Pay-for-Delay with Settlement Externalities

Transcription

1 Pay-for-Delay with Settlement Externalities Emil Palikot and Matias Pietola June 11, 2017 Abstract This paper studies settlements between an incumbent patent holder and multiple potential entrants to the market in the shadow of patent litigation. We show that there exists litigation in equilibrium for patents with intermediate strength, whereas suciently weak or strong patents are not taken to court. The incumbent pays to delay some entrants while accommodates the others, either through licensing or litigation. This identies a new source of sequentiality in equilibrium entry to markets governed by patents. Settlement externalities between the entrants are the driving force behind our results: when one more entrant is delayed from entering the market, there is less competition and the litigation threat from the other entrants is increased. Our results bring new important insights for the hotly debated topic of pay-for-delay agreements, witnessed in the pharmaceutical industry and sanctioned by antitrust authorities both in the US and Europe. 1 Introduction Patents are probabilistic rights: while they grant a legal monopoly to the incumbent patent holder, potential entrants can engage in a costly and lengthy litigation to challenge patent validity already before the patent is set to expire (Lemley and Shapiro, 2005; Shapiro, 2003). In the shadow of such litigation, incumbents have resorted to settlement agreements with potential entrants, either to delay or advance entry to the market. Pay-for-delay agreements, where the incumbent makes a reverse payment to compensate an entrant for her entry delay, have been subject to both academic and antitrust We are grateful to Yassine Lefouili, Patrick Rey, Marc Ivaldi, Jorge Padilla, Bruno Jullien, Carl Shapiro, Martin Peitz for their valuable comments on various stages of the paper. Ph.D candidate at Toulouse School of Economics, emil.palikot@gmail.com Ph.D candidate at Toulouse School of Economics, matiaspietola@gmail.com. Matias Pietola gratefully acknowledges the nancial support from the Yrjà Jahnsson Foundation and the Finnish Cultural Foundation. 1

2 scrutiny, especially in the pharmaceutical industry. 1 But licensing agreements, where the incumbent provides a license for early entry, have received little attention in this regard, although both types of settlement deals appear in practice and often simultaneously with dierent entrants. The question why incumbents discriminate against similar entrants has not been answered in the current economic literature, to our knowledge. This paper aims to ll the gap. We show that, facing a credible litigation threat from more than one entrant, the incumbent implements a divide and conquer equilibrium strategy where it pays to delay some entrants, while accommodates the others, although all entrants are completely identical in our model. This identies a new source of sequentiality in equilibrium entry to markets governed by patents. Entry accommodation happens either through licensing or litigation, depending on total litigation costs and patent strength. There is licensing when the patent is either suciently weak or strong, whereas intermediate patents are litigated. Litigation is more likely to occur when total litigation costs are low. Finally, we show that conditional settlement agreements, where a delayed entrant is allowed to enter early in the event of patent invalidation, always lead to full entry delay and should therefore be banned as restrictions to competition. To better understand the economic logic behind patent settlements, it is necessary to allow for multiple entry to the market. This is because a settlement agreement between the incumbent and one entrant imposes an externality to the other entrants, a strategic feature not present when the incumbent has only a single entrant to deal with: under single entry the incumbent can use a reverse payment to share industry prots with the entrant and full entry delay maximizes these joint prots. However, under multiple entry, the litigation threat from other entrants becomes stronger when one more entrant is delayed. The reason is that an entrant faces less competition after successful litigation against the incumbent, and hence obtains higher prots after a successful entry. Consequently, to secure full entry delay, the incumbent must compensate all entrants with expected duopoly prots. This may render a full entry delay strategy too costly for the incumbent, so that she accommodates entry to the market. Depending on total litigation costs and patent strength, such accommodation happens either through licensing or litigation, as our results indicate. 1 On 17 June 2013, the US Supreme Court gave its decision in the FTC v. Actavis case and ruled that reverse payment settlements should be subject to a rule of reason analysis instead of being per se illegal or legal. In the European Union, the European Commission has been monitoring reverse payment settlements based on its sector inquiry into the pharmaceutical industry; the First Report on monitoring was published in July According to the Commission, the aim has been to identify settlements that delay generic entry to pharmaceutical markets, to the detriment of consumers in the single market. 2

