A Dynamic Model of Mixed Duopolistic Competition: Open Source vs. Proprietary Innovation


We model the competition between a proprietary firm and an open source rival, by incorporating the nature of the GPL, investment opportunities by the proprietary firm, user-developers who can invest in the open source development, and a ladder type technology. We use a two-period dynamic mixed duopoly model, in which a profit-maximizing proprietary firm competes with a rival, the open source firm, which prices the product at zero, with the quality levels determining their relative positions over time. We analyze how the existence of open source firm affects the investment and the pricing behavior of the proprietary firm. We also study the welfare implications of the existence of the open source rival. We find that, under some conditions, the existence of an open source rival may decrease the total welfare.

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Akbulut, S. and Yılmaz, M. (2015) A Dynamic Model of Mixed Duopolistic Competition: Open Source vs. Proprietary Innovation. Theoretical Economics Letters, 5, 730-738. doi: 10.4236/tel.2015.56085.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Lerner, J. and Tirole, J. (2002) Some Simple Economics of Open Source. Journal of Industrial Economics, 50, 197-234. http://dx.doi.org/10.1111/1467-6451.00174
[2] Lerner, J. and Tirole, J. (2005) The Economics of Technology Sharing: Open Source and Beyond. The Journal of Economic Perspectives, 19, 99-120. http://dx.doi.org/10.1257/0895330054048678
[3] Johnson, J.P. (2002) Open Source Software: Private Provision of a Public Good. Journal of Economics and Management Strategy, 11, 637-662. http://dx.doi.org/10.1162/105864002320757280
[4] Modica, S. (2012) Open Source without Free-Riding. Economia Politica, 2, 247-260.
[5] Casadesus-Masanell, R. and Ghemawat, P. (2006) Dynamic Mixed Duopoly: A Model Motivated by Linux vs. Windows. Management Science, 52, 1072-1084. http://dx.doi.org/10.1287/mnsc.1060.0548
[6] Casadesus-Masanell, R. and Llanes, G. (2011) Mixed Source. Management Science, 57. http://dx.doi.org/10.1287/mnsc.1110.1353
[7] Hasnas, I., Lambertini, L. and Palestini, A. (2014) Open Innovation in a Dynamic Cournot Duopoly. Economic Modelling, 36, 79-87. http://dx.doi.org/10.1016/j.econmod.2013.09.020
[8] Jaisingh, J., See-To, E.W.K. and Tam, K.Y. (2008) The Impact of Open Source Software on the Strategic Choices of Firms Developing Proprietary Software. Journal of Management Information Systems, 25, 241-276. http://dx.doi.org/10.2753/mis0742-1222250307
[9] Suh, J. and Yilmaz, M. Economics of Open Source: A Dynamic Approach. Bogazici University Working Paper Series, EC-2015-02.

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