-
Previous Article
A new class of positive semi-definite tensors
- JIMO Home
- This Issue
-
Next Article
Upper bounds for Z$ _1 $-eigenvalues of generalized Hilbert tensors
Extension of generalized solidarity values to interval-valued cooperative games
a. | School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China |
b. | School of Architecture, Fuzhou University, Fuzhou, Fujian 350108, China |
The main purpose of this paper is to extend the concept of generalized solidarity values to interval-valued cooperative games and hereby develop a simplified and fast approach for solving a subclass of interval-valued cooperative games. In this paper, we find some weaker coalition monotonicity-like conditions so that the generalized solidarity values of the $ \alpha $-cooperative games associated with interval-valued cooperative games are always monotonic and non-decreasing functions of any parameter $ \alpha \in [0,1] $. Thereby the interval-valued generalized solidarity values can be directly and explicitly obtained by computing their lower and upper bounds through only using the lower and upper bounds of the interval-valued coalitions' values, respectively. The developed method does not use the interval subtraction and hereby can effectively avoid the issues resulted from it. Furthermore, we discuss the effect of the parameter $ \xi $ on the interval-valued generalized solidarity values of interval-valued cooperative games and some significant properties of interval-valued generalized solidarity values.
References:
[1] |
S. Z. Alparslan G$\rm{\ddot{o}}$k,
On the interval Shapley value, Optimization, 63 (2014), 747-755.
doi: 10.1080/02331934.2012.686999. |
[2] |
S. Z. Alparslan G$\rm{\ddot{o}}$k, O. Branzei, R. Branzei and S. Tijs,
Set-valued solution concepts using interval-type payoffs for interval games, Journal of Mathematical Economics, 47 (2011), 621-626.
doi: 10.1016/j.jmateco.2011.08.008. |
[3] |
S. B$\rm{\acute{e}}$al, E. R$\rm{\acute{e}}$mila and P. Solal,
Axiomatization and implementation of a class of solidarity values for TU-games, Theory and Decision, 83 (2017), 61-94.
doi: 10.1007/s11238-017-9586-z. |
[4] |
A. Bhaumik, S. K. Roy and D.-F. Li, Analysis of triangular intuitionistic fuzzy matrix games using robust ranking, Fuzzy Systems, 33 (2017), 327-336. Google Scholar |
[5] |
R. Branzei, O. Branzei, S. Z. Alparslan G$\rm{\ddot{o}}$k and S. Tijs,
Cooperative interval games: A survey, Central European Journal of Operations Research, 18 (2010), 397-411.
doi: 10.1007/s10100-009-0116-0. |
[6] |
R. Branzei, D. Dimitrov and S. Tijs, Shapley-like values for interval bankruptcy games, Economics Bulletin, 3 (2003), 1-8. Google Scholar |
[7] |
A. Calik, T. Paksoy, A. Yildizbasi and N. Y. Pehlivan, A decentralized model for allied closed-loop supply chains: Comparative analysis of interactive fuzzy programming approaches, International Journal of Fuzzy Systems, 19 (2017), 367-382. Google Scholar |
[8] |
E. Calvo and E. Guti$\rm{\acute{e}}$rrez-L$\rm{\acute{o}}$pez,
Axiomatic characterizations of the weighted solidarity values, Mathematical Social Sciences, 71 (2014), 6-11.
doi: 10.1016/j.mathsocsci.2014.03.005. |
[9] |
A. Casajus and F. Huettner,
On a class of solidarity values, European Journal of Operational Research, 236 (2014), 583-591.
doi: 10.1016/j.ejor.2013.12.015. |
[10] |
F. Guan, D. Y. Xie and Q. Zhang,
Solutions for generalized interval cooperative games, Fuzzy Systems, 28 (2015), 1553-1564.
|
[11] |
W. B. Han, H. Sun and G. J. Xu,
A new approach of cooperative interval games: The interval core and Shapley value revisited, Operations Research Letters, 40 (2012), 462-468.
