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Marketing percolation


  • Goldenberg, J
  • Libai, B
  • Solomon, S
  • Jan, N
  • Stauffer, D


A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass, Manage. Sci. 15 (1969) 215). This mean-field approach is contrasted with the discrete percolation on a lattice, with simulations of “social percolation” (Solomon et al., Physica A 277 (2000) 239) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.

Suggested Citation

  • Goldenberg, J & Libai, B & Solomon, S & Jan, N & Stauffer, D, 2000. "Marketing percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 335-347.
  • Handle: RePEc:eee:phsmap:v:284:y:2000:i:1:p:335-347 DOI: 10.1016/S0378-4371(00)00260-0

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    References listed on IDEAS

    1. Parker, Philip M., 1994. "Aggregate diffusion forecasting models in marketing: A critical review," International Journal of Forecasting, Elsevier, vol. 10(2), pages 353-380, September.
    2. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    3. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    4. Kelvin J. Lancaster, 1966. "A New Approach to Consumer Theory," Journal of Political Economy, University of Chicago Press, vol. 74, pages 132-132.
    5. Rabik Ar Chatterjee & Jehoshua Eliashberg, 1990. "The Innovation Diffusion Process in a Heterogeneous Population: A Micromodeling Approach," Management Science, INFORMS, vol. 36(9), pages 1057-1079, September.
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    Cited by:

    1. Cantono, Simona, 2012. "Unveiling diffusion dynamics: an autocatalytic percolation model of environmental innovation diffusion and the optimal dynamic path of adoption subsidies," Department of Economics and Statistics Cognetti de Martiis LEI & BRICK - Laboratory of Economics of Innovation "Franco Momigliano", Bureau of Research in Innovation, Complexity and Knowledge, Collegio 201222, University of Turin.
    2. Kanai, Yasuhiro & Abe, Keiji & Seki, Yoichi, 2015. "Price percolation model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 226-233.
    3. Silverberg, Gerald & Verspagen, Bart, 2002. "A Percolation Model of Innovation in Complex Technology," Research Memorandum 032, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    4. B. M. Roehner, 2000. "Determining bottom price-levels after a speculative peak," Papers cond-mat/0009222,
    5. Estrada, Fernando, 2011. "Theory of financial risk," MPRA Paper 29665, University Library of Munich, Germany.
    6. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140,
    7. Silverberg, G. & Verspagen, B., 2003. "Brewing the future: stylized facts about innovation and their confrontation with a percolation model," Working Papers 03.06, Eindhoven Center for Innovation Studies.
    8. Silverberg, Gerald & Verspagen, Bart, 2005. "A percolation model of innovation in complex technology spaces," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 225-244, January.
    9. Martin Hohnisch & Sabine Pittnauer & Dietrich Stauffer, 2003. "Percolation-Based Model of New-Product Diffusion with Macroscopic Feedback Effects," Papers cond-mat/0308358,
    10. Groot, Robert D., 2005. "Lévy distribution and long correlation times in supermarket sales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 501-514.
    11. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354,
    12. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541,, revised Mar 2008.
    13. repec:eee:trapol:v:63:y:2018:i:c:p:10-29 is not listed on IDEAS
    14. Solomon Sorin & Golo Natasa, 2013. "Minsky Financial Instability, Interscale Feedback, Percolation and Marshall–Walras Disequilibrium," Accounting, Economics, and Law: A Convivium, De Gruyter, vol. 3(3), pages 167-260, October.
    15. Maslov, Lev A. & Chebotarev, Vladimir I., 2017. "Modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 691-697.
    16. Estrada, Fernando, 2009. "Tamaño y Riesgo en los Mercados Financieros
      [Size and Risk in the Finanzal Markets]
      ," MPRA Paper 19267, University Library of Munich, Germany.
    17. Martin Hohnisch & Sabine Pittnauer & Dietrich Stauffer, 2006. "A Percolation-Based Model Explaining Delayed Take-Off in New-Product Diffusion," Bonn Econ Discussion Papers bgse9_2006, University of Bonn, Germany.
    18. R. D. Groot, 2004. "Levy distribution and long correlation times in supermarket sales," Papers cond-mat/0412163,
    19. Andrea Ellero & Giovanni Fasano & Annamaria Sorato, 2008. "A Modified Galam's Model," Working Papers 180, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    20. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," 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. 20(2), pages 183-230, June.
    21. Silverberg, Gerald, 2002. "The discrete charm of the bourgeoisie: quantum and continuous perspectives on innovation and growth," Research Policy, Elsevier, vol. 31(8-9), pages 1275-1289, December.
    22. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    23. Weisbuch, Gérard & Stauffer, Dietrich, 2000. "Hits and flops dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 563-576.

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