Actual Problems of
Economics and Law




DOI: 10.21202/1993-047X.11.2017.4.66-81

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Authors :
1. Inna A. Biryukova, student
Samara National Research University named after Acad. S. P. Korolev (Samara University)

2. Mikhail I. Geras’kin, Doctor of Economics, professor, Head of the Department of Matyhematical methods in Economics
Samara National Research University named after Acad. S. P. Korolev (Samara University)

Structural analysis of oligopoly market based on the reflective game model by the example of telecommunication market in Russia

Objective: to analyze the possible structures of the oligopoly market distribution by the example of telecommunication industry in terms of the agents’ reflexive behavior.


Methods: game theory, economic-mathematical modeling.

Results: the article states that one of the first objects in the game theory is an oligopoly market. Based on the analysis of game theory studies, it was found that there is a need to achieve information equilibrium in reflexive games of three agents in the oligopoly market. To solve this problem, we analyzed all possible representations of the agents, leading to the set of games in the Russian telecommunications market for three agents: OJSC “MTS”, OJSC “Megafon” and OJSC “Vympelcom”. Three reflection grades were studied: 1) representations of the agent about other agents, 2) representations of the agent’s perception of other agents about it and 3) representations of the agent about what its competitors think about the first agent’s opinion about the other two. As a result, the general patterns were revealed of the expressions of conjectural variations in each case; it was proved that further detailing of the reflection is not needed. As a result of calculations, the models of informational equilibriums of the Russian telecommunication market were constructed; for that, the averaged values of the demand and cost functions parameters functions of cellular communication operators were taken. It was also revealed that in 2015 the actual telecommunication market in the Russian Federation qualitatively, i.e. by the ratio of market shares, was close to equilibrium on condition of first rank reflexive behavior for the case when the market leader, OJSC “MTS”, represents its counterparties – OJSC “Megafon” and OJSC “Vympelcom” – as the driven agents.

Scientific novelty: the analytical expressions for the information equilibrium parameters (issues and profits of the agents, aggregate output and prices) are obtained in the oligopoly market with a linear demand function, linear cost functions of agents with equal marginal and fixed costs, for arbitrary reflection grades.

Practical significance: the obtained set of informational equilibriums may be used to compare it to the actual equilibriums of the Russian telecommunications market to assess the reflection grades of its agents.

Keywords :

Economics and national economy management; Reflection; Grade; Reflexive games; Agent; Stackelberg equilibrium; Oligopoly; Conjectural variation; Telecommunication market

Bibliography :