doi: 10.1016/j.orl.2012.08.002. |
[12] |
F. X. Hong and D.-F. Li, Nonlinear programming approach for interval-valued n-person cooperative games, Operational Research: An International Journal, 17 (2017), 479-497. Google Scholar |
[13] |
X. F. Hu and D.-F. Li,
A new axiomatization of the Shapley-solidarity value for games with a coalition structure, Operations Research Letters, 46 (2018), 163-167.
doi: 10.1016/j.orl.2017.12.006. |
[14] |
Y. Kamijo and T. Kongo,
Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value, European Journal of Operational Research, 216 (2012), 638-646.
doi: 10.1016/j.ejor.2011.08.011. |
[15] |
G. Kara, A. $\rm{\ddot{O}}$zmen and G. W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European Journal of Operations Research, (2017), 1--21.
doi: 10.1007/s10100-017-0508-5. |
[16] |
B. B. Kirlar, S. Erg$\rm{\ddot{u}}$n, S. Z. Alparslan G$\rm{\ddot{o}}$k and G. W. Weber,
A game-theoretical and cryptographical approach to crypto-cloud computing and its economical and financial aspects, Annals of Operations Research, 260 (2018), 217-231.
doi: 10.1007/s10479-016-2139-y. |
[17] |
D.-F. Li, Linear programming approach to solve interval-valued matrix games, Omega: The International Journal of management Science, 39 (2011), 655-666. Google Scholar |
[18] |
D.-F. Li and J. C. Liu, A parameterized nonlinear programming approach to solve matrix games with payoffs of I-fuzzy numbers, IEEE Transactions on Fuzzy Systems, 23 (2015), 885-896. Google Scholar |
[19] |
F. Y. Meng, X. H. Chen and C. Q. Tan, Cooperative fuzzy games with interval characteristic functions, Operational Research: An International Journal, 16 (2016), 1-24. Google Scholar |
[20] |
R. Moore, Methods and Applications of Interval Analysis, SIAM Studies in Applied Mathematics, Philadelphia, 1979. |
[21] |
A. S. Nowak and T. Radzik,
A solidarity value for n-person transferable utility games, International Journal of Game Theory, 23 (1994), 43-48.
doi: 10.1007/BF01242845. |
[22] |
B. Oksendal, L. Sandal and J. Uboe,
Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models, Control, 37 (2013), 1284-1299.
doi: 10.1016/j.jedc.2013.02.010. |
[23] |
A. $\rm{\ddot{O}}$zmen, E. Kropat and G. W. Weber,
Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155.
doi: 10.1080/02331934.2016.1209672. |
[24] |
A. $\rm{\ddot{O}}$zmen, G. W. Weber, I. Batmaz and E. Kropat,
RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 4780-4787.
doi: 10.1016/j.cnsns.2011.04.001. |
[25] |
O. Palanci, S. Z. Alparslan G$\rm{\ddot{o}}$k, S. Erg$\rm{\ddot{u}}$n and G. W. Weber,
Cooperative grey games and the grey Shapley value, Optimization, 64 (2015), 1657-1668.
doi: 10.1080/02331934.2014.956743. |
[26] |
O. Palanci, S. Z. Alparslan G$\rm{\ddot{o}}$k, M. O. Olgun and G. W. Weber,
Transportation interval situations and related games, OR Spectrum, 38 (2016), 119-136.
doi: 10.1007/s00291-015-0422-y. |
[27] |
O. Palanci, S. Z. Alparslan G$\rm{\ddot{o}}$k and G. W. Weber,
An axiomatization of the interval Shapley value and on some interval solution concepts, Contributions to Game Theory and Management, 8 (2015), 243-251.
|
[28] |
M. Pervin, S. K. Roy and G. W. Weber,
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.
