Patent Licensing and Litigation

1 Introduction

This paper examines the impact of imperfect imitation and court efficiency on firms licensing and litigation strategies. The probability of successful imitation depends on the level of investment in imitation and the efficiency of the technology to imitate, making imitation costly and uncertain. Typically, firms are constrained in their capacity to innovate or imitate, and courts are similarly constrained in their ability to interpret and apply the law. Successful imitation can lead to litigation, a costly process that may impede progress and innovation (Granstrand 2003). Scholars and policy makers have long addressed the problem of litigation and settlement disputes (see, for example, Lanjouw and Schankerman 2001, 2003, 2004; Lemley and Shapiro 2005, 2013; Lerner 2006; Yeh 2016; Galasso and Schankerman 2018). It is crucial for firms to maximize the value of their property rights to remain competitive, preserve their incentives to innovate, and secure credit (Baum and Silverman 2004; Hsu and Ziedonis 2008; Farre-Mensa, Hegde, and Ljungqvist 2017).

These issues are increasingly significant given the growing number of firms that value licensing activities more than the commercial exploitation of their innovations (Mallinson 2016). Ineffective licensing of technological innovations due to lengthy patent infringement disputes adversely impacts firms’ incentives to invest in research and development (R&D). This may result in a reduction in innovation, higher transaction costs, and slower technology diffusion, potentially reducing social welfare (see, for example, Galasso and Schankerman 2010; Spulber 2013; Gallini 2017; Heiden and Petit 2017).

This paper develops a theoretical foundation for patent licensing and litigation, building on earlier work by Aoki and Hu (1999a, 1999b, 2003). I specifically focus on a non-cooperative game with perfect information between two incumbent firms that compete in quantities a la Cournot (Cournot 1838) within the same industry. Initially both firms use an unpatented technology to produce a homogenous good. Subsequently, one of the incumbent firms patents a new cost-efficient technology, resulting in an increase in the market share and profits of the patent holder and a corresponding reduction for the rival firm. Nevertheless, the patent holder faces the prospect of imitation from the high-cost firm. Clearly, imitation, patent protection, and the role of the courts are imperfect. Previous literature has considered the imperfect protection afforded by patents but has assumed that imitation occurs with certainty (Katz and Shapiro 1987; Aoki and Hu 1999b; Crampes and Langinier 2002). This analysis focuses exclusively on the legal challenge of the validity of imitation, despite the inherent limitations of patent protection. In other words, I assume that the rights of the patent holder cannot be invalidated in court.

Allowing patent validity to be challenged affects the probability of the patent holder (plaintiff) prevailing in trial and, thus, influences the outcome of the game. Lemley and Shapiro (2005) introduce the concept of probabilistic patents, which they define as patents with a high risk of being invalidated in court. This risk is positively correlated with the imperfect enforceability of patents and the inherent uncertainty associated with them.^[1] This paper posits that firms’ licensing and litigation strategies depend on the size of innovation, the efficiency of the technology to imitate, and the capacity of litigants to influence the court’s resolution through increased litigation expenditures. It is common for the outcome of a court case to depend on the level of litigation spending, demonstrating that the court system is imperfect and patent protection is not absolute. Consequently, licensing and litigation depend on the strength of the court and the size of innovation and imitation.

Prior literature indicates that an inventor is more likely to share minor technological innovations in exchange for a licensing fee rather than substantial or large innovations, particularly those that offer monopoly profits (see, for example, Mansfield and Romeo 1980; Katz and Shapiro 1985; Rockett 1990; Arora and Fosfuri 2003; Sakakibara 2010; Hall et al. 2014). These considerations suggest that firms may have new incentives to innovate or imitate, potentially leading to different equilibrium outcomes. The model developed here differs from existing literature in three main respects. First, in contrast to Aoki and Hu (1999a, 1999b, 2003), I consider the impact of innovation size, defined as the reduction in cost due to the patented technology, on firms’ licensing and litigation strategies across a range of potential equilibrium scenarios. Specifically, I examine the implications of non-drastic, non-drastic but sufficiently large, and drastic technological innovations. This analysis explains the implications of technology transfer on market competition. Second, I acknowledge that imitation is an imperfect process and discuss the limiting case of perfect imitation as addressed in Aoki and Hu (1999a, 1999b, 2003). The model can thus be used to infer the types of licensing agreements that are more likely to emerge under different legal regimes and provide new insights into the incentives of firms to imitate. Third, I assume a quadratic imitation cost function that depends on the efficiency of the technology to imitate and the probability of successful imitation, as in Denicolo and Franzoni (2004). Consequently, the probability of successful imitation is determined endogenously. This approach provides a better understanding of the relationship between legal costs and socially wasteful imitation.

