Solving the Cournot Oligopoly Game under Incomplete Information with the Possibility of Cooperative Interaction
УДК 519.8
Abstract
The balance of commodity markets is an extremely important and pressing challenge. There is an active development of research aimed at solving such problem. However, well-known theoretical models do not always adequately reflect the desire of agents to make such individual decisions and search for such compromises to ensure the greatest profit and bring the market to equilibrium.
The article considers the solution of the Cournot oligopoly game under incomplete information for the case of linear demand and linear costs. The approaches of the reflexive games theory and collective behavior theory are the basis for the construction of the decision-making process by agents. The policy of optimal responses of agents to the expected output volumes of the environment under traditional assumptions about the independence of agents may not lead to equilibrium. Therefore, the article considers and proposes non-traditional solutions that allow agents to cooperate. It is shown that it is enough to jointly regulate the process only at initial stage. After that, it should come to equilibrium if, in the future, agents independently adjust their own output, counting on the maximum expected profit. The necessary assertions and their mathematical proofs are given.
Downloads
Metrics
References
Novikov D.A., Chkhartishvili A.G. Reflexion and Control: Mathematical Models. Leiden, 2014.
Nash J. Non-Cooperative Games // Annals of Mathematics. 1951. № 54.
Askar S.S., Elettrebybc M.F.The Impact of Cost Uncertainty on Cournot Oligopoly Games // Applied Mathematics and Computation. 2017. Vol. 312.
Algazin G.I., AlgazinaYu.G. Reflexive Dynamics in the Cournot Oligopoly under Uncertainty // Automation and Remote Control. 2020. Vol. 81. № 2.
Алгазин Г.И., Алгазина Д.Г. Моделирование динамики коллективного поведения в рефлексивной игре с произвольным числом лидеров // Информатика и автоматизация. 2022. № 21 (2). DOI: t0.t5622/ia.21.2.5.
Гераськин М.И. Рефлексивный анализ равновесий в игре триполии при линейных функциях издержек агентов // Автоматика и телемеханика. 2022. № 3. DOI: 10.31857/ S0005231022030084.
Ueda M. Effect of Information Asymmetry in Cournot Duopoly Game with Bounded Rationality // Applied Mathematics and Computation. 2019. Vol. 362. DOI: 10.1016/j. amc.2019.06.049.124535.
Опойцев В.И. Равновесие и устойчивость в моделях коллективного поведения. М., 1977.
Cournot A. Researches into the Mathematical Principles of the Theory of Wealth // London, 1960. (Original 1838).
Малишевский А.В. Качественные модели в теории сложных систем. М., 1998.
Fedyanin D.N. Monotonicity of Equilibriums in Cournot Competition with Mixed Interactions of Agents and Epistemic Models of Uncertain Market // Procedia Computer Science. 2021. Vol. 186 (3).
Copyright (c) 2022 Юлия Геннадьевна Алгазина ; Дарья Геннадьевна Алгазина
This work is licensed under a Creative Commons Attribution 4.0 International License.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
