Dynamics of Reflexive Collective Behavior in the Oligopoly Model with Leaders
Abstract
The problem of achieving Nash equilibrium in the oligopoly market with oligopolistic firms that acted on Stackelberg using reflexive repetitive games and models of collective behavior dynamics is considered. Oligopolists observe the product current price and use their own reflections on what actions should produce the best response from remaining firms. They repeat the game and clarify output using collective behavior models, making steps towards the current optimal release. The development of the dynamics can be directed by rules of the game with the step size. In case of reflexive games, step sizes can change over time, but firms at each time point must follow a unified policy of the same step size. The necessary and sufficient conditions for the convergence of dynamics in discrete time to the Nash equilibrium are obtained in the class of linear demand and cost functions of oligopolists. Dynamics converge for any initial output and price. Studies of the convergence dynamics when each firm may follow its own independent policy of step size choice are seemed to be prospective.
DOI 10.14258/izvasu(2018)1-11
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Myerson R. Game Theory: Anaysis of Conflict. — London, 1991.
Sakovics J. Games of incomplete information without common knowledge priors // Theory and decision. — 2001. — № 50.
Novikov D., Chkhartishvili A. Reflexion and Control: Mathematical Models. — London, 2014.
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/isvasu(2017)1-11.
Опойцев В.И. Равновесие и устойчивость в моделях коллективного поведения. — М., 1977.
Васин А.А., Васина П.А., Рулева П.Ю. Об организации рынков однородных товаров // Известия РАН. Теория и системы управления. — 2007. — № 1.
Algazin G.I., Algazina D.G. Collective Behavior in the Stackelberg Model under Incomplete Information // Automation and Remote Control. — 2017. — Vol. 78, № 9. DOI: 10.1134/S0005117917090077
Алгазин Г.И., Алгазина Д.Г. Информационное равновесие в модели динамики коллективного поведения на конкурентном рынке // Управление большими системами. — 2016. — № 64.
Geras’kin M.I., Chkhartishvili A.G. Game-theoretic models of an oligopoly market with nonlinear agent cost functions // Automation and Remote Control. — 2017. — Vol. 78, № 9. DOI: 10.1134/S0005117917090089.
Корепанов В.О., Новиков Д.А. Метод рефлексивных разбиений в моделях группового поведения и управления // Проблемы управления. — 2011. — № 1.
Айзенберг Н.И., Зоркальцев В.И., Мокрый И.В. Исследование нестационарных олигопольных рынков // Сибирский журнал индустриальной математики. — 2017. — Т. 20, № 1. DOI: 10.17377/SIBJIM.2017.20.102.
Дюсуше О.М. Статическое равновесие Курно — Нэша и рефлексивные игры олигополии: случай линейных функций спроса и издержек // Экономический журнал ВШЭ. — 2006. — № 1.
Copyright (c) 2018 Г.И. Алгазин, Д.Г. Алгазина
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