American Institute of Mathematical Sciences

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

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, 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].
Keywords: dynamic process., the Shapley value, reduction, The multi-choice games, solution.
Mathematics Subject Classification: Primary: 91A; Secondary: 91.
Citation: Yan-An Hwang, Yu-Hsien Liao. Reduction and dynamic approach for the multi-choice Shapley value. Journal of Industrial & 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, (1974).   Google Scholar

[2]

E. Calvo and J. C. Santos, A value for multichoice games,, Mathematical Social Sciences, 40 (2000), 341.  doi: 10.1016/S0165-4896(99)00054-2.  Google Scholar

[3]

S. Hart and A. Mas-Colell, Potential, value and consistency,, Econometrica, 57 (1989), 589.  doi: 10.2307/1911054.  Google Scholar

[4]

Y. A. Hwang and Y. H. Liao, Potentializability and consistency for multi-choice solutions,, Spanish Economic Review, 10 (2008), 289.   Google Scholar

[5]

M. Maschler and G. Owen, The consistent Shapley value for hyperplane games,, International Journal of Game Theory, 18 (1989), 389.  doi: 10.1007/BF01358800.  Google Scholar

[6]

H. Moulin, On additive methods to share joint costs,, The Japanese Economic Review, 46 (1995), 303.   Google Scholar

[7]

R. Myerson, Conference structures and fair allocation rules,, International Journal of Game Theory, 9 (1980), 169.  doi: 10.1007/BF01781371.  Google Scholar

[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.  doi: 10.1007/BF01432361.  Google Scholar

[9]

L. S. Shapley, A value for $n$-person game,, in, 28 (1953), 307.   Google Scholar

show all references

References:
[1]

R. J. Aumann and L. S. Shapley, "Values of Non-Atomic Games,", Princeton University Press, (1974).   Google Scholar

[2]

E. Calvo and J. C. Santos, A value for multichoice games,, Mathematical Social Sciences, 40 (2000), 341.  doi: 10.1016/S0165-4896(99)00054-2.  Google Scholar

[3]

S. Hart and A. Mas-Colell, Potential, value and consistency,, Econometrica, 57 (1989), 589.  doi: 10.2307/1911054.  Google Scholar

[4]

Y. A. Hwang and Y. H. Liao, Potentializability and consistency for multi-choice solutions,, Spanish Economic Review, 10 (2008), 289.   Google Scholar

[5]

M. Maschler and G. Owen, The consistent Shapley value for hyperplane games,, International Journal of Game Theory, 18 (1989), 389.  doi: 10.1007/BF01358800.  Google Scholar

[6]

H. Moulin, On additive methods to share joint costs,, The Japanese Economic Review, 46 (1995), 303.   Google Scholar

[7]

R. Myerson, Conference structures and fair allocation rules,, International Journal of Game Theory, 9 (1980), 169.  doi: 10.1007/BF01781371.  Google Scholar

[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.  doi: 10.1007/BF01432361.  Google Scholar

[9]

L. S. Shapley, A value for $n$-person game,, in, 28 (1953), 307.   Google Scholar

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