the multi-choice Shapley value

Yan-An Hwang; Yu-Hsien Liao

doi:10.3934/jimo.2013.9.885

Article Contents

2013, Volume 9, Issue 4: 885-892. Doi: 10.3934/jimo.2013.9.885

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Reduction and dynamic approach for the multi-choice Shapley value

Yan-An Hwang^1, and
Yu-Hsien Liao^2,

1.
Department of Applied Mathematics, National Dong Hwa University, Hualien 974
2.
Department of Applied Mathematics, National Pingtung University of Education, Pingtung 900

Received: March 2012

Revised: February 2013

Published online: August 2013

Abstract / Introduction Related Papers Cited by

Abstract

In the framework of multi-choice games, we propose a specific reduction to construct a dynamic process for the multi-choice Shapley value introduced by Nouweland et al. [8].

Keywords:

Mathematics Subject Classification: Primary: 91A; Secondary: 91B.

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References

[1]	R. J. Aumann and L. S. Shapley, "Values of Non-Atomic Games," Princeton University Press, Princeton, N.J., 1974.
[2]	E. Calvo and J. C. Santos, A value for multichoice games, Mathematical Social Sciences, 40 (2000), 341-354.doi: 10.1016/S0165-4896(99)00054-2.
[3]	S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica, 57 (1989), 589-614.doi: 10.2307/1911054.
[4]	Y. A. Hwang and Y. H. Liao, Potentializability and consistency for multi-choice solutions, Spanish Economic Review, 10 (2008), 289-301.
[5]	M. Maschler and G. Owen, The consistent Shapley value for hyperplane games, International Journal of Game Theory, 18 (1989), 389-407.doi: 10.1007/BF01358800.
[6]	H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1995), 303-332.
[7]	R. Myerson, Conference structures and fair allocation rules, International Journal of Game Theory, 9 (1980), 169-182.doi: 10.1007/BF01781371.
[8]	A. van den Nouweland, J. Potters, S. Tijs and J. M. Zarzuelo, Core and related solution concepts for multi-choice games, ZOR-Mathematical Methods of Operations Research, 41 (1995), 289-311.doi: 10.1007/BF01432361.
[9]	L. S. Shapley, A value for $n$-person game, in "Contributions to the Theory of Games II" (eds. H. W. Kuhn and A. W. Tucker), Annals of Mathematics Studies, 28, Princeton University Press, Princeton, (1953), 307-317.