October  2013, 9(4): 885-892. doi: 10.3934/jimo.2013.9.885

Reduction and dynamic approach for the multi-choice Shapley value

1. 

Department of Applied Mathematics, National Dong Hwa University, Hualien 974, Taiwan

2. 

Department of Applied Mathematics, National Pingtung University of Education, Pingtung 900, Taiwan

Received  March 2012 Revised  February 2013 Published  August 2013

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].
Citation: Yan-An Hwang, Yu-Hsien Liao. Reduction and dynamic approach for the multi-choice Shapley value. Journal of Industrial and Management Optimization, 2013, 9 (4) : 885-892. doi: 10.3934/jimo.2013.9.885
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.

show all references

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.

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