The main findings of the analysis are as follows. First, I demonstrate that if settlement out of court will occur in equilibrium and the technology to imitate is highly efficient, there may be a greater prevalence of licensing before imitation (ex ante licensing) for minor technological innovations and a greater prevalence of licensing after imitation (ex post licensing) for substantial or large innovations. This result aligns with evidence showing that large firms not only license fewer technologies but also primarily license minor innovations (Gambardella, Giuri, and Luzzi 2007; Sakakibara 2010). It is observed that inventors are disinclined to license substantial innovations, which are also the most litigated, unless it is the result of a litigation process aimed at avoiding a trial (Allison, Lemley, and Walker 2011; Hall and Harhoff 2012). Second, I show that in scenarios where settlement out of court will occur in equilibrium, but the capacity to imitate is constrained, there may be no litigation over a substantial innovation. This is expected given the relationship between high imitation rates and litigation, which is influenced by the complexity of imitation and varies among industries (Mansfield, Schwartz, and Wagner 1981; Allison, Lemley, and Walker 2011). Third, I find that litigation may go to trial, irrespective of the size of innovation or imitation. This result is uncommon when settlement is a potential outcome because costly litigation reduces firms’ profits and, in turn, social welfare. In other words, this contrasts with prior theoretical research on patent litigation, which suggests that settlement out of court is the optimal choice of litigants. I find that under certain strict conditions, particularly concerning the size of the damage award and the extent to which litigants can influence the court’s decision, litigation to completion may also be optimal from the perspective of the firms involved. One reason for this finding is that firms may have different expectations about the trial’s outcome.

Section 2 reviews the literature on licensing and litigation. In Sections 3 and 4, I present the problem and develop the model, respectively. In Section 5, I use backward induction to characterize the equilibrium of the game and apply Nash bargaining to determine the settlement fee in equilibrium. I also discuss the welfare implications and offer relevant policy recommendations. Section 6 summarizes the main findings. All proofs are provided in the Appendix A.

2 Literature Review

Patenting and licensing of intellectual property rights (IPRs) have experienced unprecedented growth over the past decade.^[2] However, empirical evidence indicates that patents provide imperfect protection for new industrial technology (Taylor and Silberston 1973). This imperfection often leads to imitation of protected proprietary technology by competitors in various industries. Moreover, empirical research has highlighted litigation as a direct consequence of such imitation (see, for example, Lerner 1995; Lanjouw and Lerner 1996). Furthermore, most court systems worldwide are, to some extent, unable to resolve disputes and enforce rights quickly and efficiently (Maskus 2006; Shapiro 2010). The effectiveness of property rights protection, alongside these limitations, impacts firms’ decisions to innovate, imitate, license, and litigate (Llobet 2003). This paper examines firms’ incentives to license and litigate in the context of imperfect imitation and constrained courts.

Meurer (1989) suggests that resorting to the court is often a failure to settle rather than an intended choice. In contrast, I demonstrate that litigation can be an optimal strategy, primarily influenced by the strength of the court, defined as the way in which litigation spending by each firm affects the resolution of the lawsuit. In this context, Hause (1989) develops a model showing that the probability of the plaintiff winning at trial increases with the plaintiff’s own legal cost and decreases with the defendant’s cost. Hause (1989) shows that the court impacts settlement rates and the magnitude of trial expenditures, but does not consider how innovation size and the efficiency of the technology to imitate may impact the outcome of the dispute. Similarly, Hay (1995) develops a model to identify factors leading disputes to trial rather than settlement, suggesting that asymmetric information and the preparation strength of a legal dispute are key reasons for disputes proceeding to trial. I endogenously determine the cost spent on litigation and the probability of successful imitation.

