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

Service Business volume 2, pages 83–98 (2008)Cite this article

Abstract

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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Notes

  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 c´. 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.

References

  • Amit R, Zott C (2001) Value creation in e-Business. Strateg Manage J 22:493–520

    Article  Google Scholar 

  • Angelelli P, Butler I, Chambouleyron A, Diegues P, Madanes R (2000) Com.ar. La revolución de las tecnologías de la informática y las comunicaciones en Argentina. Instituto de Estudios para la Realidad Argentina (IERAL)

  • Arroyo JL, López JI (2004). Externalidades de red en la economía digital. Comunicación en el XIV Congreso Nacional ACEDE, Murcia

  • Arthur BW (1989) Competing technologies, increasing returns and lock-in by historical events. Econ J 99:116–131

    Article  Google Scholar 

  • Arthur BW (1990) Positive feedbacks in the economy. Sci Am 262:92–99

    Article  Google Scholar 

  • Besen MS, Farrell J (1994) Choosing how to compete: strategies and tactics in standardization. J Econ Perspect 8(2):117–131

    Google Scholar 

  • Briscoe B, Odlyzko A, Tilly B (2006) Metcalfe’s law is wrong. IEEE Spectrum, July, pp 26–31

  • David PA (1984) Clio and the economics of QWERTY. The American Economic Review. In: Papers and proceedings of the 97th annual meeting of the American Economic Association, pp 332–337

  • Economides N, Himmelberg C (1995) Critical mass and network evolution in telecommunications. In Gerard Brock (ed), Toward a competitive telecommunications industry: selected papers from the 1994 telecommunications policy research conference. Disponible en Internet en http://www.stern.nyu.edu/networks/tprc.pdf

  • Economides N (1996a) The economics of networks. Int J Ind Organ 14:673–699

    Article  Google Scholar 

  • Economides N (1996b) Network externalities, complementarities, and invitation to enter. Eur J Pol Econ 12(2):211–233

    Article  Google Scholar 

  • Economides N (2000) Notes on network economics and the new economy. Lecture Notes, Stern School of Business. Disponible en Internet en http://www.stern.nyu.edu/networks/exmba/netnotes2000.pdf

  • Fuentelsaz L, Maicas JP, Polo Y (2003) Economía digital y estrategia empresarial: Un análisis desde la dirección estratégica. Revista de Empresa 5:54–69

    Google Scholar 

  • Gandal N (1994) Hedonic prices index for spreadsheets and an empirical test for network externalities. RAND J Econ 25(1):160–170

    Article  Google Scholar 

  • Katz ML, Shapiro C (1985) Network externalities, competition and compatibility. Am Econ Rev 75:424–440

    Google Scholar 

  • Katz ML, Shapiro C (1986) Technology adoption in the presence of network externalities. J Pol Econ 94:822–841

    Article  Google Scholar 

  • Katz ML, Shapiro C (1992) Product introduction with network externalities. J Ind Econ XL(1):55–83

    Article  Google Scholar 

  • Keilbach M, Posch M (1998) Network externalities and the dynamics of markets. Interim report of the international institute for applied systems analysis ITR-98–089

  • Loch CH, Huberman BA (1999) A punctuated-equilibrium model of technology diffusion. Manage Sci 45(2):160–177

    Google Scholar 

  • López L, Sanjuán MAF (2001) Defining strategies to win in the internet market. Physica A 301:512–534

    Article  Google Scholar 

  • Mcgee J, Sammut TA (2002) Network industries in the new economy. Eur Bus J 14(3):116–132

    Google Scholar 

  • Oren S, Smith S (1982) Nonlinear pricing and network externalities in telecommunications. In: the 6th international conference on computer communication

  • Oren S, Dhebar A (1985) Optimal dynamics pricing for expanding networks. Mark Sci 4:336–351

    Google Scholar 

  • Oren S, Smith S, Wilson R (1982) Nonlinear pricing in markets with interdependent demand. Mark Sci 1:287–313

    Google Scholar 

  • Rohlfs J (1974) A theory of interdependent demand for a communication service. Bell J Econ Manage Sci 5(1):16–37

    Article  Google Scholar 

  • Schilling MA (1998) Technological lockout: An integrative model of the economic and strategic factors driving technology success and failure. Acad Manage Rev 23:267–284

    Article  Google Scholar 

  • Schilling MA (2002) Technology success and failure in winner-take-all markets: The impact of learning orientation, timing and network externalities. Acad Manage J 45:387–398

    Article  Google Scholar 

  • Sevick P (2004) Innovation diffusion. Bus Commun Rev 34(9):8–11

    Google Scholar 

  • Shapiro C, Varian HR (1998) Information rules: a strategic guide to the network economy. Harvard Business School Press, Boston

    Google Scholar 

  • Wade J (1995) Dynamics of organizational communities and technological bandwagons: An empirical investigation of community evolution in the microprocessor market. Strateg Manage J 16(Special Issue):111–133

    Article  Google Scholar 

  • Xie J, Sirbu M (1995) Price competition and compatibility in the presence of positive demand externalities. Manage Sci 41:909–926

    Article  Google Scholar 

  • Zodrow GR (2003) Network externalities and indirect tax preferences for electronic commerce. Int Tax Public Financ 10(1):79–97

    Article  Google Scholar 

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Acknowledgments

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

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Authors and Affiliations

  1. Complutense University of Madrid, Madrid, Spain

    José Ignacio López-Sánchez & José Luis Arroyo-Barrigüete

  2. University of Valencia, Valencia, Spain

    Domingo Ribeiro

Authors
  1. José Ignacio López-Sánchez
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  2. José Luis Arroyo-Barrigüete
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  3. Domingo Ribeiro
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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). https://doi.org/10.1007/s11628-007-0025-z

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Keywords

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