Cumulative innovation, open source, and distance to frontier

• Published date: 01 December 2020
• Author: Luigi Balletta,Antonio Tesoriere
• Date: 01 December 2020
• DOI: http://doi.org/10.1111/jpet.12446

J Public Econ Theory. 2020;22:1875–1920.wileyonlinelibrary.com/journal/jpet© 2020 Wiley Periodicals LLC

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1875

Received: 12 June 2019

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Accepted: 20 April 2020

DOI: 10.1111/jpet.12446

ORIGINAL ARTICLE

Cumulative innovation, open source, and

distance to frontier

Luigi Balletta

1

|Antonio Tesoriere

2

1

Dipartimento di Economia, Management,

Istituzioni, Università Federico II, Napoli,

Italy

2

S.E.A.S., Università di Palermo, Viale delle

Scienze, Palermo, Italy

Correspondence

Antonio Tesoriere, S.E.A.S. Università di

Palermo, Viale delle Scienze, Ed. 13, 90128

Palermo, Italy.

Email: antonio.tesoriere@unipa.it

Abstract

We develop a multistage game in which firms do

cumulative research and development (R&D) to

complete a lengthy process, and we study whether

firms patent intermediate results or release them in

Open Source. A patent holder obtains a larger reward

in the market, but since in equilibrium it forecloses

R&D, it remains alone to complete the process and so

pays a larger cost than an Open Source firm. We have

Open Source equilibria when R&D is highly com-

plementary, R&D costs are large, and firms are suf-

ficiently different and far from the frontier. We

identify two market failures, in the forms of free

riding and coordination failure, and we discuss public

intervention.

1|INTRODUCTION

In many industries, to obtain a valuable innovation firms have to undertake a lengthy research

and development (R&D) process with many intermediate stages. They pay the operating cost of

the process until it is over, and only then they make a profit by marketing the final result. How

firms grant access to intermediate results determines who may contribute to the innovation and

eventually bring it to the market, and therefore affects both the duration of the process and the

structure of profits downstream. For some processes firms protect their results with proprietary

rights, while for others they leave them open to everyone. In this paper we study firms involved

in a lengthy process, and we provide conditions that in equilibrium firms, markets, and tech-

nology must jointly satisfy for firms to adopt a specific regime of intellectual property rights.

We study processes with some specific characteristics. (i) Firms' R&D activities are com-

plementary. As the number of firms that do R&D increases, so does the probability that one of

them accomplishes a stage. (ii) R&D is sequential and cumulative. By accomplishing a stage a

firm adds a new piece to the technology, but to do so it needs to combine it with the existing

ones. If these are covered by proprietary rights, the firm has to license from the right holder. (iii)

Firms cannot patent infringing innovations, nor can they bargain over research effort. They

bargain over a license, and only after they have done R&D.

We develop a dynamic game of R&D in which firms choose whether to adopt a proprietary

or a nonproprietary regime of licenses. Proprietary licenses work like patent licenses. In ex-

change for a fee the licensor discloses the intermediate result to the licensee and gives this firm

the exclusive right to use the result, but not the right to make copies. Nonproprietary licenses

work like the Open Source General Public License (GPL) in the software industry.

1

The licensee

pays no fee and receives the right both to use the result and to make and distribute copies, but it

agrees to release every copy and improvement under the same terms.

2

In this setup patents create a hold‐up problem. Since a patent holder can refuse to license

the technology all the times, and complete the process alone, when it bargains over a license it

will ask a fee so large that in the continuation equilibria of the proprietary regime a nonpatent

holder gives up R&D and leaves the game—we show that this occurs no matter how little is the

patent holder's bargaining power. This in turn generates the trade‐off between final profit and

R&D costs that underlies a firm's choice. The firm anticipates that on the continuation path

with patents the patent holder completes the process by itself and eventually becomes the only

supplier of the good, while on the path with Open Source many firms contribute and then they

share the final market. Since the patent holder faces no competition downstream, it obtains a

final value higher than does an Open Source contributor, but since it forecloses the process to

complementary innovations, it expects to wait longer until completion and hence to pay a

higher operating cost.

In equilibrium firms choose Open Source if and only if (i) the average profit an Open Source

firm obtains over the duration of the process (which is to say the ratio of the profit in the final

market to the expected time to completion) is higher than the operating cost of R&D, and (ii)

this same cost is higher than the average increase in profit that a firm obtains over the incre-

mental duration of the process by choosing patents over Open Source. Firms choose patents if

and only if condition (ii) is violated, and a condition analogous to (i) is satisfied so that the

patent holder breaks even.

