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An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality

School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China
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Mathematics 2020, 8(1), 45; https://doi.org/10.3390/math8010045
Received: 1 December 2019 / Revised: 17 December 2019 / Accepted: 23 December 2019 / Published: 1 January 2020
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. View Full-Text
Keywords: vector equilibrium problems; approximation theorem; bounded rationality; generic convergence vector equilibrium problems; approximation theorem; bounded rationality; generic convergence
MDPI and ACS Style

Jia, W.; Qiu, X.; Peng, D. An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality. Mathematics 2020, 8, 45.

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