doi: 10.1007/s10479-016-2355-5. |
[29] |
S. K. Roy and P. Mula, Solving matrix game with rough payoffs using genetic algorithm, Operational Research: An International Journal, 16 (2016), 117-130. Google Scholar |
[30] |
S. K. Roy, G. Maity and G. W. Weber,
Multi-objective two-stage grey transportation problem using utility function with goals, Central European Journal of Operations Research, 25 (2017), 417-439.
doi: 10.1007/s10100-016-0464-5. |
[31] |
E. Savku and G. W. Weber,
A stochastic maximum principle for a markov regime-switching jump-diffusion model with delay and an application to finance, Journal of Optimization Theory and Applications, 179 (2018), 696-721.
doi: 10.1007/s10957-017-1159-3. |
[32] |
G. J. Xu, H. Dai, D. S. Hou and H. Sun,
A-potential function and a non-cooperative foundation for the Solidarity value, Operations Research Letters, 44 (2016), 86-91.
doi: 10.1016/j.orl.2015.12.002. |
show all references
References:
[1] |
S. Z. Alparslan G$\rm{\ddot{o}}$k,
On the interval Shapley value, Optimization, 63 (2014), 747-755.
doi: 10.1080/02331934.2012.686999. |
[2] |
S. Z. Alparslan G$\rm{\ddot{o}}$k, O. Branzei, R. Branzei and S. Tijs,
Set-valued solution concepts using interval-type payoffs for interval games, Journal of Mathematical Economics, 47 (2011), 621-626.
doi: 10.1016/j.jmateco.2011.08.008. |
[3] |
S. B$\rm{\acute{e}}$al, E. R$\rm{\acute{e}}$mila and P. Solal,
Axiomatization and implementation of a class of solidarity values for TU-games, Theory and Decision, 83 (2017), 61-94.
doi: 10.1007/s11238-017-9586-z. |
[4] |
A. Bhaumik, S. K. Roy and D.-F. Li, Analysis of triangular intuitionistic fuzzy matrix games using robust ranking, Fuzzy Systems, 33 (2017), 327-336. Google Scholar |
[5] |
R. Branzei, O. Branzei, S. Z. Alparslan G$\rm{\ddot{o}}$k and S. Tijs,
Cooperative interval games: A survey, Central European Journal of Operations Research, 18 (2010), 397-411.
doi: 10.1007/s10100-009-0116-0. |
[6] |
R. Branzei, D. Dimitrov and S. Tijs, Shapley-like values for interval bankruptcy games, Economics Bulletin, 3 (2003), 1-8. Google Scholar |
[7] |
A. Calik, T. Paksoy, A. Yildizbasi and N. Y. Pehlivan, A decentralized model for allied closed-loop supply chains: Comparative analysis of interactive fuzzy programming approaches, International Journal of Fuzzy Systems, 19 (2017), 367-382. Google Scholar |
[8] |
E. Calvo and E. Guti$\rm{\acute{e}}$rrez-L$\rm{\acute{o}}$pez,
Axiomatic characterizations of the weighted solidarity values, Mathematical Social Sciences, 71 (2014), 6-11.
doi: 10.1016/j.mathsocsci.2014.03.005. |
[9] |
A. Casajus and F. Huettner,
On a class of solidarity values, European Journal of Operational Research, 236 (2014), 583-591.
doi: 10.1016/j.ejor.2013.12.015. |
[10] |
F. Guan, D. Y. Xie and Q. Zhang,
Solutions for generalized interval cooperative games, Fuzzy Systems, 28 (2015), 1553-1564.
|
[11] |
W. B. Han, H. Sun and G. J. Xu,
A new approach of cooperative interval games: The interval core and Shapley value revisited, Operations Research Letters, 40 (2012), 462-468.
doi: 10.1016/j.orl.2012.08.002. |
[12] |
F. X. Hong and D.-F. Li, Nonlinear programming approach for interval-valued n-person cooperative games, Operational Research: An International Journal, 17 (2017), 479-497. Google Scholar |
[13] |
X. F. Hu and D.-F. Li,
A new axiomatization of the Shapley-solidarity value for games with a coalition structure, Operations Research Letters, 46 (2018), 163-167.
