Control over chaotic price dynamics in a price competition model

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• 作者：E. V. Orlova
• 关键词：Key wordsnonlinear economic dynamics ; model of price competition ; periodic and chaotic dynamic modes ; nonlinear market dynamics ; control over pricing ; bifurcation analysis ; Lyapunov stability ; strategic interaction between companies ; Nash equilibrium
• 刊名：Automation and Remote Control
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：78
• 期：1
• 页码：16-28
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Control, Robotics, Mechatronics; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design;
• 出版者：Pleiades Publishing
• ISSN：1608-3032
• 卷排序：78

文摘

The dynamic model of price competition in which processes of strategic interaction between companies on an imperfect competition market are described with the game-theoretic approach and methods of nonlinear dynamics. The pricing dynamics for the companies is modeled with difference equations (mappings). We study the stability of the fixed point of the price mapping. Results of our numerical modeling have shown the existence of periodic and chaotic solutions in the price competition model. We present intra-company adaptation mechanisms based on changing the prices in a way proportional to the rate of change in the companies’ profits; this lets us reduce the prices to a local Nash equilibrium and stabilize the chaotic dynamics of the market.