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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 |
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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