1. Blinova T. V., Mitrofanov A. Yu., Rusanovskii A. V. Forecasting the service sector development in the structure of the Russian economy, Vestnik Tomskogo gosudarstvennogo universiteta, 2008, No. 9 (65), pp. 336–344 (in Russ.).
2. Mas-Collel A., Whinston M., Green J. Microeconomic Theory, N. Y.: Oxford Univ. Press, 1995, 618 p.
3. Geras'kin M. I. Issues of determining the reflective equilibrium in the oligopoly market, Vestnik Samarskogo gosudarstvennogo ekonomicheskogo universiteta, 2017, No. 1 (147), pp. 17–25 (in Russ.).
4. Nash J. Non-cooperative Games, Annals of Mathematics, 1951, vol. 54, pp. 286–295.
5. Naimzada A. K., Sbragia L. Oligopoly games with nonlinear demand and cost functions: Two boundedly rational adjustment processes, Chaos, Solitons and Fractals, 2006, vol. 29 (3), pp. 707–722.
6. Novikov D. A. Strategic reflection in bi-matrix games, Regional economics in informational dimension: models, estimations, forecasts, collection of scientific works, ed. E. Yu. Ivanova, R. M. Nizhegorodtseva, Moscow: Biznes-Yunitek, 2003, pp. 296–307 (in Russ.).
7. Novikov D. A., Chkhartishvili A. G. Reflective games, Moscow: SINTEG, 2003, 160 p. (in Russ.)
8. Cournot A. A. Researches into the Mathematical Principles of the Theory of Wealth, London: Hafner, 1960 (Original 1838).
9. Vasin A. Game-theoretic study of electricity market mechanisms, Procedia Computer Science, 2014, vol. 31, pp. 124–132.
10. Colacicco R. Ten years of general oligopolistic equilibrium: A survey, Journal of Economic Surveys, 2015, vol. 29 (5), pp. 965–992.
11. Ino H., Matsumura T. Welfare-Improving Effect of a Small Number of Followers in a Stackelberg Model, B. E. Journal of Theoretical Economics, 2016, vol. 16 (1), pp. 243–265.
12. Sherali H. D. Multiple leader Stackelberg model and analysis, Operations Research, 1984, vol. 32 (2), pp. 390–404.
13. Geras'kin M. I., Chkhartishvili A. G. Theoretical-game models of oligopoly market with non-linear functions of agents’ costs, Avtomatika i telemekhanika, 2017, No. 9, pp. 106–130 (in Russ.).
14. Karmarkar U. S., Rajaram K. Aggregate production planning for process industries under oligopolistic competition, European Journal of Operational Research, 2012, vol. 223 (3), pp. 680–689.
15. Ledvina A., Sigar R. Oligopoly games under asymmetric costs and an application to energy production, Mathematics and Financial Economics, 2012, vol. 6 (4), pp. 261–293.
16. Currarini S., Marini M. A. Sequential play and cartel stability in Sournot oligopoly, Applied Mathematical Sciences, 2013, vol. 7 (1–4), pp. 197–200.
17. Askar S., Alnowibet K. Nonlinear oligopolistic game with isoelastic demand function: Rationality and local monopolistic approximation, Chaos, Solitons and Fractals, 2016, vol. 84, pp. 15–22.
18. Naimzada A., Tramontana F. Two different routes to complex dynamics in an heterogeneous triopoly game, Journal of Difference Equations and Applications, 2015, vol. 21 (7), pp. 553–563.
19. Cavalli F., Naimzada A., Tramontana F. Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity, Communications in Nonlinear Science and Numerical Simulation, 2015, vol. 23 (1–3), pp. 245–262.
20. Geras’kin M. I., Chkhartishvili A. G. Structural modeling of oligopoly market under the nonlinear functions of demand and agents’ costs, Automation and Remote Control, 2017, vol. 78, is. 2, pp. 332–348.
21. Novikov D. A., Chkhartishvili A. G. Mathematical Models of Informational and Strategic Reflexion: a Survey, Advances in Systems Science and Applications, 2014, vol. 3, pp. 254–277.
22. Geras’kin M. I., Chkhartishvili A. G. Structural modeling of oligopoly market under the nonlinear functions of demand and agents’ costs, Automation and Remote Control, 2017, vol. 78 (2), pp. 332–348.
23. Chkhartishvili A. G., Korepanov V. O. Adding Informational Beliefs to the Players Strategic Thinking Model, IFACPapersOnLine, 2016, vol. 49 (32), pp. 19–23.
24. Liu Y., Gao L., Guan J. Marketing strategy of price competition and product differentiation in duopoly enterprises with asymmetric information, International Conference on Services Systems and Services Management, Proceedings of ICSSSM'05, 2005, vol. 1. (1499557), pp. 665–668.
25. Gilpatric S. M., Li Y. Information value under demand uncertainty and endogenous market leadership, Economic Inquiry, 2015, vol. 53 (1), pp. 589–603.
26. Geras’kin M. Game-theoretic analysis of Stackelberg oligopoly with arbitrary rank reflexive behavior of agents, Kybernetes, 2017, vol. 46, is. 6. DOI: 10.1108/K-12-2016-0351
27. Korn G., Korn T. Reference book on mathematics for academic workers and engineers, Moscow: Nauka, 1973, 832 p. (in Russ.).
28. Yudina S. V., Geras'kin M. I. Scientific seminar of students and post-graduate of the Institute of Economics and Management “Analysis of reflective game of three agents in a linear model of oligopoly”, Samara, 2017 (in Russ.).

Citation :

Biryukova I. A., Geras’kin M. I. Structural analysis of oligopoly market based on the reflective game model by the example of telecommunication market in Russia, Actual Problems of Economics and Law, 2017, vol. 11, No. 4, рp. 66–81 (in Russ.). DOI: http://dx.doi.org/10.21202/1993-047X.11.2017.4.66-81

Type of article : The scientific article

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