doi: 10.1016/j.orl.2017.12.006. |
[14] |
Y. Kamijo and T. Kongo,
Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value, European Journal of Operational Research, 216 (2012), 638-646.
doi: 10.1016/j.ejor.2011.08.011. |
[15] |
G. Kara, A. $\rm{\ddot{O}}$zmen and G. W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European Journal of Operations Research, (2017), 1--21.
doi: 10.1007/s10100-017-0508-5. |
[16] |
B. B. Kirlar, S. Erg$\rm{\ddot{u}}$n, S. Z. Alparslan G$\rm{\ddot{o}}$k and G. W. Weber,
A game-theoretical and cryptographical approach to crypto-cloud computing and its economical and financial aspects, Annals of Operations Research, 260 (2018), 217-231.
doi: 10.1007/s10479-016-2139-y. |
[17] |
D.-F. Li, Linear programming approach to solve interval-valued matrix games, Omega: The International Journal of management Science, 39 (2011), 655-666. Google Scholar |
[18] |
D.-F. Li and J. C. Liu, A parameterized nonlinear programming approach to solve matrix games with payoffs of I-fuzzy numbers, IEEE Transactions on Fuzzy Systems, 23 (2015), 885-896. Google Scholar |
[19] |
F. Y. Meng, X. H. Chen and C. Q. Tan, Cooperative fuzzy games with interval characteristic functions, Operational Research: An International Journal, 16 (2016), 1-24. Google Scholar |
[20] |
R. Moore, Methods and Applications of Interval Analysis, SIAM Studies in Applied Mathematics, Philadelphia, 1979. |
[21] |
A. S. Nowak and T. Radzik,
A solidarity value for n-person transferable utility games, International Journal of Game Theory, 23 (1994), 43-48.
doi: 10.1007/BF01242845. |
[22] |
B. Oksendal, L. Sandal and J. Uboe,
Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models, Control, 37 (2013), 1284-1299.
doi: 10.1016/j.jedc.2013.02.010. |
[23] |
A. $\rm{\ddot{O}}$zmen, E. Kropat and G. W. Weber,
Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155.
doi: 10.1080/02331934.2016.1209672. |
[24] |
A. $\rm{\ddot{O}}$zmen, G. W. Weber, I. Batmaz and E. Kropat,
RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 4780-4787.
doi: 10.1016/j.cnsns.2011.04.001. |
[25] |
O. Palanci, S. Z. Alparslan G$\rm{\ddot{o}}$k, S. Erg$\rm{\ddot{u}}$n and G. W. Weber,
Cooperative grey games and the grey Shapley value, Optimization, 64 (2015), 1657-1668.
doi: 10.1080/02331934.2014.956743. |
[26] |
O. Palanci, S. Z. Alparslan G$\rm{\ddot{o}}$k, M. O. Olgun and G. W. Weber,
Transportation interval situations and related games, OR Spectrum, 38 (2016), 119-136.
doi: 10.1007/s00291-015-0422-y. |
[27] |
O. Palanci, S. Z. Alparslan G$\rm{\ddot{o}}$k and G. W. Weber,
An axiomatization of the interval Shapley value and on some interval solution concepts, Contributions to Game Theory and Management, 8 (2015), 243-251.
|
[28] |
M. Pervin, S. K. Roy and G. W. Weber,
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.
doi: 10.1007/s10479-016-2355-5. |
[29] |
S. K. Roy and P. Mula, Solving matrix game with rough payoffs using genetic algorithm, Operational Research: An International Journal, 16 (2016), 117-130. Google Scholar |
[30] |
S. K. Roy, G. Maity and G. W. Weber,
Multi-objective two-stage grey transportation problem using utility function with goals, Central European Journal of Operations Research, 25 (2017), 417-439.
