Comparative Analysis of Iterative Processes of Equilibrium Calculation in Oligopoly Models
УДК 519.677
Abstract
The problem of choosing the optimal behavior of agents in the classic one-product model of the competitive market under linear functions of demand and costs of agents is considered. The dynamic decision-making processes under conditions of uncertainty of decision making by competitors, performed as repeatable static games within a range of admissible answers, are investigated. The analysis targets processes with rational agents using approaches of multi-step reflexive games and models of collective behavior to refine the solutions while observing the current market prices of goods. The processes are distinguished by choosing the current targets: in one case, the agents choose their current output as the current targets when refining the solutions; in another case, the current targets are perceptions of agents about the current equilibrium marginal cost of other agents. It is shown that for oligopolies with Cournot and/ or Stackelberg competition, processes with agents focused on the expected optimum output are more preferable than processes with agents focused on their perceptions of the equilibrium marginal costs of competitors because there are greater opportunities for finding equilibrium states.
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Nash J. Non-Cooperative Games // Annals of Mathematics. 1951. № 54. DOI: 10.2307/1969529.
Опойцев В.И. Равновесие и устойчивость в моделях коллективного поведения. М., 1977.
Беленький В.З., Волконский В.А. и др. Итеративные методы в теории игр и программировании. М., 1974.
Novikov D.A., Chkhartishvili A.G. Reflexion and Control: Mathematical Models. Leiden, 2014. DOI: 10.1201/b16625.
Algazin G.I., Algazina D.G. Collective Behavior in the Stackelberg Model under Incomplete Information // Automation and Remote Control. 2017. № 78 (9). DOI: 10.1134/S0005117917090077.
Алгазин Г.И., Алгазина Д.Г., Пятковский О.И. Неравновесие по Штакельбергу и динамика коллективного поведения // Изв. Алт. гос. ун-та. 2017. № 1 (93). DOI: 10.14258/izvasu(2017)1-11.
Geras’kin M.I. Modeling Reflection in the Non-Linear Model of the Stakelberg Three-Agent Oligopoly for the Russian Telecommunication Market // Automation and Remote Control. 2018. № 79 (5). DOI: 10.1134/S0005117918050065.
Алгазин Г.И., Алгазина Д.Г. Динамика рефлексивного коллективного поведения в модели олигополии с лидерами // Изв. Алт. гос. ун-та. 2018. № 1 (99). DOI: 10.14258/izvasu(2018)1-11.
Алгазина Д.Г., Алгазина Ю.Г. Динамика и равновесие в модели Курно при неполной информации // Вестник СибГУТИ. 2019. № 4.
Айзенберг Н.И., Зоркальцев В.И., Мокрый И.В. Исследование нестационарных олигопольных рынков // Сиб. журнал индустриальной математики. 2017. Т. 20. № 1. DOI: 10.17377/SIBJIM.2017.20.102.
Gao X., Zhong W., Mei S. Convergence of a Cournot Oligopoly Game with Extrapolative Expectations. Southeast University. China. 2012. URL: http://www.ecocyb.ase.ro/32012/Xing%20Gao.pdf.
Yang H., Zhang Y. Complex Dynamics Analisis for Cournot Game with Bounded Rationality in Power Market // J. Electromagnetics Analisis & Applicftions. 2009. № 1.
Kamalinejad H., Majd V.J., Kebriaei H., Kian A.R. Cournot Games with Linear Regression Expectations in Oligopolistic Markets // Mathematics and Computers in Simulation. 2010. V. 80. № 9. DOI: 10.1016/j.matcom.2010.02.002.
Vasin A. Game-Theoretic Study of Electricity Market Mechanism s // Procedia Computer Science. 2014. № 31. DOI: 10.1016/j.procs.2014.05.252.
Cournot A. Researches into the Mathematical Principles of the Theory of Wealth. London, 1960 (Original 1838).
Stackelberg H. Market Structure and Equilibrium: 1 st Edition. Translation into English. Basin, Urch&Hill, Springer. 2011 (Original 1934).
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