An optimal rule for patent damages under sequential innovation

• Author: David E.M. Sappington,Yongmin Chen
• Published date: 01 June 2018
• DOI: http://doi.org/10.1111/1756-2171.12229
• Date: 01 June 2018

RAND Journal of Economics

Vol.49, No. 2, Summer 2018

pp. 370–397

An optimal rule for patent damages under

sequential innovation

Yongmin Chen∗

and

David E.M. Sappington∗∗

Weanalyze the optimal design of damages for patent infringement when a follow-oninnovator may

infringe the patent of an initial innovator. We consider damage rules that are linear combinations

of the popular “lost profit” (LP) and “unjust enrichment” (UE) rules, coupled with a lump-sum

transfer between innovators. Such linear rules can sometimes induce the socially optimal levels

of sequential innovation and the optimal allocation of industry output. The optimal linear rule

achieves the highest welfare among all rules that ensure a balanced budget for the industry, and

often secures substantially more welfare than either the LP rule or the UE rule.

1. Introduction

Innovation is a key driver of economic growth and prosperity. To encourage innovation,

successful innovators often are awarded patents for their inventions. A patent grants an innovator

exclusive rights to her invention for a specified period of time. An extensive literature analyzes

optimal patent protection, focusing on issues such as the optimal strength and breadth of patents.1

An important, but less developed, literature studies financial penalties (“damages” ) for patent

infringement. Todate, this literature has primarily analyzed the performance of individual damage

rules that are employed in practice, including the lost profit (LP) rule and the unjust enrichment

(UE) rule.2In contrast, the purpose of this article is to analyze the optimal design of patent

∗University of Colorado; Yongmin.Chen@colorado.edu.

∗∗University of Florida; sapping@ufl.edu.

Wegratefully acknowledge helpful comments from the Coeditor, Kathryn Spier, twoanonymous referees, Ted Bergstrom,

Richard Gilbert, Michael Meurer, Michael Riordan, Marius Schwartz,Yair Tauman,John Turner, Dennis Yao,and seminar

participants at Columbia University, Fudan University, Queens University, the State University of New York at Stony

Brook, the University of California at Santa Barbara, the University of Georgia, the University of Groningen, the 2016

Workshopon IO and Competition Policy at the Shanghai University of Finance and Economics, and the 2016 Workshop

on Industrial Organization and Management Strategy at the Hong Kong Universityof Science and Technology.

1Earlystudies of optimal patent protection include Nordhaus (1969), Gilber t and Shapiro (1990), Klemperer (1990),

and Scotchmer (1991).

2Anton and Yao(2007) examine the performance of the LP rule. Schankerman and Scotchmer (2001), Choi (2009),

and Henry and Turner(2010) examine the performance of both the LP and the UE r ules. (These rules are described below.)

Choi and Henry and Turner also analyze the performance of the reasonable royalty damage rule, which is discussed in

370 C2018, The RAND Corporation.

CHEN AND SAPPINGTON / 371

damage rules under sequential innovation, where an initial innovator’s patent may be infringed by

a follow-on innovator whose differentiated product, possibly of higher quality, expands market

demand.

Sequential innovation is important to consider because it drives progress in many important

industries. Scotchmer (1991) identifies severalproducts—including antibiotic dr ugs, incandescent

lights, lasers, and computer operating systems—whose development was fueled by sequential

innovation.3Today’s smartphones are estimated to embody innovations protected by as many as

250,000 patents that have been developedsequentially (Sparapani, 2015).4The design of damages

for patent infringement is particularly subtle in the presence of sequential innovation because,

although stringent damage rules can encourage early innovation, theymay discourage subsequent

innovation, especially when uncertainty prevails about whether follow-on innovations infringe

earlier patents.5

We consider a model in which innovation is not certain because of stochastic variation in

innovation costs. Patentprotection also is uncer tain in our model, as it is in practice.6Hundreds of

thousands of patents are granted annually, and patent descriptions can be vague and incomplete.7

Therefore, in practice, it is often difficult to discern whether an innovation infringes an existing

patent.8The parameter λ∈(0,1] in our model denotes the probability that the patent of an initial

innovator, firm 1, is infringed by the differentiated product of a follow-on innovator, firm 2. The

value of λcan be viewed as a measure of the strength of patent protection (e.g., Choi, 1998;

Farrell and Shapiro, 2008).

We consider damage rules that are linear combinations of the LP rule and the UE rule,

coupled with a lump-sum transfer between the innovators. The LP rule requires the infringer to

compensate the patent holder for the reduction in profit the latter suffers due to the infringement.9

Section 7. Schankerman and Scotchmer (2005) report that although the UE rule was commonly employed in the United

States prior to the implementation of patent reforms in 1946, the LP rule has been employed relatively frequently since

then. See Blair and Cotter (2005) for additional discussion of the use of patent damage rules in the United States and

Reitzig, Henkel, and Heath (2003) for corresponding discussion of international experience.

3In addition, gene sequencing discoveries are valuable inputs in follow-onscientific research and in commercial

applications (Sampat and Williams, 2015). Murray et al. (2016) examine the effects of affording academic researchers

expanded access to newly discovered information about genetically engineered (transgenic) mice. The authors report

that expanded access increases follow-on discoveries by new researchers and promotes diverse follow-on research

methodologies without reducing the rate of innovation.

4It has been observed that modern computing technologies like smartphones “tightly and efficiently integrate the

engineering of other companies and other earlier inventors, and are enhanced with new functions and features to attract

consumer interest and drive demand” (Sparapani, 2015). Scotchmer (2004) notes that although no product development

fits the basic model of sequential innovation perfectly, “if one takes a more metaphorical view, [the model] fits almost

every important technology,including the laser and desktop software.”

5Green and Scotchmer (1995) examine the patent length and division of surplus required to induce efficient

sequential innovation. We extend their work in part by explicitly modelling competition between innovators in the

presence of uncertainty about the applicability of existing patents.

6Anton and Yao(2007), Choi (2009), and Henry and Turner (2010) also analyze probabilistic patent enforcement.

7See, for example, Choi (1998), Lemley and Shapiro (2005), Bessen and Meurer (2008), and Farrell and Shapiro

(2008).

8The recent protracted patent infringement ligation between Apple and Samsung is a case in point (e.g., Vascellaro,

2012). In addition, Lemley and Shapiro (2005) report that the US Patent and Trademark Office issues nearly 200,000

patents annually,so the time that a patent officer can devote to assessing the merits of any individual patent application is

limited. Consequently,even after a patent is issued, its validity may be successfully contested in court. Uncertainty about

prevailing patent protection also can complicate the licensing of innovations.See Kamien and Tauman (1986), Katz and

Shapiro (1986), and Scotchmer (1991), for example, for analyses of the licensing of innovations.

9US patent law stipulates that the damage penalty for patent infringement must be “adequate to compensate for the

infringement, but in no event less than a reasonable royalty for the use made of the inventionby the infringer, together

with interest and costs as fixed by the court.” Courts have interpreted this stipulation to require “an award of lost profits,

or other compensatory damages, where the patentee can prove, and elects to prove,such damages” (Frank and DeFranco,

2000–2001).

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