3 Relation to the Literature This paper relates to two strands of economic literature: licensing and litigating uncertain patents (Farrell and Shapiro, 2008; Lemley and Shapiro, 2005; Kamien and Tauman, 1986; Katz and Shapiro, 1987) and pay-for-delay settlement agreements (Shapiro, 2003; Meunier and Padilla, 2015; Elhauge and Krueger, 2012; Edlin et al., 2015; Manganelli, 2014; Gratz, 2012). The main contribution is to connect these areas of economic research. To our knowledge, pay-for-delay agreements and licensing have not been captured in the same economic model before. Yet assuming that dierent agreements are made independently from each other obfuscates an important economic mechanism, triggered by settlement externalities between the entrants. Therefore, we believe, studying dierent settlement agreements together is essential for building an economic theory for patent settlements. The notion of a probabilistic patent as established in the economic literature is central to our analysis. A patent does not grant an absolute right to exclude others from practicing the invention at hand (Lemley and Shapiro, 2005). Patents can be, and in reality frequently are, challenged in court. Therefore, a patent gives to its owner a right to exclude others only with some probability. 2 Yet an important aspect of patent disputes is that individual rms have sub-optimal incentives to challenge the patents asserted against them (Lemley and Shapiro, 2005). This has a resemblance with private incentives in the public good provision problem: rivals to the litigator will benet from a judgment that declares the patent invalid. This feature of free-riding is also present in our model. Insucient incentives to challenge patent validity may lead to an anti-competitive outcome, unless there are antitrust rules limiting the scope of patent settlements. At the limit, when patent strength approaches zero, a weak patent can be used as a leaf to cover an agreement no to compete (Lemley and Shapiro, 2005). The canonical pay-for-delay model is introduced by Shapiro (2003). He considers a setup with a single entrant who may challenge an incumbent patent holder in a court of law. The parties have the opportunity to settle their dispute instead of going to court, by agreeing on a reverse payment from the incumbent to the entrant as well as an entry date for the entrant. In this case parties will agree on extending the monopoly period and divide the resulting prots. Our model builds on 2 Resulting uncertainty of the property rights is an unavoidable feature of the patent system. The fact that patents are invalidated neither is an accident nor a mistake; it is impossible to perfectly review hundreds of thousands of patents applications. Inventors le over patent applications a year with the U.S. Patent and Trademark Oce, and spend over USD 5 billion a year just on the process of obtaining those patents (Lemley, 2000). Economic literature, often, focuses on litigation, despite the fact that a great majority of patents are never asserted in litigation. Only 1.5 percent of all patents are ever litigated, and only 0.1 percent are litigated to trail (Lemley, 2000; Lanjouw and Schankerman, 2001). The quality of the patent application review system has to be weighted against the associated costs. The patent system is usually skewed towards granting patents, based on a brief process (Lemley and Shapiro, 2005). 3

