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Summary description of the project objectives:

The project aims to provide a solid theory of the intriguing and rapidly growing phenomenon of open source production by incorporating the very nature of the licenses GPL and EUPL, through a dynamic model, which is new to the literature. Specifically, the objectives of the project are: (1) Build a solid theoretical model that captures the essence of the GPL and EUPL in a very direct way, unlike other papers that use a private provision of a public good type of model, and study the dynamics of economics of open source production. (2) Analyze the competition dynamics between a proprietary firm and an open source firm, and show how it is possible that the open source production wins the battle with a proprietary production. (3) Provide useful policy recommendations. In this regard, the theory that will be developed in this project will be used to evaluate welfare gains of certain policies, for instance a subsidy to the open source economy, or to the developers working for open source projects, or policies regarding property rights.

Description of the work performed and the main and final results achieved:

We worked on the project in three phases in line with the three objectives stated above. We developed two models that directly incorporate (1) the nature of the open source software production and (2) the main feature of the licenses GPL and EUPL, which is, ''get it for free now, pay back when/if you succeed''.

The baseline model regarding the first phase of the project is as follows. There are more than 2 firms interacting over finitely many and more than 3 periods. Each firm produces a good at a firm specific unit cost, which is stochastically determined by firm’s investment in cost-reducing innovation. There is also a public production technology, called open source, which can produce the good at a positive unit cost, which is stochastically determined by the open source using firms’ investments in cost-reducing innovation. Chain of events within a period is as follows: In each period, there are three stages: (1) each firm decides whether to adopt the open source or not, (2) each firm invests in cost-reducing innovation, and (3) firms compete in quantities in a Cournot fashion. To capture the effect of open source under GPL, we make the following two assumptions. (1) Each firm is free to use the open source at no cost. (2) Any innovation made by a firm which uses the open source in a period, will be open source from next period on.

Our findings suggest that each firm stays out of the open source as long as it’s not behind the open source. A firm, which has the same technology level as the open source, may fail while the open source may succeed, thus next period the firm is one step behind the open source. At that point the firm starts using the open source. Thus, in the equilibrium, at end of the first stage of any period, the number of firms behind the technology level of the open source is zero. But there may be firms ahead of the open source, which are not using the open source.

In terms of the evolution of the open source community, in the light of the above result we got, as long as the open source users are successful in innovation, the open source community will grow and sweep the non-users, and the set of non-user firms will shrink. As long as, the open source is not always successful in innovation, and the non-user firms that are ahead of the open source technology level succeed, there will be a set of proprietary firms with a higher technology level.

The second leg of the project focuses on the competition dynamics between two firms, one proprietary firm and one open source firm is constructed. The proprietary firm is assumed not to use the open source; hence it goes through R&D by private investments over time. However, open source firm develops through the open source community in which a population of innovators freely accesses the open source code and modify/develop it. We again incorporate 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.

For this second phase, we developed a two period dynamic mixed duopoly model, in which a profit- maximizing proprietary firm competes with a rival, the open source firm, in prices, with the quality levels determining their relative positions over time. At the beginning of each period, a new cohort of potential users enters into the model. The first period has two stages: competition and investment. In the second period, being the last period of the model, there is no investment stage. In the two competition stages, proprietary firm and open source firm compete in a mixed duopolistic industry, where the former charges a price to maximize its overall expected profit, whereas, the latter is freely available. At the beginning of the competition stage, each potential user observes the quality levels and the price of proprietary firm’s product, and they decide which operating system to use during their lifetime of one period. In the investment stage of the first period, while proprietary firm invests in probability to increase its products quality level, a user-developer’s incentive for involving in this costly investment activity is to signal their abilities.

We solved this model and characterized the optimal pricing and investment decision of the proprietary firm when it’s a monopoly and also when there is an open source rival. We also characterized the optimal investment decisions of the user developers under the duopolistic competition case. We found that for large enough bonus a user developer gets if she is successful, proprietary firm produces less in the first period of the duopolistic competition as opposed to the case in which it is a monopoly. We also found that proprietary firm makes more investment in the duopoly industry competition as opposed to the case where it is a monopoly. Our results are slighlty off the line with the second objective of the project, that is, to figure out how it is possible that the open source production wins the battle with a proprietary production. However, we are still able to shed light on the dynamics of a competition between a proprietary firm and open source rival, which is as important as our initial line of question.

Regarding the third phase of our project, that is, to conduct some welfare analysis, we calculated the total welfare gains in our mixed dupoly model for both cases, one is where the proprietary firm is a monopoly (no open source rival) and the other is where proprietary firm faces an open source rival and they compete. We found that, under some conditions, it is possible that the total welfare is more in the monopoly case than in the competition case, that is, it might be more when there is no open source production is higher than the total welfare when there is open source production. That is, competition does not necessarily increase the welfare in an oligopoly industry when compared to the monopoly case with no open source production. The presence of a rival induces the proprietary firm to set lower prices and those users who do not buy the proprietary firm’s product are not left empty handed; they can get the open source freely, which increases the total surplus. However, the decrease in proprietary firm’s and its users’ surpluses does not always, need to be compensated by the increase in user-developers’ surpluses. Thus, in terms of policy recommendations, there is no definitive policy recommendation, as it turns out that it might be both welfare increasing and welfare decreasing to have an open source production. Thus, we refrain from strong policy recommendations, as the conditions we found are too involved with the model parameters, and it is not easy to draw conclusions regarding what to do when a model parameter is changed.