Aoki and Hu (1999a) extend Hause (1989)’s work by examining how the distribution rules of litigation cost affect litigants’ behavior, modeling settlement as a Nash bargaining game. Their model aligns with previous literature in suggesting that avoiding litigation costs is a key factor driving settlement. In a companion paper, Aoki and Hu (1999b) acknowledge that courts cannot enforce patent rights perfectly and propose that the imperfect nature of courts and patent protection may encourage strategic licensing aimed at deterring or preventing entry. In another follow-up paper, Aoki and Hu (2003) find that high litigation costs may lead to more ex ante than ex post patent licensing. Conversely, low imitation costs can discourage licensing by increasing the imitator’s bargaining power, thereby making licensing a less attractive option. In this paper, I build on the works of Aoki and Hu (1999a, 1999b, 2003) by analyzing the joint impact of court strength, innovation size, and the efficiency of the technology to imitate on litigants’ strategic behavior. The combined effect of these factors offers a better understanding of how firms choose their licensing and litigation strategies. Specifically, I demonstrate that litigation to completion, or the failure to settle, may arise due to imperfect patent protection and differing expectations among litigants regarding the trial’s outcome.

It is widely accepted among scholars that the use of licenses by firms has shifted from the conventional economic rationale of stimulating innovation and facilitating technology diffusion toward a more strategic application. Firms now often use licenses to prevent entry, enhance bargaining power, reinforce infringement claims, and ensure participation in technology standards (see, for example, Cohen, Nelson, and Walsh 2000; Kash and Kingston 2001; Hussinger 2006; Hall 2007; Qian 2007; Pepall, Richards, and Norman 2008; Choi and Gerlach 2015). This shift may increase the number of claims that proceed to court, potentially leading to a costly drain on the economy. Such litigation can, in turn, impact investment in R&D, technological advancement, and overall social welfare. In this paper, I analyze the strategic use of licenses in the context of imperfect enforcement and imitation, aiming to identify the main determinants of technology transfer and understand the regulatory policy implications of technological change.^[3]

3 Problem Statement

Consider two incumbent firms that produce some good using an unpatented technology. These two firms are symmetric, earning the same profit in the status quo stage of the game. Subsequently, one of the incumbent firms patents a new technology. This new technology is more efficient than the unpatented one in that it reduces the cost of production and thus increases the profits of the patent holder.

At this stage of the game (Stage A), the patent holder has two options: offer the other firm a license to use the patented technology for a fixed fee or exclusively produce using the new technology. The firm with the unpatented technology has three options: accept the patent holder’s license offer (an ex ante license), reject the offer and continue using the less efficient technology, or pursue costly imitation. Given the imperfect enforcement of property rights, which makes patent protection less than absolute, imitation becomes a likely choice.

If imitation happens, the game moves to the next stage (Stage B), where the patent holder has three options: offer the competing firm another fixed-fee license (an ex post license) to avoid legal dispute, file a lawsuit for potential infringement, or take no action. Imitation can result in patent infringement, making it a strategic choice that may trigger legal action.

If a lawsuits is filed in Stage B, the game proceeds to the final stage (Stage C), where the parties can either settle out of court or go to trial. Litigation costs during the trial include court fees, attorney fees, and other related expenses.^[4]

The crucial question here is whether it is optimal for the two incumbent firms to compete or share technology. This analysis helps to identify which innovations – drastic or non-drastic – are more likely to be licensed, and which licenses – ex ante or ex post – are more likely to arise when courts have varying sensitivities to litigation costs. Firms face limitations in their capacity to innovate or imitate, and imitation may lead to patent infringement and subsequent litigation. These factors influence whether firms opt for trial or settle out of court.

