A Note on Well-posedness of Nash-type Games Problems with Set Payoff

Volume 9, Issue 2, pp 486--492 http://dx.doi.org/10.22436/jnsa.009.02.14

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Authors

Yu Zhang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China. Tao Chen - College of Public Foundation, Yunnan Open University, Kunming, 650223, China.

Abstract

In this paper, Nash-type games problems with set payoff (for short, NGPSP) are first introduced. Then, in terms of the measure of noncompactness, some well-posedness results for Nash-type games problems with set payoff are obtained in Banach spaces.

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Keywords

• Well-posedness
• Nash-type games problems
• Hausdorff distance
• set payoff.

MSC

•  47H10
•  54H25

References

• [1] J. P. Aubin, I. Ekeland , Applied Nonlinear Analysis, Dover Publications, Inc., New York (2006)


• [2] J. W. Chen, Y. J. Cho, X. Q. Ou , Levitin-polyakwell-posedness for set-valued optimization problems with constraints, Filomat, 28 (2014), 1345-1352.


• [3] J. W. Chen, Y. J. Cho, Z. P. Wang, The existence of solutions and well-posedness for bilevel mixed equilibrium problems in Banach spaces, Taiwan. J. Math., 17 (2013), 725-748.


• [4] J. W. Chen, Y. C. Liou , Systems of parametric strong quasi-equilibrium problems:existence and well-posedness aspects , Taiwan. J. Math., 18 (2014), 337-355.


• [5] J. W. Chen, Z. P. Wang, Y. J. Cho , Levitin-Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems, Math. Methods Oper. Res., 77 (2013), 33-64.


• [6] J. W. Chen, Z. P. Wang, L. Y. Yuan , Existence of solutions and \(\alpha\)-well-posedness for a system of constrained set-valued variational inequalities, Numer. Algebra Control Optim., 3 (2013), 567-581.


• [7] N. J. Huang, X. J. Long, C. W. Zhao , Well-posedness for vector quasi-equilibrium problems with application, J. Ind. Manag. Optim., 5 (2009), 341-349.


• [8] X. X. Huang, X. Q. Yang, Generalized Levitin-Polyak well-posedness in constrained optimization, SIAM J. Optim., 17 (2006), 243-258.


• [9] K. Kuratowski , Topology, Editions Jacques Gabay, Sceaux (1992)


• [10] S. J. Li, M. H. Li , Levitin-Polyak well-posedness of vector equilibrium problems, Math. Methods Oper. Res., 69 (2009), 125-140.


• [11] S. J. Li, K. L. Teo, X. Q. Yang, Generalized vector quasi-equilibrium problems, Math. Methods Oper. Res. , 61 (2005), 385-397.


• [12] S. J. Li, W. Y. Zhang, Hadamard well-posed vector optimization problems, J. Global Optim., 46 (2010), 383-393.


• [13] M. B. Lignola, J. Morgan , \(\alpha\)-Well-posedness for Nash equilibria and for optimization problems with Nash equilibrium constraints, J. Global Optim., 36 (2006), 439-459.


• [14] A. N. Tykhonov, On the stability of the functional optimization problem, Filomat, 6 (1966), 28-33.


• [15] W. Y. Zhang, Well-posedness for convex symmetric vector quasi-equilibrium problems, J. Math. Anal. Appl., 387 (2012), 909-915.


• [16] W. Y. Zhang, S. J. Li, K. L. Teo, Well-posedness for Set Optimization Problems, Nonlinear Anal., 71 (2009), 3769-3778.


• [17] J. Zeng, S. J. Li, W. Y. Zhang, X. W. Xue, Hadamard well-posedness for a set-valued optimization problem, Optim. Lett., 7 (2013), 559-573.