Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models

Yekini Shehu (), Lulu Liu (), Xiaolong Qin () and Qiao-Li Dong ()
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Yekini Shehu: Zhejiang Normal University
Lulu Liu: Civil Aviation University of China
Xiaolong Qin: Zhejiang Normal University
Qiao-Li Dong: Civil Aviation University of China

Networks and Spatial Economics, 2022, vol. 22, issue 1, No 6, 153-180

Abstract: Abstract In this paper, we introduce a numerical iterative algorithm with a reflected step to solve the equilibrium problem, which involves non-monotone bifunctions, in real Hilbert spaces. We give weak convergence analysis when the bifunctions are convex and jointly weakly continuous alongside the associated Minty equilibrium problem with a solution. The assumptions in this paper are weaker than the pseudo-monotonicity Lipschitz-type continuity assumptions used recently on equilibrium problems in the literature. Numerical results on Nash-Cournot equilibrium models show that our algorithm is competitive and efficient.

Keywords: Convergence; Iterative method; Nash-cournot equilibrium model; Non-monotone equilibrium problem; 47H05; 47J20; 47J25; 65K15; 90C33 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11067-022-09562-z

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