4 this model with the novelty of allowing for multiple entry to the market. This important extension reveals the connection between pay-for-delay agreements, licensing and litigation, and allows us to capture a source of sequentiality commonly observed in market entry. Previous work assumes only one entrant can credibly threaten the patent holder with litigation, while entrants with weaker incentives to challenge the patent holder will free ride on the litigation eorts taken by the more aggressive one (Meunier and Padilla, 2015). Instead of incorporating this economic logic to our model exogenously, we show that in equilibrium at most one entrant follows through with litigation. Others will free ride, even if all entrants are symmetric and have the ability to litigate. Thus we show that the assumption taken in some models is actually an outcome of strategic interaction between the entrants. Shapiro (2003) proposes a general rule for evaluating patent settlements in antitrust policy: consumers should not be worse o from the settlement as compared to no settlement and hence litigation. This welfare analysis simplies to comparing the duration of exclusion resulting from the settlement (entry date agreed) to the expected entry date when there is no settlement and entry may occur through patent invalidation only. When the reverse payment exceeds the litigation cost incurred by the incumbent, the settlement exclusion period exceeds the expected exclusion period from litigation (Shapiro, 2003). Elhauge and Krueger (2012) argue that all pay-for-delay settlements with a reverse payment higher than litigation costs should be per se illegal, independently from patent strength. Our results have implications for this policy debate: focusing solely on pay-for-delay agreements is not sucient, but the incentives to license and litigate should also be taken into account. Banning reverse payments may have the side-eect of removing the incentives for early licensing. The paper is organized as follows. The next section is devoted to case studies in the pharmaceutical industry, which shed light on the environment of patent settlements in practice. Section 3 introduces our baseline model for two entrants, which is then generalized in Section 4 to allow for more than two entrants. Section 5 considers dierent policy implications and extensions of our model. 2 Pay-for-Delay in the Pharmaceutical Industry Contracts between an incumbent patent holder and potential entrants to the market is a case of general interest. One of the applications, and the main motivation for our work, stems from the pharmaceutical industry. In this sector, branded pharmaceutical companies hold patents on original drugs they have invented, but face competitive pressure from generic producers of bio-equivalent medicines. Generic entrants can simultaneously contest the brand once the primary patent, protecting the main chemical 4

5 compound, has expired. Since then, usually several generic producers race to the market neck-to-neck. Yet often, despite the expiry of the main patent, the legal situation is unclear: the brand has applied for a secondary patent protection and sometimes holds patents on alternative ways of manufacturing the medicine. Therefore, even if the chemical compound itself is no longer protected, a generic entrant may still infringe some other patents owned by the brand. A natural way to clarify the legal environment is to resolve uncertainty in a court of law. However, as such litigation is both lengthy and costly, parties tend to enter into settlement agreements. These agreements settle the patent dispute, provide an entry date for the generic producer and involve money transfers. Cases Pay-for-delay settlement agreements have raised a major attention both in the United States and in Europe. These are agreements with a long settlement exclusion period and a reverse payment from the branded company to the generic entrant, in return to her entry delay. The European Commission has deemed reverse payments as restrictions to competition by object, pursuant to the Article 101 of the Treaty on the Functioning of the European Union. The Commission imposed large nes to both branded and generic rms in its landmark decisions, the Lundbeck decision in June 2013 and the Perindopril decision in July The Lundbeck case considers a number of agreements between a Danish pharmaceutical company Lundbeck and several generic drugs producers. In the 1970's and the 1980's Lundbeck developed an antidepressant drug citalopram that started being marketed in the 1990's. The medicine was largely successful and constituted a major product for Lundbeck; for example 80-90% of the company's revenues in At the time of the settlements, years 2002 and 2003, patents related to the chemical compound and the original process had expired. In principle, the market was free for generic producers to enter. However, Lundbeck still had a number of patents related to more ecient or alternative ways of manufacturing the drug. Lundbeck implemented a so-called generic strategy that involved dierent kinds of agreements with several entrants. For example, in UK it allowed one rm to enter the market, but oered a reverse payment to another one. In Iceland, Lundbeck allowed a market entry without litigation. Overall, the generic strategy was a mixture of reverse payments, takeovers, licensing, accommodation and even introduction of own authorized generic producers. 3 See also the Fentanyl decision in December

