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An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality

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  • Wensheng Jia

    (School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China)

  • Xiaoling Qiu

    (School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China)

  • Dingtao Peng

    (School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China)

Abstract

In this paper, our purpose is to investigate the vector equilibrium problem of whether the approximate solution representing bounded rationality can converge to the exact solution representing complete rationality. An approximation theorem is proved for vector equilibrium problems under some general assumptions. It is also shown that the bounded rationality is an approximate way to achieve the full rationality. As a special case, we obtain some corollaries for scalar equilibrium problems. Moreover, we obtain a generic convergence theorem of the solutions of strictly-quasi-monotone vector equilibrium problems according to Baire’s theorems. As applications, we investigate vector variational inequality problems, vector optimization problems and Nash equilibrium problems of multi-objective games as special cases.

Suggested Citation

  • Wensheng Jia & Xiaoling Qiu & Dingtao Peng, 2020. "An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:45-:d:304177
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    References listed on IDEAS

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    5. Jean Strodiot & Phan Vuong & Thi Nguyen, 2016. "A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 64(1), pages 159-178, January.
    6. Q. Ansari & W. Oettli & D. Schläger, 1997. "A generalization of vectorial equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 147-152, June.
    7. Li, S.J. & Li, X.B. & Wang, L.N. & Teo, K.L., 2009. "The Hölder continuity of solutions to generalized vector equilibrium problems," European Journal of Operational Research, Elsevier, vol. 199(2), pages 334-338, December.
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    Cited by:

    1. Carlos Sáenz-Royo & Francisco Chiclana & Enrique Herrera-Viedma, 2022. "Functional Representation of the Intentional Bounded Rationality of Decision-Makers: A Laboratory to Study the Decisions a Priori," Mathematics, MDPI, vol. 10(5), pages 1-17, February.

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