The model predicts how the regime of intellectual property rights depends on para-

meters that describe both the R&D process and the downstream market. A first implica-

tion is that firms choose Open Source only when the number of intermediate stages, which

is our measure of distance to frontier, is sufficiently large. For instance, when R&D is not

cumulative they have a dominant strategy in seeking a patent. We can conceive distance to

frontier as the number of institutional steps that a firm has to take to receive the go ahead

from a regulatory agency. More substantively we may conceive it as the number of

cumulative improvements that later movers in an industry has to achieve to catch up

with the current leaders. Our theory suggests that entrants or laggard firms have more

incentives to choose Open Source than established incumbents. It also suggests that firms

aremorelikelytosharetheirintellectualproperty rights when the industry is at its early

stages, at the time they are trying to develop a new technology to replace the existing

1

For a definition of the GNU GPL, see http://www.gnu.org/licenses/gpl‐3.0.en.html.

2

The way we conceive the proprietary regime applies not just to patents but also to copyrights. Just like patent holders,

copyright holders disclose their innovations through individual license contracts, which often include nondisclosure

clauses that commit the licensee not to make copies (see Cohen & Lemley, 2001; Maurer & Scotchmer, 2006). Ana-

logously, the Open Source regime is also consistent with practices that firms use in industries different from software,

like, the automotive, the biomedical, and the pharmaceutical.

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alternatives.

3

A second implication is that firms choose Open Source when either the

operating cost or the degree of complementarity of R&D is sufficiently high. Therefore,

given the size of the R&D lab, firms that hire researchers in markets with higher average

earnings have more incentives to choose OpenSource.Sodofirmspursuingprocesses

involving small risk of R&D duplication, for which the probability of discovery is more

likely to increase with the number of labs. Even though we are not concerned with R&D

cooperation, here we note that since saving on duplicative R&D is a main objective of

cooperative R&D agreements, our theory suggests that Open Source licenses and R&D

cooperation should emerge in alternative environments. A final implication is that firms

choose Open Source when the ratio of profits with Open Source to profits with patents is

sufficiently high. This condition depends on the strength of patent protection and on the

cost of imitation in a natural way. It depends also on the effect of entry on joint profit, and

therefore on a set of properties that involve consumers' preferences and firms' costs and

conduct in the final market. Here we remark that this is more likely to happen when the

final good generates network effects, and when firms make most of their profit by selling

goods complementary to the innovation, on which they retain specific competencies and

market power. The model may help us understand the diffusion of the GPL license and of

similar licensing practices both in the software and in other industries. In the paper we

discuss the empirical implications of the model, and go over two examples from the

automotive and the pharmaceutical industry.

We characterize the equilibrium set for all the parameters. We find equilibria in which no

firm does R&D, which occur when the operating cost and the distance to frontier are so large

that a patent holder alone would not afford the process. Associated with these equilibria we find

two types of market failures that block R&D even though firms would afford Open Source. First,

when a firm chooses Open Source, the other has a stronger incentive to free ride and seek a

patent than when the firm is out of the game. When firms break even only with Open Source,

this free‐riding motive may preclude equilibria with R&D. Second, when Open Source is ne-

cessary to break even, each firm will do R&D only if it expects the opponent to do so. This

coordination problem supports multiplicity of equilibria, namely, equilibria with Open Source

or equilibria with no R&D. The free‐rider problem is specific of a region of parameters so small,

and it involves information so detailed to be dealt with that we suggest that a social planner

should not interfere. Instead the coordination problem is pervasive, and we note that, using

only local information, the social planner may address it by subsidizing Open Source R&D in

the same way a multisided platform subsidizes one side to stimulate participation.

1.1 |Related literature

Our paper brings together two strands of the literature on intellectual property rights and

innovation. The recent literature on patents questions that patents are necessary for innovation,

and indeed argues that when innovation is sequential they may slow it down. See Heller and

Eisenberg (1998), Shapiro (2001), and Boldrin and Levine (2008). Bessen and Maskin (2009)

introduce the notion of complementarity we use in this paper, and compare the cases with and

3

Our prediction is broadly consistent with historical evidence. Bessen and Nuvolari (2014) provide examples from the

eighteenth century, like, the Bessemer steel, the steam engineers in the Cornish mining district, and the first two

decades of power weaving in the US textile industry.

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