6 The Perindopril case involves a French pharmaceutical manufacturer Servier and generic producers of perindopril, a medicine for treating high blood pressure developed by Servier in the 1980's. Perindopril became Servier's most successful product with annual global sales in years 2006 and 2007 exceeding USD 1 billion with average operating margins beyond 90%. Generic entry started to impose a credible threat to Servier once the patent governing the main compound expired in May Anticipating this, Servier had started to design and implement a generic strategy from the late 1990's. This strategy included acquiring new patents and resulted in ve settlement agreements with dierent generic producers, between the years 2005 and Four of these agreements were considered pay-for-delay settlements, while the fth one was a licensing deal. Servier considered litigation and licensing as alternative tools in its strategy. In the US, the Drug Price Competition and Patent Term Restoration Act of 1984 (the so-called Hatch-Waxman Act) shapes the regulatory approval of generic drugs. The aim of this legislation is to promote entry of generics by guaranteeing the rst one of them a duopolistic position. When a generic producer of a bio-equivalent drug les an Abbreviated New Drug Application (ANDA) to the Food and Drug Administration (FDA), the Hatch-Waxman Act requires to declare a relationship to a patent mentioned in the Orange Book, a list of approved drug products together with a catalog of patents related to each of them. If a generic producers states that the relevant patents are no longer valid, or that it is not infringing, a certication is granted. The Hatch-Waxman Act provides 180 days of exclusivity for a generic producer who makes such a certication: no other generic producer can obtain approval from the FDA during this time. The aim of the exclusivity is to promote litigation of weak patents, but many patent disputes between pharmaceutical companies have been settled with reverse payments. The authorities in the US had many views on how to deal with reverse payments, until the US Supreme Court gave its decision in the FTC v. Actavis Inc. case in June The Department of Justice and the Federal Trade Commission presumed reverse payments illegal, but rebuttable. The courts of lower instances adopted dierent approaches, including per se illegality, a scope of the patent test and a quick rule of reason analysis, depending on the court. The Supreme Court rejected all these legal standards, and held that the reverse payments are subject to a complete rule of reason analysis. The FTC vs. Actavis case was brought to the US Supreme Court by the Federal Trade 6

7 Commission (FTC) in The case considers a deal made between a Belgian pharmaceutical company Solvay Pharmaceuticals and a generic producer Actavis, Inc. Solvay was granted a new patent for AndroGel in Later on, Actavis led an ANDA to the FDA and stated that Solvay's new patent was invalid and the generic version produced by Actavis did not infringe upon the AndroGel patent. Solvay settled the case with Actavis: the settlement agreement included a reverse payment from Solvay to Actavis in return for an exclusion period during which Actavis agreed to stay out of the market. The agreed entry date was 65 months before the AndroGel patent expired. The FTC considered the arrangement between Solvay and Actavis as an antitrust violation and brought a lawsuit against them. The District Court and the appellate court, the Eleventh Circuit, dismissed the case. The Eleventh Circuit applied the scope of the patent test to conclude that the reverse payment settlement was not anti-competitive, since the settlement exclusion period did not exceed the scope of the AndroGel patent. According to the Court, the parties were not obliged to continue litigation for the sole purpose of avoiding antitrust liability. The US Supreme Court rejected this analysis and held that it is not sucient to base the legal analysis on patent law policy and that the antitrust question must be addressed. The Supreme Court argued that: (1) FTC's complaint could not have been dismissed without analyzing the potential justications for such decision; (2) the patentee is likely to have enough power to implement antitrust harm in practice; (3) the antitrust action is likely to prove more feasible administratively than the Eleventh Circuit believed: a large, unexplained payment from the patentee to the generic producer can provide a workable surrogate for a patent's weakness; (4) the parties could have made another type of settlement agreement, by allowing the generic producer to enter the market before the patent expires without a need for a reverse payment. Main Lessons The basic logic behind reverse payments is the following. On one hand, the brand would like to postpone generic entry until patent expiration, as generic entry leads to two major changes in the market: prices decrease and the brand loses its market share. 4 On the other hand, generic entrants also care about the settlement exclusion periods, because priority to enter the market results in higher prots than late entry under established competition. Thus, to provide the right incentives to settle with late entry, the brand must compensate the generic producer, typically with 4 See paragraphs 3 and 2133 of the Perindopril decision. 7

