Licensing of a product innovation by an outside innovator to a Stackelberg duopoly

ABSTRACT

We examine the optimal strategy of an outside innovator owning a quality-improved product when licensing it to a Stackelberg duopoly. We show that only a single licence is granted, regardless of whether there is quantity or price competition in the marketplace. However, both the licensee and contractual terms in each context differ. Under quantity competition, the licence is granted to the market-leading firm by means of a non-distorting contract, whereas under price competition the licence is granted to the market-following firm by means of a distorting two-part tariff contract with per-unit royalty. From a welfare perspective, exclusive licensing is beneficial in both contexts compared to the pre-licensing scenario, although under price competition, consumers can be harmed if the innovation is small. Finally, licensing leads price competition to yield a less efficient outcome than quantity competition due to greater market collusion. Licensing by means of three-part tariff contracts is also discussed, as well as licensing when potential licensees operate as a mixed duopoly.

KEYWORDS:

• Product innovation, licensing, Stackelberg duopoly, quantity and price competition, welfare, mixed duopoly

JEL CLASSIFICATIONS:

• D43
• D45

Acknowledgements

The authors are grateful to Cristiano Antonelli (Managing Editor) and two anonymous reviewers for their valuable comments and constructive suggestions. We naturally assume responsibility for any remaining errors or omissions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 According to a McKinsey survey, more than 25% of total revenue and profits of firms across sectors comes from the launch of new products (Buffoni et al. 2017).

2 Some prominent examples of this practice can be found in Parhankangas, Holmlund, and Kuusisto (2003), Fradkin (2014), Hoffman (2014), Arce (2015), and Jiang and Shi (2018).

3 That universities are important (external) innovators is evidenced by the fact that US universities, for instance, have expanded basic research since the 1970s, from 49% in 1979 (National Science Foundation 2012) to almost 59% in 2006 (National Science Board 2016). In parallel, the expansion in their basic research role has coincided with increased patenting and licensing of their discoveries, particularly in biotechnology (Thompson, Ziedonis, and Mowery 2018).

4 Besides licensing, other means to acquire innovations from an external source include acquisitions, partnerships, collaborations, corporate venture capital, accelerators and incubators, and innovation labs. For example, Cisco Systems Inc. has stayed ahead of the networking technology curve in part by making more than 175 acquisitions since 1993 – almost eight a year. Likewise, the $11.2 billion acquisition in November 2011 of Pharmasset Inc. (a clinical-stage pharmaceutical company committed to discovering, developing, and commercializing novel drugs to treat viral infections) by Gilead Sciences, Inc. (a biopharmaceutical firm that discovers, develops, and commercializes innovative therapeutics in areas of unmet medical need) was pivotal for the development of the Sovaldi and Harvoni breakthrough treatments for hepatitis C (see Ringel, Taylor, and Zablit 2017.) For a brief look at firms’ external innovation sources see https://www.itonics-innovation.com/blog/8-external-innovation-sources-you-should-know

5 Anderson and Engers (1992) argue that the Stackelberg model fits well the competitive behavior of industries when lags in the observation of output decisions by rivals are short.

6 This contrasts with the Cournot duopoly case, where an external innovator with a product innovation licenses it to both firms (non-exclusive licensing) if the quality improvement embedded in the innovation is sufficiently small (see Antelo and Bru 2023).

7 Li and Wang (2010) document several cases to illustrate the use of exclusive (and non-exclusive) contracts.

8 Therefore, the difference $1-t$ reflects the degree of innovation, and so a small (large) value of parameter$t$ denotes a substantial (small) improvement in product quality from $t$ to 1.

9 This utility function, also assumed by Filippini and Vergari (2012), Tian (2016), and Zou and Chen (2020), among others, rules out income effects (Tian 2016).

10 As Li and Song (2009) and Li and Wang (2010), we assume that the innovation quality is exogenous, meaning that the strategic quality choice by the innovator is absent.

11 Our findings hold if both variants are produced at a positive constant marginal cost $c>0$. However, this cannot be assured if the low-quality good is produced at a lower cost than the high-quality good. In this case, even reflecting the cost asymmetry in the simplest possible form, i.e., by assuming that the respective marginal costs are 0 and $c>0$, the admissible values for parameters $c$ and $t$ for both firms to be active in the market are related in such a way that they make it extremely difficult to obtain clearcut results. Hence, to ensure tractability and avoid miscellaneous results that may cause the loss of economic intuition, we assume that firms produce at zero cost.

