Patent licensing in a Cournot oligopoly: General results

Abstract

This paper presents a comprehensive analysis of patent licensing in a Cournot oligopoly with general demand and looks at both outside and incumbent innovators. The licensing policies considered are upfront fees, unit royalties and combinations of fees and royalties (FR policies). It is shown that (i) royalties unambiguously ensure full diffusion of the innovation while diffusion is limited under upfront fees, (ii) the Cournot price is higher under royalties compared to upfront fees and the price could even exceed the post-innovation monopoly price, (iii) for generic values of magnitudes of the innovation, when the industry size is relatively large, royalties are superior to upfront fees for the innovator and (iv) for any m, there is always a non empty subset of m-drastic innovations such that for relatively large industry sizes, upfront fee policy results in higher consumer surplus as well as welfare compared to both royalty and FR policies.

Equivalence between fixed fee and ad valorem profit royalty

“…Since Ω(p) is increasing for p < p M (ε) and p F = p 0 < p v < p M (ε) (see Lemma 2), we have Ω(p v ) > Ω(p F ). Then the result follows by ( 13) and (16).…”

“…As , by (1) and (3), . This shows auction is better than posted price for and by Theorem 1, equivalence between fixed fee and ad valorem royalty holds.The last part of (II) is immediate from the result of Sen and Tauman (2018) (see Proposition 3(II), p.42) that with generic magnitudes of the innovation, for any nondrastic innovation licensing by per unit royalty is superior to licensing by fixed fee through auction.Part (III) is immediate from parts (I)–(II). …”

“…Such situations are better captured by modeling the innovator as an external entity who is an outsider to the industry. Although the literature has looked at fixed fees, per unit royalties as well as their combinations for both outside and incumbent innovators (e.g., Kamien et al, 1992; Sen, 2005; Sen & Tauman, 2007, 2018), the analysis of ad valorem profit royalty licensing has been mostly limited to the case where the innovator is an incumbent firm. Seeking to fill this gap, this paper presents an analysis of ad valorem profit royalty licensing with an outside innovator in a general setting.…”

“…(ii) Recall the price elasticity η(p) = −pQ ′ (p)/Q(p) is non decreasing by Assumption A4. LetH(p, v) := p[1 − 1/(2 − v)η(p)](24)(When v = 0, this function coincides with H 2 (p) defined in (5), p.40,Sen and Tauman, 2018). Also note that if H(p, v) is positive, then H(p, v) < H(p, v) for p <p and H(p, v) > H(p, v) for p >p.Adding the equations of (23) and noting thatQ(v) = (2 − v)q 2 (v), it follows that Cournot price p v satisfies H(p v , v) = c − ε (25) Since H(p, v) is decreasing for any positive p, by (25), p v is increasing in v. Note that when v = 0, the equations in (23) coincides with the first order conditions under a fixed fee policy, so we have H(p F , 0) = c − ε (where p F is the Cournot price under fixed fee).…”

Patent Protection, Optimal Licensing, and Innovation With Endogenous Entry

“…2 On the other hand, numerous studies in IO have analyzed the optimal licensing strategy for a patented firm. For example, as an application of non-cooperative game theory, Kamien and Tauman (1986), Rockett (1990), Muto (1993), Sen and Tauman (2007), Sen and Stamatopoulos (2009), Kitagawa et al (2014), Chen (2017), and Sen and Tauman (2018) investigate how a patented firm should charge a license fee for profit maximization in several situations. Kamien and Tauman (1986), a seminal study, develop a three-stage model in which an innovator determines the fixed licensing fee or per-unit output royalty in the first stage, other firms individually decide whether to contract the license or not in the second stage, and all of them engage in Cournot competition in the third stage.…”