8 money. Otherwise the generic producer takes its chances in court and enters early in the event of patent invalidation. The odds in court have been quite good for the generic producers. The generic producers have won 62% of all patent litigation cases that resulted in a ruling, according to the Pharmaceutical Sector Inquiry conducted by the European Commission between the years 2000 and In fact, the term weak patent has even entered the business jargon. 6 But even a weak patent can be useful for the incumbent brand, due to free-riding between the generic companies in their litigation eorts. Success in trial opens the market for everybody, not merely for the generic producer who took litigation eort and incurred, often a signicant, litigation cost. The generic entrants have expressed their concern to win the battle, but lose the war due to follow-up entry to the market. 7 The incentives to settle litigation are pronounced when other generic producers lie in wait in the shadow of the litigation. All in all, we can identify three strategies available to generic producers: 8 1. Actively seek settlement with the patent holder; 2. Continue litigation and seek to launch at earliest possibility; 3. Pull litigation and wait for the market to open and ensure readiness for launch. Several other observations can be made from the case studies in the pharmaceutical industry. Firstly, the entry game starts after the expiry of a certain patent and this date is common knowledge. Secondly, the entrants arrive to the market simultaneously and their subsequent sequential entry is an outcome of an interplay between the patent holder and the entrants. Some entrants may be accommodated, while the others are delayed. Such divide and conquer strategies are achieved through a myriad of decisions: pay-for-delay agreements, licensing deals, litigation and take-overs. 3 A Model with Two Entrants We consider the following environment as our baseline model. There is one incumbent patent holder and two symmetric entrants to the market. The incumbent has a legal monopoly unless a court of law declares the patent invalid. The patent is valid with probability θ [0, 1] (patent strength) and 5 For process patents, the corresponding gure was 74%. For litigations initiated by branded companies, 32% of the judgments found the invoked patent to be infringed, and in an additional 12% of the cases the court annulled the invoked patent. See Pharmeceutical Sector Inquiry by the European Commission. 6 See paragraph 280 of Lundbeck decision 7 See paragraph 493 of the Perindopril decision by the European Commission. 8 See paragraph 1020 of the Perindopril decision. 8

9 invalid otherwise; patent strength is common knowledge. The entrants can challenge the incumbent at date zero and the patent expires at date one. Each entrant chooses from three strategies: litigate over patent validity, wait for the market to open or settle with the incumbent. An entrant who litigates incurs a litigation cost c 0 and obtains a court ruling at date l [0, 1); the incumbent has a litigation cost C 0. Litigation outcomes are assumed perfectly correlated: the court declares the patent invalid with probability 1 θ if at least one entrant litigates. An entrant who waits saves on the litigation cost and is free to enter the market if the other entrant litigates and wins in court. An entrant who settles makes a payment p R to the incumbent and agrees on a future entry date t [0, 1]. A settlement agreement includes a non-challenge clause and remains in force even if the other entrant litigates and wins in court (agreements must be kept). 9 The following game formalizes the interaction between the incumbent and the entrants. The incumbent moves rst and makes a public take-it-or-leave-it settlement oer (p, t) to each entrant. Then, after observing these oers, the entrants simultaneously but independently choose to litigate, wait or settle. The equilibrium concept is subgame perfect Nash equilibrium in pure strategies and we use backwards induction to solve the game. The game is played at date zero and time runs continuously afterwards. Competition is modeled in reduced form, with instantaneous prot functions Π ( ) for the incumbent and π ( ) for an entrant. These are mappings from the number of rms in the market to rm-level prot. The individual prots, as well as the industry prot, are assumed weakly decreasing in the number of rms in the market. Payos from Litigate, Wait or Settle Each rm has an objective to maximize her own expected payo from date zero until patent expiration. The settlement payo of an entrant, given the strategy taken by the other entrant, writes (1 max {t, l}) (1 θ) if litigate S = p + (1 t) π (2) [π (2) π (3)] 0 if wait (1) (1 max {t, x}) if settle with date x By accepting the settlement oer from the incumbent, the entrant pays p and enters the market at date t. If the other entrant waits, the entrant obtains the duopoly prot between her date of entry and 9 We consider conditional settlement terms as one extension of our model below. 9

