General equilibrium of Bertrand game: A spatial computational approach

Bingyuan Gao; Yaxin Zheng; Jieyu Huang; Bingyuan Gao; Yaxin Zheng; Jieyu Huang

doi:10.3934/math.2021582

AIMS Mathematics

2021, Volume 6, Issue 9: 10025-10036. doi: 10.3934/math.2021582

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Research article

General equilibrium of Bertrand game: A spatial computational approach

1.
Department of Economics and Management, Yuncheng university, Yuncheng 044000, China
2.
Department of Finance, University of International Business and Economics, Beijing 100029, China

Received: 16 February 2021 Accepted: 30 June 2021 Published: 07 July 2021
MSC : 91B50, 37N05

In this paper, the competitive equilibrium of the Bertrand game is discussed with bounded rationality and the utility function. When the parameters changing and the number of firms increasing, the competitive equilibrium valve of Bertrand duopoly game is gradually being blurred. When the number of competitors is more than four, it is very difficult to derive the value of the equilibrium points. How to find the general competitive equilibrium points for Bertrand game, which is studied from spatial agglomeration with mean value theorem. A Bertrand duopoly game is proposed based on a demand function. Celestial bodies motion as method is introduced to handle the number and stability of competitive equilibrium points, and the stable points is symmetry. The results are supported by numerical computation and simulations.
- chaotic district,
- celestial bodies motion,
- equilibrium points,
- spatial agglomeration,
- mean value theorem
Citation: Bingyuan Gao, Yaxin Zheng, Jieyu Huang. General equilibrium of Bertrand game: A spatial computational approach[J]. AIMS Mathematics, 2021, 6(9): 10025-10036. doi: 10.3934/math.2021582

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Abstract

In this paper, the competitive equilibrium of the Bertrand game is discussed with bounded rationality and the utility function. When the parameters changing and the number of firms increasing, the competitive equilibrium valve of Bertrand duopoly game is gradually being blurred. When the number of competitors is more than four, it is very difficult to derive the value of the equilibrium points. How to find the general competitive equilibrium points for Bertrand game, which is studied from spatial agglomeration with mean value theorem. A Bertrand duopoly game is proposed based on a demand function. Celestial bodies motion as method is introduced to handle the number and stability of competitive equilibrium points, and the stable points is symmetry. The results are supported by numerical computation and simulations.

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