An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality

Wensheng Jia, Xiaoling Qiu and Dingtao Peng
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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

Mathematics, 2020, vol. 8, issue 1, 1-9

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.

Keywords: vector equilibrium problems; approximation theorem; bounded rationality; generic convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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