doi: 10.1007/s10100-016-0464-5. |
[31] |
E. Savku and G. W. Weber,
A stochastic maximum principle for a markov regime-switching jump-diffusion model with delay and an application to finance, Journal of Optimization Theory and Applications, 179 (2018), 696-721.
doi: 10.1007/s10957-017-1159-3. |
[32] |
G. J. Xu, H. Dai, D. S. Hou and H. Sun,
A-potential function and a non-cooperative foundation for the Solidarity value, Operations Research Letters, 44 (2016), 86-91.
doi: 10.1016/j.orl.2015.12.002. |
[1] |
Sergio Zamora. Tori can't collapse to an interval. Electronic Research Archive, , () : -. doi: 10.3934/era.2021005 |
[2] |
Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020047 |
[3] |
David W. K. Yeung, Yingxuan Zhang, Hongtao Bai, Sardar M. N. Islam. Collaborative environmental management for transboundary air pollution problems: A differential levies game. Journal of Industrial & Management Optimization, 2021, 17 (2) : 517-531. doi: 10.3934/jimo.2019121 |
[4] |
Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051 |
[5] |
Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020347 |
[6] |
Alain Bensoussan, Xinwei Feng, Jianhui Huang. Linear-quadratic-Gaussian mean-field-game with partial observation and common noise. Mathematical Control & Related Fields, 2021, 11 (1) : 23-46. doi: 10.3934/mcrf.2020025 |
[7] |
Qingfeng Zhu, Yufeng Shi. Nonzero-sum differential game of backward doubly stochastic systems with delay and applications. Mathematical Control & Related Fields, 2021, 11 (1) : 73-94. doi: 10.3934/mcrf.2020028 |
[8] |
Zhongbao Zhou, Yanfei Bai, Helu Xiao, Xu Chen. A non-zero-sum reinsurance-investment game with delay and asymmetric information. Journal of Industrial & Management Optimization, 2021, 17 (2) : 909-936. doi: 10.3934/jimo.2020004 |
[9] |
Nguyen Thi Kim Son, Nguyen Phuong Dong, Le Hoang Son, Alireza Khastan, Hoang Viet Long. Complete controllability for a class of fractional evolution equations with uncertainty. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020104 |
[10] |
Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2020 doi: 10.3934/jcd.2021006 |
[11] |
Vieri Benci, Marco Cococcioni. The algorithmic numbers in non-archimedean numerical computing environments. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020449 |
[12] |
Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discrete-time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 299-336. doi: 10.3934/dcdsb.2020331 |
[13] |
Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310 |
[14] |
Shasha Hu, Yihong Xu, Yuhan Zhang. Second-Order characterizations for set-valued equilibrium problems with variable ordering structures. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020164 |
[15] |
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina, Alberto Tesei. Signed Radon measure-valued solutions of flux saturated scalar conservation laws. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3143-3169. doi: 10.3934/dcds.2020041 |
[16] |
Marek Macák, Róbert Čunderlík, Karol Mikula, Zuzana Minarechová. Computational optimization in solving the geodetic boundary value problems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 987-999. doi: 10.3934/dcdss.2020381 |
[17] |
Nguyen Huy Tuan. On an initial and final value problem for fractional nonclassical diffusion equations of Kirchhoff type. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020354 |
[18] |
Vo Van Au, Hossein Jafari, Zakia Hammouch, Nguyen Huy Tuan. On a final value problem for a nonlinear fractional pseudo-parabolic equation. Electronic Research Archive, 2021, 29 (1) : 1709-1734. doi: 10.3934/era.2020088 |
[19] |
Nguyen Huu Can, Nguyen Huy Tuan, Donal O'Regan, Vo Van Au. On a final value problem for a class of nonlinear hyperbolic equations with damping term. Evolution Equations & Control Theory, 2021, 10 (1) : 103-127. doi: 10.3934/eect.2020053 |
[20] |
Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]