The conventional wisdom is that the formation of patent pools is welfare enhancing when patents are complementary, since the pool avoids a double-marginalization problem associated with independent licensing. This conventional wisdom relies on the effects that pooling has on downstream prices. However, it does not account for the potentially significant role of the effect of pooling on downstream product development and commercialization. We consider development technologies that entail spillovers between rivals and assume that final-demand products are imperfect substitutes. When pool formation facilitates information sharing and spillovers in development, then decreases in the degree of product differentiation can adversely affect welfare by reducing the incentives towards product development and product market competition – even with perfectly complementary patents. The analysis modifies and even negates the conventional wisdom for some settings and suggests why patent pools are uncommon in science-based industries such as biotech and pharmaceuticals that are characterized by tacit knowledge and incomplete patents.
Appendix A: Derivations
The Bertrand-Nash equilibrium of this game yields:
Note also that
To derive consumer surplus in the market, we use the representative consumer’s preferences that underlie the demand structure (see Singh and Vives 1984). For the symmetric equilibrium, this reduces to
Further substitution into eq. (26) yields
Appendix B: Proofs
Proof of Lemma 1 Equilibrium effort is given by eq. (5). After taking the derivative, dropping the denominator and consolidating it follows that carries the same sign as
Setting this equal to zero and solving for yields
The first factor can be written as
which is clearly positive. Setting the second factor equal to zero and solving for yields and the derivative properties follow.
Proof of Proposition 3 It can be shown that carries the same sign as
Setting this equal to zero gives an implicit equation that can be solved for to yield
Note that whenever .
Proof of Lemma 3 Equilibrium effort is given by eq. (5). After taking the derivative, dropping the denominator and consolidating it follows that carries the same sign as
Both factors are obviously positive so that the negative of their product is negative, which is also sufficient to prove the second statement.
Proof of Proposition 4 Applying the quotient rule in taking the derivative of eq. (9) with respect to , it follows after some simplification that carries the same sign as
Of the three factors it is straightforward to show that the first is negative and the third is positive. The middle factor is shown to be positive in the proof to Proposition 1, from which it follows that .
Proof of Proposition 5 We undertake the same steps as in the proof to Proposition 2, but now take derivatives with respect to . From this it follows that has the same sign as
Setting this equal to 0 and solving for yields
Similarly one derives that has the same sign as
Of the three factors it is straightforward to show that the first is negative, and in the proof to Proposition 1 it is shown that the second is positive. Setting the third factor equal to zero and solving for yields
Setting gives an implicit equation that can be solved for to yield
Then whenever .
Proof of Theorem 1 For given product differentiation and spillovers in development, the pooling of patents eliminates double marginalization and increases welfare. Therefore a necessary condition for overall welfare to nonetheless decrease is that spillover effects and differentiation effects must be on net negative, which is only the case when pooling is undesirable without double marginalization.
Proof of Theorem 2 Setting (i.e. the bounds under which the second-order conditions hold) and Mathematica’s FindInstance shows that no such instance exists on the given domain. Since consumer surplus is concave, it then follows that the theorem holds for the entire domain.
Part of this research was completed while Jeitschko was working at the Antitrust Division of the US Department of Justice. The views expressed in this paper, however, are those of the authors and are not purported to reflect the views of the US Department of Justice.
We thank Jay Choi, Tony Creane, Patrick Greenlee, Erik Hovenkamp, Sue Majewski, Nate Miller, Alex Raskovich, Ruth Raubitschek, Markus Reisinger, Carl Shapiro, Xianwen Shi, Bruno Versaevel, Greg Werden and Junjie Zhou, as well as seminar participants at the National University of Ireland, Maynooth, the Antitrust Division of the US Department of Justice, the University of Kentucky, and conference participants at the IIOC, the FTC Microeconomics Conference, and the Conference on Entrepreneurship and Innovation: US Patent and Trademark Office Ewing Marion Kauffman Foundation Conference on Intellectual Property and Innovation at the Searle Center at Northwestern University Law School. The paper has benefited considerably from comments by an anonymous referee.
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See, e.g. E. Bement & Sons v. National Harrow Co., 186 U.S. 70 (1902).
