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A note on symmetry breaking in a non linear marketing model

Author

Listed:
  • Andrea Caravaggio

    (University of Foggia)

  • Lorenzo Cerboni Baiardi

    (University of Calabria)

  • Mauro Sodini

    (University of Pisa
    Technical University of Ostrava)

Abstract

In this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.

Suggested Citation

  • Andrea Caravaggio & Lorenzo Cerboni Baiardi & Mauro Sodini, 2021. "A note on symmetry breaking in a non linear marketing model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 507-531, December.
    • Handle: RePEc:spr:decfin:v:44:y:2021:i:2:d:10.1007_s10203-021-00339-6
    DOI: 10.1007/s10203-021-00339-6
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    References listed on IDEAS

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    More about this item

    Keywords

    Nonlinearity; Synchronization; Market share models; Representative agent;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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