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Dynamic monopoly with multiple continuously distributed time delays

Author

Listed:
  • Matsumoto, Akio
  • Szidarovszky, Ferenc

Abstract

Two time delays are assumed in a boundedly rational monopoly. The characteristic equation is derived for the general case, and a complete stability analysis is conducted both analytically and numerically in two special cases. In the first case, wherein the continuously distributed time delays have different weights, it is shown that a monopoly equilibrium is destabilized to generate a limit cycle via Hopf bifurcation. In the second case in which one delay is continuously distributed and the other is fixed, it is demonstrated that the stability of the monopoly equilibrium can change finite number of times and eventually becomes periodically or aperiodically unstable. It is of interest to notice that the two delay dynamics can be qualitatively different from the one delay dynamics.

Suggested Citation

  • Matsumoto, Akio & Szidarovszky, Ferenc, 2015. "Dynamic monopoly with multiple continuously distributed time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 99-118.
    • Handle: RePEc:eee:matcom:v:108:y:2015:i:c:p:99-118
    DOI: 10.1016/j.matcom.2014.01.003
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    References listed on IDEAS

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    1. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
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    Cited by:

    1. Caravaggio, Andrea & Sodini, Mauro, 2020. "Monopoly with differentiated final goods and heterogeneous markets," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Liu, Ping & Fu, Zao & Cao, Jinde & Wei, Yun & Guo, Jianhua & Huang, Wei, 2020. "A decentralized strategy for generalized Nash equilibrium with linear coupling constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 221-232.
    3. Luca Guerrini & Nicolò Pecora & Mauro Sodini, 2018. "Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 239-257, November.

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    More about this item

    Keywords

    Boundedly rational; Continuously distributed time delay; Fixed time delay; Hopf bifurcation; Complex dynamics;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly

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