Additionally, litigation spending can affect court efficiency and thus influence the outcome of the lawsuit. If the plaintiff wins the case, the defendant may incur higher costs than those associated with a technology transfer fee, potentially leading to severe consequences. The defendant would not only bear the legal expenses and the cost of imitation but may also be subject to punitive damages for intentional imitation or compensatory damages to cover the plaintiff’s lost profits.

In the next section, I develop a model that demonstrates when litigation becomes the optimal choice for firms, rather than their failure to settle and avoid litigation costs.

4 The Model

Firms 1 and 2 produce a homogeneous good. Let Q denote the industry output, and P(Q) = a − Q be the inverse market demand.^[5] Additionally, let q ₁ and q ₂ denote the quantities produced by firms 1 and 2, respectively. Each profit-maximizing firm determines its output assuming that the other firm’s output is fixed, leading to Cournot competition (Cournot 1838).^[6]

In the status quo of the game, both firms have identical production technologies, resulting in the same unit cost c. Firm 1 then develops a new technology that reduces its unit cost to c′, where 0 ≤ c′ < c. The investment in R&D to develop the new technology is assumed to be a sunk cost and is not considered in the analysis. Now, consider a three-stage litigation game as described in Section 3.

Stage A: In the first stage, firm 1 offers an ex ante license to firm 2. If firm 2 accepts the offer, both firms produce using the new technology, resulting in a symmetric duopoly where each firm earns π d ( c ′ ) = 1 9 ( a − c ′ ) 2 . Additionally, firm 2 (the licensee) must transfer a fixed license fee F _A  > 0 to firm 1 (the licensor).^[7] Let an ordered pair denote the allocation of net profits for each outcome of the game, where the first entry denotes firm 1’s profit and the second entry denotes firm 2’s profit. In this case, the distribution of net profits is (π ^d (c′) + F _A , π ^d (c′) − F _A ).

Firm 2 can also choose not to adopt the patented technology, continuing to use the status quo technology. This decision leads to an asymmetric duopoly, where firm 1 (the low-cost firm) uses the new technology and earns π 1 d ( c ′ , c ) = 1 9 ( a − 2 c ′ + c ) 2 , while firm 2 (the high-cost firm), relying on the status quo technology, earns π 2 d ( c ′ , c ) = 1 9 ( a − 2 c + c ′ ) 2 . The net profit outcome in this scenario is ( π 1 d ( c ′ , c ) , π 2 d ( c ′ , c ) ) . It can be shown that it is unprofitable for firm 2 to continue using the status quo technology if the innovation size, defined as the cost reduction from the patented technology, Δc ≡ c − c′, is substantial (Arrow 1962). Specifically, when Δc ≥ a − c, the new technology is considered drastic, forcing firm 2 out of the market. In this case, firm 1 earns the monopoly profit π m ≡ 1 4 ( a − c ′ ) 2 .

Firm 2 can also reject the licensing offer and choose to imitate the new technology. However, imitation is imperfect due to limitations on firm’s ability to replicate the patented technology, and I rule out any scenario where imitation results in a technology superior to the patented one (Posen, Lee, and Yi 2013). Specifically, if imitation is successful, firm 2 achieves a unit cost c″, where 0 ≤ c′ ≤ c″ < c. Assume the cost of imitation is C ( y ) = 1 2 α y 2 , where α denotes the difficulty of imitation, and y denotes the probability of successful imitation (see, Denicolo and Franzoni 2004). Let α be sufficiently large to ensure the probability of successful imitation remains within 0 ≤ y ≤ 1. With probability y, firm 2 reduces its production cost to c″; with probability 1 − y, it fails to imitate.

Stage B: Imitation leads to Stage B, where three cases must be considered. First, firm 1 offers an ex post license to firm 2, considering the cost reduction achieved through the imitated technology. If firm 2 accepts this new offer, both firms produce at the same unit cost c′, and each firm earns a payoff of π ^d (c′), as defined in Stage A. Let the licensee now pay a license fee F _B to the licensor, resulting in a net profit distribution of (π ^d (c′) + F _B , π ^d (c′) − F _B ).

