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Oligopolistic market: stability conditions of the equilibrium point of the generalized Cournot-Puu model

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Języki publikacji
EN
Abstrakty
EN
The paper presents a model describing the behavior of participants of the oligopolistic market. Economic model of the oligopoly – a generalized Cournot-Puu model is constructed. Notion of Cournot equilibrium is introduced. Study on the stability of the equilibrium point of the constructed model is described. As an example, the model of duopoly is considered in detail.
Twórcy
autor
  • AGH University of Science and Technology, Krakow, Faculty of Management
autor
  • Lviv Polytechnic National University, Lviv, Institute of Applied Mathematics and Fundamental Sciences, Applied Mathematics Department
Bibliografia
  • 1. Agiza H.N., Bischi G.I. and Kopel M. 1999. Multistability in a Dynamic Cournot Game with Three Oligopolists. Math. Comput. Simulation, Vol. 51, 63–90.
  • 2. Agiza H.N, Hegazi A.S. and Elsadany A.A. 2001. The dynamics of Bowley’s model with bounded rationality. Chaos, Solitons and Fractals, Vol. 9, 1705–1717.
  • 3. Agiza H.N, Hegazi A.S. and Elsadany A.A. 2002. Complex dynamics and synchronization of duopoly game with bounded rationality. Mathematics and Computers in Simulation, Vol. 58, 133–146.
  • 4. Agiza H.N. and Elsadany A.A. 2003. Nonlinear Dynamics in the Cournot duopoly game with heterogeneous players. Physica A, Vol. 320, 512–524.
  • 5. Agiza H.N. and Elsadany A.A. 2004. Chaotic Dynamics in nonlinear duopoly game with heterogeneous players. Applied Math, and computation, Vol. 149, 843–860.
  • 6. Agliari A., Gardini L. and Puu T. 2000. The Dynamics of a triopoly game. Chaos, Solitons and Fractals, Vol. 11, 2531–2560.
  • 7. Agliari A., Gardini L. and Puu T. 2006a. Global bifurcation in duopoly when the Cournot point is destabilized via a subcritical Neimark bifurcation. International Game Theory Review, Vol. 8, No. 1, 1–20.
  • 8. Agliari A., Chiarella C. and Gardini L. 2006. A Reevaluation of the Adaptive Expectations in Light of Global Nonlinear Dynamic Analysis. Journal of Economic Behavior and Organization, Vol. 60, 526–552.
  • 9. Agliari A. 2006. Homoclinic connections and subcritical Neimark bifurcations in a duopoly model with adaptively adjusted productions. Chaos, Solitons and Fractals, Vol. 29, 739–755.
  • 10. Ahmed E., Agiza, H.N. and Hassan, S.Z. 2000. On modifi cations of Puu’s dynamical duopoly. Chaos, Solitons and Fractals, Vol. 11, 1025-1028.
  • 11. Alekseyev I.V., Khoma I.B., Kavalets I.I., Kostrobii P.P. and Hnativ B.V. 2012. Matematychni modeli rehuliuvannia khaosu v umovakh olihopolistychnoho rynku. Rastr-7, Lviv.
  • 12. Angelini N., Dieci R. and Nardini F. 2009. Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules. Mathematics and Computers in Simulation, Vol. 79, 3179–3196.
  • 13. Bischi G.I. and others. 2009. Nonlinear Oligopolies: Stability and Bifurcations. Springer-Verlag, New York.
  • 14. Bischi G. I., Lamantia F. and Sushko I. 2012. Border collision bifurcations in a simple oligopoly model with constraints. International Journal of Applied Mathematics and Statistics, Vol. 26, Issue No. 2.
  • 15. Chen L. and Chen G. 2007. Controlling chaos in an economic model. Physica A, No. 374, 349–358.
  • 16. Chukhray N. 2012. Competition as a strategy of enterprises functioning in the ecosystem of innovations. Econtechmod, Vol. 1, No. 3, 9–16.
  • 17. Cournot A.A. 1838. Recherches sur les principes mathematiques de la theorie des richesses. Hachette, Paris.
  • 18. Den-Haan W.J. 2001. The importance of the number of different agents in a heterogeneous asset-pricing model. Journal of Economic Dynamics and Control, Vol. 25, 721–746.
  • 19. Elabbasy E.M. and others, 2007. The dynamics of triopoly game with heterogeneous players. International Journal of Nonlinear Science, Vol. 3, No. 2, 83–90.
  • 20. Encyclopedia of Business and Finance by Kaliski B.S. 2001. MacMillan Reference Books Hardcover.
  • 21. Feshchur R., Samulyak V., Shyshkovskyi S. and Yavorska N. 2012. Analytical instruments of management development of industrial enterprises. Econtechmod, Vol. 1, No. 3, 17–22.
  • 22. Jakimowicz A. 2012. Stability of the Cournot–Nash Equilibrium in Standard Oligopoly. Acta Physica Polonica A, Vol. 121, B-50–B-53.
  • 23. Kirman A. and Zimmermann J.B. 2001. Economics with heterogeneous Interacting Agents. Lecture Notes In Economics and Mathematical Systems. Springer, Berlin.
  • 24. Matsumoto A. 2006. Controlling the Cournot–Nash chaos. Journal of Optimization Theory and Applications, No. 128, 379–392.
  • 25. Matsumoto A. and Szidarovszky F. 2011. Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games. Discrete Dynamics in Nature and Society.
  • 26. Moroz O., Karachyna N. and Filatova L. 2012. Economic behavior of machine-building enterprises: analytic and managerial aspects. Econtechmod, Vol. 1, No. 4, 35–42.
  • 27. Onazaki T., Sieg G. and Yokoo M. 2003. Stability, chaos and multiple attractors: A single agent makes a difference. Journal of Economic Dynamics and Control, Vol. 27, 1917–1938.
  • 28. Petrovich J.P. and Nowakiwskii I.I. 2012. Modern koncept of a model design of an organizational system of enterprises management. Econtechmod, Vol. 1, No. 4, 43–50.
  • 29. Puu T. 1991. Chaos in duopoly pricing. Chaos, Solitons and Fractals, Vol. 6, No. 1, 573–581.
  • 30. Puu T. 2000. Attractors, Bifurcations, and Chaos: Nonlinear Phenomena in Economics. Springer, New York.
  • 31. Puu T. 2007. On the Stability of Cournot Equilibrium when the Number of Competitors Increases. Journal of Economic Behavior and Organization.
  • 32. Puu T. and Sushko I. 2002. (Ed. s). Oligopoly and Complex Dynamics: Models and Tools. Springer, New York.
  • 33. Rosser B. The development of complex oligopoly dynamic theory. (Available: http://www.belairsky.com/coolbit/econophys/ complexoligopy.pdf).
  • 34. Sonis M. 1997. Linear Bifurcation Analysis with Applications to Relative Socio-Spatial Dynamics. Discrete Dynamics in Nature and Society, Vol. 1, 45-56.
  • 35. Sonis M. 2000. Critical Bifurcation Surfaces of 3D Discrete Dynamics. Discrete Dynamics in Nature and Society, Vol. 4, 333-343.
  • 36. Tramontana F., Gardini L. and Puu T. 2010. New properties of the Cournot duopoly with isoelastic demand and constant unit costs. Working Papers Series in Economics, Mathematics and Statistics. WP-EMS, No. 1006.
  • 37. Tramontana F. 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling, Vol. 27, 350–357.
Typ dokumentu
Bibliografia
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