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Development of a technological competition model in the presence of network effects from the modified law of Metcalfe


The objective of this paper is to propose a new model of competence in presence of network effects. We will introduce some modifications in the Lotka-Volterra model, in order to solve its deficiencies. The main improvement is to introduce a modification of Metcalfe’s Law, what allow us to reflect the effect of congestion externalities. The model’s validation, developed by numerical simulation, confirms that its behaviour is quite similar to that observed in real markets.

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  1. Even though the majority of network effects that emerge in electronic markets are positive (Shapiro and Varian 1998), there may also emerge negative network effects originating for example from congestion (Zodrow 2003).

  2. Note that although they have identical interpretations, the constant c will not coincide numerically with the constant . This is because the model expressed as so much by one is a reparametrisation of the model expressed in the number of users.

  3. In the original model (1) the approach is very similar.

  4. Growth based on the logistical equation, which is characterised by a sigmoidal-type evolution or in “s”.

  5. Although the simulation algorithms are different in each case, in all cases the Runge-Kutta method of order 4 with pass h = 0.001 has been employed for the numerical resolution of equations.

  6. The algorithm proposed stops the simulation when a standard achieves a market share equal to 1 and the other equal to 0, or when the 100 time units are reached.


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This paper has been supported by the Foundation Rafael del Pino.

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Correspondence to José Luis Arroyo-Barrigüete.

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López-Sánchez, J.I., Arroyo-Barrigüete, J.L. & Ribeiro, D. Development of a technological competition model in the presence of network effects from the modified law of Metcalfe. Service Business 2, 83–98 (2008).

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  • Network effects
  • Technology competence
  • Metcalfe’s law
  • Dynamical systems