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Market share dynamics using Lotka–Volterra models

Author

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  • Marasco, A.
  • Picucci, A.
  • Romano, A.

Abstract

Although competition in the marketplace is inherently dynamic and firms change their competitive behavior over time, firms' competitive struggle is generally described using autonomous Lotka–Volterra (LV) models. A great limitation of autonomous LV systems is that the interaction coefficients are constant, and hence firms are assumed to have constant competitive strategies. Also, the solutions of LV models are generally unknown. To address these shortcomings, we introduce a class of integrable nonautonomous LV models. Our LV models present some relevant advantages. First, the analytical solutions of this system are known, therefore we no longer need to fit the LV coefficients. Second, the analytical solutions only depend on the utility functions of the competing firms. Third, our model has a strong connection with the logit model. As mainstream economics extensively use the logit model to describe market demand, our approach has solid economic foundations. In the second part of the article, we test the performance of our approach by studying two cases in competition economics. We find that our model has a better ability to describe and forecast market evolution than the LV autonomous models proposed in the literature.

Suggested Citation

  • Marasco, A. & Picucci, A. & Romano, A., 2016. "Market share dynamics using Lotka–Volterra models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 49-62.
  • Handle: RePEc:eee:tefoso:v:105:y:2016:i:c:p:49-62
    DOI: 10.1016/j.techfore.2016.01.017
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    References listed on IDEAS

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    Cited by:

    1. Hoang-Sa Dang & Ying-Fang Huang & Chia-Nan Wang & Thuy-Mai-Trinh Nguyen, 2016. "An Application of the Short-Term Forecasting with Limited Data in the Healthcare Traveling Industry," Sustainability, MDPI, Open Access Journal, vol. 8(10), pages 1-14, October.
    2. repec:spr:qualqt:v:52:y:2018:i:4:d:10.1007_s11135-017-0581-9 is not listed on IDEAS
    3. repec:eee:tefoso:v:125:y:2017:i:c:p:116-124 is not listed on IDEAS

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