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 & 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

[1]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006

[2]

Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228

[3]

Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021

[4]

M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072

[5]

Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 151-196. doi: 10.3934/dcds.2010.26.151

[6]

Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109

[7]

Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1

[8]

Xianchao Xiu, Ying Yang, Wanquan Liu, Lingchen Kong, Meijuan Shang. An improved total variation regularized RPCA for moving object detection with dynamic background. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1685-1698. doi: 10.3934/jimo.2019024

[9]

Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021035

[10]

Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024

[11]

Zaihong Wang, Jin Li, Tiantian Ma. An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1995-1997. doi: 10.3934/dcdsb.2013.18.1995

[12]

Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521

[13]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]