We present a model of industry equilibrium to study the coexistence of open-source and proprietary firms. Two novel aspects of the model are (i) participation in open source arises as the optimal ...decision of profit-maximizing firms, and (ii) open-source and proprietary 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 and a complementary private good. Open-source firms share their technological advances on the primary good, whereas proprietary firms keep their innovations private. The main contribution of the paper is to determine conditions under which open-source and proprietary firms coexist in equilibrium. Interestingly, this equilibrium is characterized by an asymmetric market structure, with few large proprietary firms and many small open-source firms. We also study the limiting economy and present conditions under which large numbers favor cooperation in R&D.
► We model an industry with profit-maximizing open-source and proprietary firms. ► Decision to participate in open source and market structure are endogenous. ► We show conditions for coexistence of open-source and proprietary firms. ► Under coexistence, equilibrium is characterized by an asymmetric market structure. ► We find conditions under which large numbers favor cooperation in R&D.
We present a model of sequential innovation in which innovators use several research inputs to invent new goods. We extend work by Shapiro (2001) and Lerner and Tirole (2004) by studying the effects ...of increases in the number of patented research inputs on innovation incentives and optimal patent policy. We consider not only the effects on the incentives to invent final goods, but also on the incentives to invent research inputs (ex-ante effect). We find increasing complexity has a negative effect on innovation activity in the final goods sector when research inputs are complements. Either limiting market power through weaker patents or reducing the lack of coordination through patent pools may solve this problem. We also find the optimal patent breadth and show it is increasing in the elasticity of substitution between the inputs used in research and decreasing (increasing) in the complexity of the R&D process when research inputs are complements (substitutes).
We present a model of sequential innovation in which innovators use several research inputs to invent new goods. We extend work by Shapiro (2001) and Lerner and Tirole (2004) by studying the effects ...of increases in the number of patented research inputs on innovation incentives and optimal patent policy. We consider not only the effects on the incentives to invent final goods, but also on the incentives to invent research inputs (ex-ante effect). We find increasing complexity has a negative effect on innovation activity in the final goods sector when research inputs are complements. Either limiting market power through weaker patents or reducing the lack of coordination through patent pools may solve this problem. We also find the optimal patent breadth and show it is increasing in the elasticity of substitution between the inputs used in research and decreasing (increasing) in the complexity of the R&D process when research inputs are complements (substitutes).
We study a class of repeated games with Markovian private information and characterize optimal equilibria as players become arbitrarily patient. We show that seemingly non-cooperative action may ...occur in equilibrium and serve as signals of changes in private information. Players forgive such actions, and use the information they convey to adjust their continuation play. However, to forgive is not to forget: players keep track of the number of aggressions and enter into a punishment phase if that number becomes suspiciously high. Our model explains features of long-run relationships that are only barely understood, such as equilibrium defaults, unilateral price cuts, collusive price leadership, graduated sanctions, and restitutions. We also explore a model in which interactions are frequent and show how increasing the persistence of the process of types reduces informational fictions. Key words: Keywords: Repeated games, adverse selection, signaling, tacit collusion, price leadership, price cuts, equilibrium defaults, graduated sanctions.
We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We compare innovation activity under three regimes -patents, ...no-patents, and patent pools- and find that none of them can reach the first best. We find that the first best can be reached through a decentralized tax-subsidy mechanism, by which innovators receive a subsidy when they innovate, and are taxed with subsequent innovations. This finding implies that optimal transfers work in the exact opposite way as traditional patents. Finally, we consider patents of finite duration and determine the optimal patent length.
We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We compare innovation activity under three regimes ...patents,no-patents,andpatentpoolsand find that none of them can reach the first best. We find that the first best can be reached through a decentralized tax-subsidy mechanism, by which innovators receive a subsidy when they innovate, and are taxed with subsequent innovations. This finding implies that optimal transfers work in the exact opposite way as traditional patents. Finally, we consider patents of finite duration and determine the optimal patent length.
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