A Differential Game of a Duopoly with Network Externalities

  • Mario Alberto García-MezaEmail author
  • José Daniel López-Barrientos
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


In this work, we develop a differential game of a duopoly where two firms compete for market share in an industry with Network Externalities. Here the evolution of the market share is modeled in such a way that the effects of advertising efforts that both firms make are a function of the share itself. This means that the efficacy of marketing efforts are diminished with low market share and enhanced when it is higher. We show that Network Externalities can influence the decision a firm makes about marketing expenditures. Particularly, when a firm is large enough, the creation of a monopoly is easier when this market structure is present. For this, we obtain the optimal strategies for the firms and test them on a simulation, where we compare the market with and without this kind of externalities. We find that the value of the market share in proportion with the cost of obtaining it by advertising efforts is the key to know the long term equilibrium market share.


Differential games Advertising competition Network externalities 



The work of the first author was supported by Mexico’s Science Council CONACyT scholarship 419727.


  1. 1.
    Case, J.: Economics and the Competitive Process. University Press, New York (1979)Google Scholar
  2. 2.
    Clements, M., Ohashi, H.: Indirect network effects and the product cycle: video games in the US, 1994–2002. J. Ind. Econ. 53(4), 515–542 (2005)CrossRefGoogle Scholar
  3. 3.
    Dranove, D., Gandal, N.: The Dvd-vs.-Divx standard war: empirical evidence of network effects and preannouncement effects. J. Econ. Manage. Strateg. 12(3), 363–386 (2003)Google Scholar
  4. 4.
    Dockner, E., Jørgensen, S., Long, N., Sorger, G.: Differential Games in Economics and Management Science. Blackwell, London (2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    Economides, N.: The economics of Networks. Int. J. Ind. Organ. 14(6), 673–699 (1996)CrossRefGoogle Scholar
  6. 6.
    Erickson, G.: A model of advertising competition. J. Mark. Res. 22(3), 297–304 (1985)CrossRefGoogle Scholar
  7. 7.
    Erickson, G.: An empirical comparison of oligopolistic advertising strategies. In: Jørgensen, S., Zaccour, G. (eds.) Dynamic Competitive Analysis in Marketing, pp. 27–36. Springer, Montreal (1996)CrossRefGoogle Scholar
  8. 8.
    Erikson, G.: Dynamic conjectural variations in a Lanchester oligopoly. Manage. Sci. 43(11) 1603–1608 (1997)CrossRefzbMATHGoogle Scholar
  9. 9.
    Gandal, N.: Hedonic price indexes for spreadsheets and an empirical test for network externalities. RAND J. Econ. 25(1), 160–170 (1994)CrossRefGoogle Scholar
  10. 10.
    Gandal, N.: Competing compatibility standards and network externalities in the PC software market. Rev. Econ. Stat. 77, 599–603 (1995)CrossRefGoogle Scholar
  11. 11.
    Gandal, N., Salant, D., Waverman, L.: Standards in wireless telephone networks. Telecommun. Policy 27, 325–332 (2003)CrossRefGoogle Scholar
  12. 12.
    Hitt, L., Brynjolfsson, E.: Productivity, business profitability, and consumer surplus: three different measures of information technology value. MIS Q. 20(2), 121–142 (1996)CrossRefGoogle Scholar
  13. 13.
    Katz, M.L., Shapiro, C.: Network Externalities, competition, and compatibility. Am. Econ. Rev. 75(3), 424–440 (1985)Google Scholar
  14. 14.
    Lich, G., Moch, D.: Innovation and information technology in services. Can. J. Econ. 32(2), 363–383 (1997)CrossRefGoogle Scholar
  15. 15.
    Leibenstein, H.: Bandwagon, snob, and Veblen effects in the theory of consumers’ demand. Q. J. Econ. 64(2), 183–207 (1950)CrossRefGoogle Scholar
  16. 16.
    Ohashi, H.: The role of network effects in the US VCR market, 1978–1986. J. Econ. Manage. Strateg. 12(4), 447–494 (2003)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Park, S.: Quantitative analysis of network externalities in competing technologies: the VCR case. Rev. Econ. Stat. 86(4), 937–945 (2004)CrossRefGoogle Scholar
  18. 18.
    Prieger, J., Hu, W.: An empirical analysis of indirect network effects in the home video game market. NET Institute Working Paper 06–25 (2006)Google Scholar
  19. 19.
    Sethi, S.: Deterministic and stochastic optimization of a dynamic advertising model. Optim. Control Appl. Methods 4(2), 179–184 (1983)CrossRefzbMATHGoogle Scholar
  20. 20.
    Shankar, V., Bayus, B.: Network effects and competition: an empirical analysis of the home video game industry. Strateg. Manage. J. 24(4), 375–384 (2003)CrossRefGoogle Scholar
  21. 21.
    Sorger, G.: Competitive dynamic advertising: a modification of the case game. J. Econ. Dyn. Control 13(1), 55–80 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yong, J, Zhou, X.: Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer, New York (1999)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mario Alberto García-Meza
    • 1
    Email author
  • José Daniel López-Barrientos
    • 2
  1. 1.Escuela Superior de EconomíaInstituto Politécnico NacionalMexico CityMexico
  2. 2.Facultad de Ciencias ActuarialesUniversidad Anáhuac MéxicoHuixquilucan, Edo. de MéxicoMexico

Personalised recommendations