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

Suat Akbulut,Murat Yılmaz

doi:10.4236/tel.2015.56085

Suat Akbulut, Murat Yılmaz

Open Access

https://doi.org/10.4236/tel.2015.56085

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Abstract

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.

Highlights

Software is called open source, if its source code is open in the sense that anyone has free access to it
We examine the effects of the existence of an open source firm that is competing with the proprietary firm on the proprietary firm’s investment in innovation and production behavior, and how it affects the total welfare in the market
We find that under some circumstances, the proprietary firm supplies less and invests more in the presence of the open source rival, which leads the proprietary firm to make less profit in the duopolistic industry compared to its monopoly, suggesting that a duopoly is likely to dominate the proprietary firm’s monopoly in terms of total welfare generation

Summary

Introduction

Software is called open source, if its source code is open in the sense that anyone has free access to it. We find that under some circumstances, the proprietary firm supplies less and invests more in the presence of the open source rival, which leads the proprietary firm to make less profit in the duopolistic industry compared to its monopoly, suggesting that a duopoly is likely to dominate the proprietary firm’s monopoly in terms of total welfare generation. This is not always true, that is, it might be better for the total welfare when there is only proprietary firm in the market, and no open source rival

The Model

Benchmark

Equilibrium in the Duopoly

Welfare Comparison

Conclusion and Discussion