Beckmann’s Bertrand–Edgeworth Duopoly Model: New Pure Strategy Equilibria

In this paper, the concept of weak active equilibrium, which was introduced in the eighties of the twentieth century by Smol’yakov, is used for the first time for a study of Bertrand–Edgeworth oligopoly (that is, competition among firms when firms’ strategies are prices and firms’ production capacit...

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Bibliographic Details
Published in:Automation and remote control 2024-08, Vol.85 (8), p.711-717
Main Author: Shvedov, A. S.
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Control in Social Economic Systems
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Robotics
Systems Theory
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Summary:In this paper, the concept of weak active equilibrium, which was introduced in the eighties of the twentieth century by Smol’yakov, is used for the first time for a study of Bertrand–Edgeworth oligopoly (that is, competition among firms when firms’ strategies are prices and firms’ production capacities are limited). All symmetric weak active equilibria are found for the basic model of Bertrand–Edgeworth duopoly, which was analysed in the sixties of the twentieth century by Beckmann. However, this model is highly simplified. Also, the question of existence of nonsymmetric weak active equilibria is studied.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117924700140