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Reflexive Dynamics in the Cournot Oligopoly under Uncertainty

  • Control in Social Economic Systems
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Abstract

A model of dynamic behavior in the Cournot market in the class of linear demand and cost functions of agents is presented. Observing the current state of the market and considering current economic restrictions, agents refine their outputs in game-to-game dynamics and take steps towards the current position of their goal. Sufficient conditions on the step sizes chosen by agents independently of each other under which the dynamics converge to the static Cournot-Nash equilibrium are established.

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References

  1. Myerson, R., Game Theory: Anaysis of Conflict, London: Harvard Univ. Press, 1991.

    MATH  Google Scholar 

  2. Mas-Collel, A., Whinston, D., and Green, J., Microeconomic Theory, New York: Oxford Univ. Press, 1995.

    MATH  Google Scholar 

  3. Novikov, D.A. and Chkhartishvili, A.G., Reflexion and Control: Mathematical Models, Leiden: CRC Press, 2014.

    Book  Google Scholar 

  4. Novikov, D.A., Models of Strategic Behavior, Autom. Remote Control, 2012, vol. 73, no. 1, pp. 1–19.

    Article  MathSciNet  Google Scholar 

  5. Aizenberg, N.I., Zorkal’tsev, V.I., and Mokryi, I.V., Study of Unsteady Oligopoly Markets, J. Appl. Ind. Math., 2017, vol. 11, pp. 8–16.

    Article  MathSciNet  Google Scholar 

  6. Vasin, A.A., Vasina, P.A., and Ruleva, P.Yu., On Organization of Markets of Homogeneous Goods, J. Comp. Syst. Sci. Int., 2007, vol. 46, pp. 93–106.

    Article  MathSciNet  Google Scholar 

  7. Kukushkin, N.S., Best Response Dynamics in Finite Games with Additive Aggregation, Games Econom. behavior, 2004, no. 48, pp. 94–110.

    Article  MathSciNet  Google Scholar 

  8. Weihong, H., Theory of Adaptive Adjustment, Discret. Dynam. Nature Soc., 2000, vol. 5, no. 4, pp. 247–263.

    Article  Google Scholar 

  9. Algazin, G.I. and Algazina, D.G., Informational Equilibrium in the Dynamic Model of Collective Behavior in a Competitive Market, Upravl. Bol’sh. Sist., 2016, no. 64, pp. 112–136.

  10. Kamalinejad, H., Majda, V.J., Kebriaei, H., and Kian, A.R., Cournot Games with Linear Regression Expectations in Oligopolistic Markets, Math. Comput. Simulat., 2010, vol. 80, no. 9, pp. 1874–1885.

    Article  MathSciNet  Google Scholar 

  11. Gao, X., Zhong, W., and Mei, S., Convergence of a Cournot Oligopoly Game with Extrapolative Expectations, Southeast University, China, 2012. www.ecocyb.ase.ro/32012/Xing%20Gao.pdf

  12. Novikov, D.A. and Chkhartishvili, A.G., Models of Reflexive Games in Control Problems of Ecological-Economic Systems, Upravlen. Bol’sh. Sist., 2015, no. 55, pp. 362–372.

  13. Korepanov, V.O., Control of Reflexive Behavior of Agents in the Cournot Oligopoly Model, Upravlen. Bol’sh. Sist., 2010, no. 31, pp. 225–249.

  14. Yang, H. and Zhang, Y., Complex Dynamics Analysis for Cournot Game with Bounded Rationality in Power Market, J. Electromagn. Anal. Appl., 2009, no. 1, pp. 48–60.

    Article  Google Scholar 

  15. Agiza, H.N. and Elsadany, A.A., Chaotic Dynamics in Nonlinear Duopoly Game with Heterogeneous Players, Appl. Math. Comput., 2004, vol. 149, no. 4, pp. 843–860.

    MathSciNet  MATH  Google Scholar 

  16. Bischi, G.I. and Kopel, M., Equilibrium Selection in a Nonlinear Duopoly Game with Adaptive Expectations, J. Econom. Behavior Organ., 2001, no. 46, pp. 73–100.

    Article  Google Scholar 

  17. Geras’kin, M.I. and Chkhartishvili, A.G., Analysis of Game-Theoretic Models of an Oligopoly Market under Constraints on the Capacity and Competitiveness of Agents, Autom. Remote Control, 2017, vol. 78, no. 11, pp. 2025–2038.

    Article  MathSciNet  Google Scholar 

  18. Dyusushe, O.M., Static Cournot-Nash Equilibrium and Reflexive Oligopoly Games: The Case of Linear Demand and Cost Functions, Ekon. Zh. Vyssh. Shk. Ekon., 2006, no. 1, pp. 3–32.

  19. Algazin, G.I. and Algazina, D.G., Collective Behavior in the Stackelberg Model under Incomplete Information, Autom. Remote Control, 2017, vol. 78, no. 9, pp. 1619–1630.

    Article  MathSciNet  Google Scholar 

  20. Puu, T., Attractors, Bifurcations, & Chaos: Nonlinear Phenomena in Economics, Berlin: Heidelberg, 2003.

    Book  Google Scholar 

  21. Matsumoto, A., Controlling the Cournot-Nash Chaos, J. Optim. Theory Appl., 2006, vol. 128, no. 2, pp. 379–392.

    Article  MathSciNet  Google Scholar 

  22. Vasin, A.A., Modeli dinamiki kollektivnogo povedeniya (Dynamic Models of Collective Behavior), Moscow: Mosk. Gos. Univ., 1989.

    Google Scholar 

  23. Opoitsev, V.I., Ravnovesie i ustoichivost’ v modelyakh kollektivnogo povedeniya (Equilibrium and Stability in Collective Behavior Models), Moscow: Nauka, 1977.

    Google Scholar 

  24. Belen’kii, V.Z., Volkonskii, V.A., Ivankov, S.A., et al., Iterativnye metody v teorii igr i programmirovanii (Iterative Methods in Game Theory and Programming), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  25. Geras’kin, M.I., Modeling Reflection in the Non-Linear Model of the Stakelberg Three-Agent Oligopoly for the Russian Telecommunication Market, Autom. Remote Control, 2018, vol. 79, no. 5, pp. 841–859.

    Article  MathSciNet  Google Scholar 

  26. Cournot, A., Researches into the Mathematical Principles of the Theory of Wealth, London: Hafner, 1960.

    MATH  Google Scholar 

  27. Frisch, R., Monopoly, Polypoly—The Concept of Force in the Economy, in Internat. Econom. Papers, London-New York, 1951, no. 1, pp. 23–36.

  28. Nash, J., Non-Cooperative Games, Ann. Math., 1951, no. 54, pp. 286–295.

  29. Malishevskii, A.V., Kachestvennye modeli v teorii slozhnykh sistem (Qualitative Models in Theory of Complex Systems), Moscow: Nauka, 1998.

    Google Scholar 

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Authors and Affiliations

  1. Altai State University, Barnaul, Russia

    G. I. Algazin

  2. Polzunov Altai State Technical University, Barnaul, Russia

    Yu. G. Algazina

Authors
  1. G. I. Algazin
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  2. Yu. G. Algazina
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Corresponding authors

Correspondence to G. I. Algazin or Yu. G. Algazina.

Additional information

This paper was recommended for publication by D.A. Novikov, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 2, pp. 115–133.

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Algazin, G.I., Algazina, Y.G. Reflexive Dynamics in the Cournot Oligopoly under Uncertainty. Autom Remote Control 81, 287–301 (2020). https://doi.org/10.1134/S0005117920020083

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  • DOI: https://doi.org/10.1134/S0005117920020083

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