Analysis of a Diffusion Triopoly

  • Gary M. Erickson
Part of the International Series in Quantitative Marketing book series (ISQM, volume 13)


In this chapter, we consider a triopoly with sales dynamics that involve diffusion:
$$ \begin{gathered} {{\dot{S}}_1} = \left( {{\beta_2}A_2^{{{\alpha_2}}} + \varepsilon 2{S_2}} \right)\left( {N - \sum\limits_{{i = 1}}^3 {{S_i}} } \right) - {\delta_1}{S_1} \hfill \\ {{\dot{S}}_2} = \left( {{\beta_1}A_1^{{{\alpha_1}}} + {\varepsilon_1}{S_1}} \right)\left( {N - \sum\limits_{{i = 1}}^3 {{S_i}} } \right) - {\delta_2}{S_2} \hfill \\ {{\dot{S}}_3} = \left( {{\beta_3}A_3^{{{\alpha_3}}} + {\varepsilon_3}{S_3}} \right)\left( {N - \sum\limits_{{i = 1}}^3 {{S_i}} } \right) - {\delta_3}{S_3} \hfill \\ \end{gathered} $$
The ε i , i=1, 2, 3, in (8.1), are coefficients of “internal influence” that indicate that a competitor’s existing customers are assumed to be a positive factor in attracting new customers from the part of the market that are not currently customers of any of the competitors. Advertising is assumed to exert an “external influence” on currently uncommitted customers.


Diffusion Model Costate Variable External Influence Internal Influence Advertising Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Gary M. Erickson
    • 1
  1. 1.University of WashingtonUSA

Personalised recommendations