If firm 2 rejects the licensing offer, firm 1 can either file a formal lawsuit for potential infringement of its patented technology or choose to take no action. If firm 1 takes no action against the imitation, firms 1 and 2 gain π 1 d ( c ′ , c ′ ′ ) = 1 9 ( a − 2 c ′ + c ′ ′ ) 2 and π 2 d ( c ′ , c ′ ′ ) = 1 9 ( a − 2 c ′ ′ + c ′ ) 2 , respectively. Thus, the net profit distribution is ( π 1 d ( c ′ , c ′ ′ ) , π 2 d ( c ′ , c ′ ′ ) − C ( y ) ) . If imitation is perfect (c″ = c′), the firms earn π ^d (c′), as the market becomes a Cournot duopoly with symmetric costs. Furthermore, considering a cost reduction achieved by firm 2 through imitation within the interval 0 < c′ ≤ c″ < c, it can be shown that the payoffs for firms 1 and 2 always satisfy π d ( c ′ ) < π 1 d ( c ′ , c ′ ′ ) ≤ π 1 d ( c ′ , c ) and π 2 d ( c ′ , c ) ≤ π 2 d ( c ′ , c ′ ′ ) < π d ( c ′ ) . If firm 1 files an infringement lawsuit against firm 2, it leads to the final stage of the game.^[8]

Stage C: In the final stage, there are only two cases to consider. On one hand, the litigants can negotiate a fixed fee and settle out of court. As in the licensing outcomes from earlier stages, the net profit outcome of a settlement is (π ^d (c′) + S, π ^d (c′) − S), where S > 0 denotes the fixed settlement fee transferred from the defendant to the plaintiff. The equilibrium value of S can be determined using the Nash bargaining solution.

On the other hand, the firms can litigate to completion. If they fail to settle at this stage, the case proceeds to trial, where each firm incurs its own litigation costs. Let the probability of firm 1 winning the trial, as perceived by firm 1, be θ 1 = θ 1 0 + θ [ l 1 / ( l 1 + l 2 ) ] , where l ₁ and l ₂ represent the litigation costs incurred by firms 1 and 2, respectively. Similarly, the probability of firm 1 winning the trial, as perceived by firm 2, is given by θ 2 = θ 2 0 + θ [ l 1 / ( l 1 + l 2 ) ] . Here, θ 1 0 and θ 2 0 are exogenous probabilities of firm 1 winning the trial, as perceived by firms 1 and 2, respectively, while θ is an exogenous parameter denoting how much the court is influenced by litigation costs. For example, a value of θ close to zero indicates that the litigants have minimal impact on the perceived probabilities of the plaintiff winning the dispute, suggesting a nearly insensitive court. In contrast, a value of θ close to one indicates that the litigants can significantly influence the perceived winning probabilities through the legal costs incurred, indicating a highly sensitive court. These parameters must satisfy 0 ≤ θ i 0 + θ ≤ 1 for i = 1, 2.

The likelihood function of firm 1 winning in court implies that the chances of the plaintiff prevailing at trial increase with its own legal costs and decrease with the legal costs incurred by the defendant. However, the outcome of the game depends on the verdict of the trial. If firm 2 is found to have infringed the patented technology, it is assumed to pay punitive damages D ≥ 0.^[9] In this case, the profit outcome is given by ( π 1 d ( c ′ , c ) + D − l 1 , π 2 d ( c ′ , c ) − D − l 2 ) .^[10] If the court finds firm 2 not liable for infringement, the net profit outcome is given by ( π 1 d ( c ′ , c ′ ′ ) − l 1 , π 2 d ( c ′ , c ′ ′ ) − l 2 ) . In the following section, I will characterize the subgame perfect Nash equilibrium (SPNE) of the game.

5 The Equilibrium