Cournot illustrates his point by considering the pricing decisions of a monopolist for copper and a monopolist for zinc who are providing the necessary inputs to a downstream producer of brass.
It should be noted that they recognize that, in the context discussed, the notions of complementarity and substitutability are not actually as clear-cut as it might seem, but a meaningful distinction is nonetheless possible on the basis of changes in patentees’ willingness to pay for additional patents.
Guideline on the Application of Art. 81 of the European Commission Treaty to Technology Transfer Agreements (2004/C 101/02), and Chapter 3 of USDOJ/FTC (2007).
See, for instance, the DVD6C patent pool that was formed by nine leading home entertainment companies to foster technology related to digital versatile discs; or the several MPEG patent pools that govern video and audio compression and transmission.
For example, the entities that had sequenced the severe acute respiratory syndrome associated coronavirus (SARS-CoV) failed to form a pool to facilitate the development of an effective vaccine. Similarly, the development of a DNA microarray to arrange 300 cancer-associated genes would facilitate the diagnosis and possible treatment of many cancers; yet such a DNA chip would require pooling widely dispersed patents, which has not happened. Also, patents on receptors are useful for screening potential pharmaceutical products. To learn as much as possible about the therapeutic effects and side effects of potential products at the pre-clinical stage, firms want to screen products against all known members of relevant receptor families. But when these receptors are patented and controlled by different owners, gathering the necessary licenses may be difficult. See, e.g. USTPO’s white paper on the subject, Clark et al. (2000), Gaulé (2006), Ménièr (2008), Verbeure (2009), van Zimmeren et al. (2011), van Overwalle (2012) or Jeitschko and Zhang (2013).
A rare exception is the current attempt by MPEG-LA’s Librassay to institute a genetic diagnostic testing patent pool. It is no coincidence that this is tied to molecular diagnostics testing as here there is a clear commercial application that requires less research (Jeitschko and Zhang 2013).
The aforementioned USPTO white paper on patent pools in biotechnology (see Footnote 7) also cites information sharing specifically as an advantage of pool formation (id. p. 10).
Of course, if the pooling incentives of patent holders and firms are perfectly aligned (e.g. if the licensors are also licensees, i.e. the case of cross-licensing), then our model can also be interpreted as a version RSJVs similar to Greenlee and our insights carry over to such a setting.
Thus, we assume that the upstream IP-holders are non-practicing entities. In biotech and pharmaceuticals, many IP-holders are indeed small research laboratories or universities that do not themselves commercialize. Nevertheless, the findings of the model apply to more complex settings in which patent holders are also developers and manufacturers. In those cases what is found in the present setting for firms then applies more broadly to the patent holders as well. This is akin to the case where licensing fees are used (rather than royalties) – a case that is discussed in more detail in Jeitschko and Zhang (2011).
On the role of information exchange and spillovers in R&D, see, e.g. Severinov (2001).
Ghosh and Morita (2012) also study possible trade-offs concerning development collaboration and product differentiation, using a circular city model with a focus on how insiders differ from outsiders. Bourreau and Doğan (2010) allow for cost sharing in development and study how increased collaboration in development leads to diminished product differentiation. However, effort is not part of the development process. In contrast to these approaches that postulate a positive relationship between collaboration and product similarity, Lin and Saggi (2002) consider the case where firms coordinate to increase product differentiation.
The effect of the degree of product differentiation on development efforts has also been examined elsewhere, with some models specifically examining endogenous product differentiation. Amir, Evstigneev, and Wooders (2003) use generic profit functions and consider differences between cooperative and non-cooperative R&D. As for the interplay of effort and spillovers in development, Moltó, Georgantzís, and Orts (2005) have a closed-form model with a result that is similar to one of ours (albeit in a very different set-up) in that the social planner may wish to limit the extent of spillovers in development, as these lead to under-performance due to free-riding.
The first-order conditions are sufficient and yield an interior solution (i.e. positive equilibrium effort) provided that – an assumption that we henceforth maintain.
The proofs are in Appendix B.
A more detailed analysis of spillover and differentiation effects that abstracts from the issue of royalty stacking is in Jeitschko and Zhang (2011).
The examples were calculated and the figures were generated using Mathematica®. The associated files are available from the authors upon request.
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