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Price competition in a nonlinear differentiated duopoly

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  • Gori, Luca
  • Sodini, Mauro

Abstract

This article represents an attempt to characterise the dynamics of a nonlinear duopoly with price competition and horizontal product differentiation by accounting for non-negativity constraints (on profits and the market demand). The model is set up by following the tradition led by Bischi et al. (1998), according to which players have limited information. The article shows several local and global phenomena of a two-dimensional discrete time system when the price demand elasticity varies. It also points out the differences from both a mathematical and economic point of views in terms of dynamic outcomes when the non-negativity constraints are not binding and when they are binding. This is done by combining mathematical techniques and simulation exercises.

Suggested Citation

  • Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:557-567
    DOI: 10.1016/j.chaos.2017.09.009
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    Cited by:

    1. S. S. Askar & A. Al-khedhairi, 2019. "Analysis of a Four-Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    2. Ding, Shasha & Sun, Hao & Sun, Panfei & Han, Weibin, 2022. "Dynamic outcome of coopetition duopoly with implicit collusion," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Andrea Caravaggio & Mauro Sodini, 2018. "Heterogeneous players in a Cournot model with differentiated products," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 277-295, November.
    4. Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Sarah Mignot & Fabio Tramontana & Frank Westerhoff, 2024. "Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior," Annals of Operations Research, Springer, vol. 337(3), pages 809-834, June.
    6. Ilko Vrankić & Tomislav Herceg & Mirjana Pejić Bach, 2021. "Dynamics and stability of evolutionary optimal strategies in duopoly," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 1001-1019, September.
    7. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.

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    More about this item

    Keywords

    Chaos; Local and global bifurcations; Price competition; Product differentiation;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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