12 In our setup, the assumption of zero marginal production costs for potential licensees leads the ad-valorem royalty as a percentage of the licensees’ revenue (revenue-sharing) to be equivalent to ad-valorem royalty as a percentage of the licensees’ net profit (profit-sharing).

13 Throughout the article, the superscripts $n$, $f$, $u,$ and $v$ (in equilibrium profits, quantities, prices, etc.) denote, respectively, no licensing, licensing through a fixed-fee payment, licensing involving a per-unit royalty, and licensing featuring an ad-valorem royalty. Likewise, subscripts $L$, 1, 2, and 1+2 (in equilibrium profits, quantities, prices, etc.) denote, respectively, the licensor, F1, F2, and both F1 and F2.

14 Below we will see that the optimal per-unit royalty for F2 would be $r_2(t)=0,$ so that the outside option for F1 is the same as under a fixed-fee contract.

15 In other words, the licensor can ask for a share in the ownership of the licensee in exchange of a reduction in the fixed fee.

16 Alternatively, we could consider a licensing game in which F1 decides its production level, $x_1$, in the first stage, the innovation is transferred to F2 in the second stage, and F2 chooses its production level, $x_2$, in the third stage. In this case, the fixed-fee payment the innovator could charge for the licence would be $f_2(t)={\displaystyle \frac{{(1-t{x}_1)}^2}{4}-{\displaystyle \frac{t}{16}}}$. However, since, in the first stage, F1 assumes that F2 will produce the high-quality product, the equilibrium quantities (in particular, F1’s equilibrium quantity $x_1$) are the same as when F2 is granted the licence before F1 chooses its production level. Hence, if F2 obtains an exclusive licence after F1 chooses its production level, F2 continues to pay $(1-t)(16-12t+t^2)/16(2-t{)}^2$.

17 The result of Proposition 2 also contrasts with that obtained when potential licensees are Bertrand competitors, in which case the only licence granted consists of a fixed-fee payment (see Antelo and Bru 2023). This is because including a per-unit royalty would be counterproductive, since the licensee would lose market share.

18 Or, alternatively, $\mathrm{CS}(t)={\displaystyle \frac{t}{2}[x_1^n(t)+x_2^n(t){]}^2={\displaystyle \frac{9t}{32}}}$.

19 Or, alternatively, $C{S}^f(t)={\displaystyle \frac{1}{2}[x_1^n(t){]}^2+t{x}_1^n(t)x_2^n(t)+{\displaystyle \frac{t}{2}[x_2^n(t){]}^2={\displaystyle \frac{4+5t}{32}}}}$.

20 Pal (2010) also shows that technology adoption may change the market outcome: While in a differentiated goods market, welfare is larger under Bertrand competition than under Cournot competition, with technology adoption, Cournot competition may produce greater welfare than Bertrand competition.

21 Ma, Sen, and Tauman (2022) examine the licensing of a cost-reducing innovation in a Cournot oligopoly, where an external patentee uses 3PT licensing contracts consisting of an upfront fee combined with per-unit and ad-valorem royalties.

22 Banerjee, Mukherjee, and Poddar (2023) study the licensing of a process innovation by an internal patentee in a spatial duopoly, under 2PT with fixed fee and per-unit royalty, 2PT with fixed fee and ad-valorem royalty, and 3PT with fixed fee and both per-unit and ad-valorem royalties. They show that, in general, 3PT contracts are privately optimal but not socially optimal.

23 Yang and Huang (2023), analysing the licensing of a product innovation by an external innovator in a Cournot duopoly with a private firm and a partially public firm, show that (i) constrained to exclusive contracts, fixed-fee licensing to the public firm is always optimal, (ii) constrained to non-exclusive contracts, fixed-fee licensing outperforms royalty licensing when the innovation size and the private share of the public firm are sufficiently large, and (iii) if the innovator can freely decide on contracting exclusivity, fixed-fee licensing to the public firm emerges as the optimal choice.

24 Competition in mixed oligopolies, where a state-owned public firm competes with a private firm, occurs in industries such as automobile manufacture, postal services, hospitals, education, banking, and insurance (Hirose and Matsumura 2019).

25 Like Yang and Huang (2023), we do not consider the case where $\lambda =0$, because in that case the (nationalized) public firm would set a zero price to maximize total welfare and so would drive the private firm out of the market.

26 The public firm’s position as the market follower is appropriate under the perspective that the public firm should play a complementary role to private firms (Hirose and Matsumura 2019).

Additional information

Funding

Financial aid received from a Xunta de Galicia grant (Consolidación e Estruturación – 2023 GRC GI-2060 AEMI) and from a Spanish Ministry of Science and Innovation grant (PID2020-115018RB-C33) is acknowledged.