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The dynamics of market share’s growth and competition in quadratic mappings

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  • Dominique, C-Rene
  • Rivera-Solis, Luis Eduardo

Abstract

This paper shows that the observed output of any market, placed within the confine of a quadratic map, can characterize the state of that market. Such an approach explains the process of market share’s growth and its pitfalls, the consequences of broken symmetry of scaling, as well as the limits of firms’ competition for market shares

Suggested Citation

  • Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "The dynamics of market share’s growth and competition in quadratic mappings," MPRA Paper 43652, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:43652
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    File URL: https://mpra.ub.uni-muenchen.de/43652/5/MPRA_paper_43652.pdf
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    References listed on IDEAS

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    1. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
    2. Thomas Lux, 1996. "Long-term stochastic dependence in financial prices: evidence from the German stock market," Applied Economics Letters, Taylor & Francis Journals, vol. 3(11), pages 701-706.
    3. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    4. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    5. Dominique, C-René & Rivera-Solis, Luis Eduardo, 2011. "Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index," MPRA Paper 34860, University Library of Munich, Germany.
    6. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    7. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "Could Investors’ Expectations Explain Temporal Variations in Hurst’s Exponent, Loci of Multifractal Spectra, and Statistical Prediction Errors? The Case of the S&P 500 Index," MPRA Paper 41407, University Library of Munich, Germany, revised 26 Feb 2012.
    8. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index," MPRA Paper 41408, University Library of Munich, Germany.
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    Cited by:

    1. Dominique, C-Rene, 2013. "Estimating investors' behavior and errors in probabilistic forecasts by the Kolmogorov entropy and noise colors of non-hyperbolic attractors," MPRA Paper 46451, University Library of Munich, Germany.
    2. Dominique, C-Rene, 2013. "Estimating investors' behavior and errorsin probabilistic forecasts by the Kolmogorov entropy and noise colors of multifractal attractors," MPRA Paper 46231, University Library of Munich, Germany, revised 16 Apr 2013.

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    More about this item

    Keywords

    Market Share; Quadratic Mappings; Monofractality; Broken Symmetry of Translation of Equilibria. Multi-fractality; Complexity; Chaos;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G00 - Financial Economics - - General - - - General

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