Email this article Comparison of Methods of Organization and Management Efficiency in Dynamic Models of Cournot Oligopoly
- Authors: Korolev A.V.1, Kotova M.A.1, Ugolnitsky G.A.2
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Affiliations:
- Branch of the National Research University Higher School of Economics, 190068, St. Petersburg, Russia
- Southern Federal University, Rostov-on-Don, Russia
- Issue: No 1 (2023)
- Pages: 82-105
- Section: СИСТЕМНЫЙ АНАЛИЗ И ИССЛЕДОВАНИЕ ОПЕРАЦИЙ
- URL: https://journals.rcsi.science/0002-3388/article/view/136854
- DOI: https://doi.org/10.31857/S0002338823010043
- EDN: https://elibrary.ru/HENZDJ
- ID: 136854
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Abstract
Nash and Stackelberg equilibria and cooperative solutions for dynamic game-theoretic Cournot oligopoly models in normal form with inhomogeneous agents are found analytically. Cooperative game-theoretic Cournot oligopoly models of three persons in the form of the von Neumann–Morgenstern and Gromova–Petrosyan characteristic functions are studied, including the calculation of the Shapley vector. A comparative analysis of the payoffs of agents, according to the solutions obtained, is carried out for games in normal form and in the form of a characteristic function.
About the authors
A. V. Korolev
Branch of the National Research University Higher School of Economics, 190068, St. Petersburg, Russia
Email: danitschi@gmail.com
Россия, Санкт-Петербург
M. A. Kotova
Branch of the National Research University Higher School of Economics, 190068, St. Petersburg, Russia
Email: makotova_2@edu.hse.ru
Россия, Санкт-Петербург
G. A. Ugolnitsky
Southern Federal University, Rostov-on-Don, Russia
Author for correspondence.
Email: ougoln@mail.ru
Россия, Ростов-на-Дону
References
- Algorithmic Game Theory. Eds N. Nisan, T. Roughgarden, E. Tardos, V. Vazirany. Cambridge: Cambridge University Press, 2007.
- Dubey P. Inefficiency of Nash equilibria // Math. Operations Research, 1986. V. 11(1). P. 1–8.
- Johari R., Tsitsiklis J.N. Efficiency Loss in a Network Resource Allocation Game // Math. Oper. Res. 2004. V. 29(3). P. 407–435.
- Moulin H., Shenker S. Strategy Proof Sharing of Submodular Costs: Budget Balance Versus Efficiency // Econ. Theory. 2001. V. 18(3). P. 511–533.
- Roughgarden T. Selfish Routing and the Price of Anarchy. Cambridge: MIT Press, 2005.
- Papadimitriou C.H. Algorithms, Games, and the Internet // Proc. 33rd Sympos. Theory of Computing. Cambridge: 2001. P. 749–753.
- Угольницкий Г.А. Методика сравнительного анализа эффективности способов организации активных агентов и методов управления // Проблемы управления. 2022. Т. 3. С. 29–39.
- Мулен Э. Теория игр с примерами из математической экономики. М.: Мир, 1985. 200 с.
- Mas-Colell A., Whinston M.D., Green J.R. Microeconomic Theory. Oxford: Oxford University Press, 1995.
- Vives X. Oligopoly Pricing: Old Ideas and New Tools. Cambridge: MIT Press, 1999.
- Basar T., Olsder G.Y. Dynamic Non-Cooperative Game Theory. Philadelphia: SIAM, 1999. 506 p.
- Dockner E., Jorgensen S., Long N.V., Sorger G. Differential Games in Economics and Management Science. Cambridge: Cambridge University Press, 2000. 382 p.
- Понтрягин Л.С., Болтянский В.Г., Гамкрелидзе Р.В., Мищенко Е.Ф. Математическая теория оптимальных процессов. М.: Наука, 1983.
- Petrosjan L.A., Zenkevich N.A. Game Theory. Basel: World Scientific Publishing, 1996.
- Petrosyan L.A., Yeung D.W.K. Shapley Value for Differential Network Games: Theory and Application // J. Dynamics and Games. 2021. V. 8(2). P. 151–166.
- Shapley L. A Value for n-person Games // Contributions to the Theory of Games. Vol. II Eds H.W. Kuhn, A.W. Tucker. Princeton: 1953.
- Neumann J. von, Morgenstern O. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1953.
- Petrosjan L., Zaccour G. Time-consistent Shapley Value Allocation of Pollution Cost Reduction // J. Economic Dynamics and Control. 2003. V. 27(3). P. 381–398.
- Gromova E.V., Petrosyan L.A. On an Approach to Constructing a Characteristic Function in Cooperative Differential Games // Automation and Remote Control. 2017. V. 78. P. 1680–1692.
- Gromova E., Marova E., Gromov D. A Substitute for the Classical Neumann–Morgenstern Characteristic Function in Cooperative Differential Games // J. Dynamics and Games. 2020. V. 7(2). P. 105–122.
- Угольницкий Г.А., Усов А.Б. Исследование дифференциальных моделей иерархических систем управления путем их дискретизации // АиТ. 2013. № 2. С.109–122.
- Угольницкий Г.А., Усов А.Б. Динамические модели коррупции в иерархических системах управления при эксплуатации биоресурсов // Изв. РАН. ТиСУ. 2014. № 6. С. 168–176.
- Угольницкий Г.А., Усов А.Б. Алгоритмы решения дифференциальных моделей иерархических систем управления // АиТ. 2016. № 5. С. 148–158.
- Korolev A.V., Ougolnitsky G.A. Optimal Resource Allocation in the Difference and Differential Stackelberg Games on Marketing Network // J. Dynamics and Games. 2020. V. 7(2). P. 141–162.
