Mixed Source

with Ramon Casadesus-Masanell, Harvard Business School Working Paper 10-022, September 2009.

Review and Resubmit, Management Science.

We study competitive interaction between profit-maximizing firms that sell software and complementary goods or services. In addition to tactical price competition, we allow firms to compete through business model reconfigurations. We consider three business models: the proprietary model (where all software modules offered by the firm are proprietary), the open source model (where all modules are open source), and the mixed source model (where a few modules are open). When a firm opens one of its modules, users can access and improve the source code. At the same time, however, opening a module sets up an open source (free) competitor. This hampers the firm's ability to capture value. We analyze three competitive situations: monopoly, commercial firm vs. non-profit open source project, and duopoly. We show that: (i) firms may become "more closed" in response to competition from an outside open source project; (ii) firms are more likely to open substitute, rather than complementary, modules to existing open source projects; (iii) when the products of two competing firms are similar in quality, firms differentiate through choosing different business models; and (iv) low-quality firms are generally more prone to opening some of their technologies than firms with high-quality products.

Industry Equilibrium with Open Source and Proprietary Firms

with Ramiro de Elejalde, Harvard Business School Working Paper 09-149, June 2009.

We present a model of industry equilibrium to study the coexistence of Open Source (OS) and Proprietary (P) firms. Two novel aspects of the model are as follows: (1) participation in OS arises as the optimal decision of profit-maximizing firms, and (2) OS and P firms may (or may not) coexist in equilibrium. Firms decide their type and investment in R\&D, and sell packages composed of a primary good (like software) and a complementary private good. The only difference between both kinds of firms is that OS share their technological advances on the primary good, while P keep their innovations private. The main contribution of the paper is to determine conditions under which OS and P coexist in equilibrium. Interestingly, this equilibrium is characterized by an asymmetric market structure, with a few large P firms and many small OS firms.

Anticommons and Optimal Patent Policy in a Model of Sequential Innovation

with Stefano Trento, Harvard Business School Working Paper 09-148, June 2009.

Patent Policy, Patent Pools, and the Accumulation of Claims in Sequential Innovation

with Stefano Trento, Harvard Business School Working Paper 10-005, July 2009.

Review and Resubmit, Economic Theory.

We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We study the equilibrium innovation activity under three regimes: patents, no-patents and patent pools. Patent pools increase the probability of innovation with respect to patents, but we also find that: (1) their outcome can be replicated by a licensing scheme in which innovators sell complete patent rights, and (2) they are dynamically unstable. We find that none of the above regimes can reach the first or second best. Finally, we consider patents of finite duration and determine the optimal patent length.

Innovation and Collusion in Imperfectly Competitive Factor Markets, with Stefano Trento.

We present a model of innovation in inputs markets. Innovators decide whether to invent a new input or not, and the price of their input in case they decide to invent it. When inputs are priced non-cooperatively, we find there is an inverted U relationship between the number of inputs and the degree of substitution. We also find that a decrease in the cost of invention of the inputs may decrease welfare if the inputs are highly complementary. Finally, we find that collusion always improves welfare when the inputs are complements, but may also improve welfare when they are substitutes. Our analysis has important implications for the literatures of endogenous growth and patent pools.

A Dynamic Model of Compatible and Incompatible Networks.

I present a dynamic model of competition with compatible and incompatible networks. Demand increases with the accumulated size of the network. There are n firms, which compete in quantities and maximize the discounted sum of current and future profits. Time is continuous, which allows the use of differential game theory, and the time horizon is infinite. Open-loop (pre-commitment) and Markov-perfect (feedback) equilibria are analyzed. Some preliminary findings for the compatible network case are: (1) output is larger in the open-loop equilibrium (i.e. when firms are able to pre-commit to an output path for the entire game), than in the Markov-perfect equilibrium, and (2) coordination of output decisions by firms (i.e. formation of a monopoly) decreases output with respect to the compatible network competition case.

Innovation, Entrepreneurship and Venture Capital in Open Source.

In this paper, I propose an alternative explanation for the creation of Open Source projects. With Open Source, individual software developers collaborate in the development of new software programs, and then compete in the final goods market. However, there are large incentives for a unique firm to develop the new product alone. This may be due to returns to scale in investment, higher coordination, or simply to prevent competition in the final goods market. Then, why do not developers merge in a single firm and share the benefits of a higher concentration? I intend to show that Open Source may substitute venture capital financing as a way to share the risks of a risky investment. The traditional way to share the risks of an uncertain project is to collaborate in the financing of a unique firm performing the investment. An agency problem naturally arises, with multiple principals hiring a single agent. The innovation may fail to be developed in the presence of high monitoring costs. Alternatively, if the technology is modular, the project can be partitioned in smaller sub-projects, which allows each investor to become an entrepreneur, perform only a part of the total investment and then share the proceeds of the innovation with the rest. The model can shed light on the history of Open Source and explain why competitors of a large incumbent (like Microsoft) may decide to develop their innovations under Open Source.