10 the patent expiration date. If the other entrant litigates, there is a triopoly after the expected entry date of litigation. If the other entrant settles, there is a triopoly after the latest settlement entry date. The entrant has a best response to settle if and only if the settlement payo exceeds the maximum of the litigation and waiting payos: S max {L, W } 0 (2) where (1 l) (1 θ) π (3) if litigate W = 0 if wait or settle (3) is the waiting payo of the entrant, which is at least zero, and 0 if litigate or wait L = c + (1 θ) (1 l) π (3) + (1 θ) [π (2) π (3)] max {x l, 0} if settle with date x (4) is the litigation payo of the entrant. Observe that litigate is never a best response to litigate, because waiting allows to save on the litigation cost. By litigating, the entrant pays a litigation cost c and enters the market at the expected entry date of litigation. She obtains the triopoly prot when competing against both the incumbent and the other entrant, but receives the duopoly prot if the other entrant is delayed from entering the market due to a settlement agreement with the incumbent. A settlement with the other entrant imposes a positive externality (a settlement externality) to the entrant, whose litigation and settlement payos are higher when the other entrant is delayed longer. Credibility of the Litigation Threat Intuitively, there is no credible litigation threat for a suciently strong patent: the cost of litigation is too high compared to the probability patent invalidation. Since settlement externalities are positive, the litigation payo of an entrant satises the inequality L c + (1 l) (1 θ) π (3) (5) where the lower bound is achieved when the other entrant does not settle (litigates or waits) or settles with an entry date weakly below l. The sign of the lower bound on litigation payo is crucial for the 10

11 outcome of the game. We shall say that the litigation threat is credible for a suciently weak patent, θ ˆθ 1 c (1 l) π (3) (6) in which case the lower bound on litigation payo is positive. For a suciently strong patent, θ > ˆθ, there is no credible litigation threat from the entrants. To see this, recall that S 0 is a necessary condition for a settlement. By making a settlement oer with a strictly positive payment p > 0 and an entry date t = 1, the incumbent ensures that an entrant always rejects the settlement oer, because S = p < 0 W (settle is dominated by wait). If the incumbent makes such oers to both entrants, the entrants play a litigation game (litigate or wait) with the lowest possible litigation payo, which is strictly negative when θ > ˆθ. Thus, there exists a unique subgame equilibrium in which the entrants have a dominant strategy to wait until patent expiration. The following result summarizes this reasoning. Proposition 1. Both entrants wait in equilibrium if and only if θ > ˆθ. Proof. Suppose θ > ˆθ and that the incumbent oers t = 1 and p > 0 to both entrants. Then W 0 > S and W 0 L no matter what strategy the other entrant takes, so each entrant has a dominant strategy to wait. The incumbent gets the highest possible monopoly payo I = Π (1) in equilibrium. Suppose (wait,wait) is played in equilibrium. Then θ > ˆθ must hold, because θ ˆθ implies L 0 no matter what strategy the other entrant takes. Thus wait is never a best response to wait. Proposition 1 shows that for a suciently strong patent, θ > ˆθ, there is no credible litigation threat from the entrants. By making unacceptable settlement oers, the incumbent ensures that there is never litigation, monopolizes the market and obtains the monopoly payo I = Π (1) with zero cost. The entrants receive W = 0 from waiting until patent expiration. The game becomes interesting when the patent is suciently weak, θ ˆθ (litigation is not too costly), which is assumed for now on. Then the lower bound on the litigation payo is positive. If both settlement oers are rejected, the entrants play a chicken game in going to court: the litigator is worse o than the free-rider who waits for the market to open and saves on litigation eort. Yet, there is no incentive for the litigator to wait, because the patent is never challenged if both entrants wait. Indeed, the incumbent must settle with both entrants to avoid litigation, because wait is never a best response to wait or settle. Furthermore, as litigate is never a best response to litigate, there 11

12 are essentially three potential equilibria of the game under a credible litigation threat: (litigate,wait), (litigate,settle) and (settle,settle). Table 1 summarizes these strategies. Settle Litigate Wait Settle Litigate Wait Table 1: Potential equilibria under a credible litigation threat Licensing and Pay-for-Delay Let us now consider patent settlements in more detail. At rst sight, the incumbent can choose from a large set of dierent settlement strategies: a settlement oer may specify any date of entry t [0, 1] and any transfer of value p R (positive or negative) between the incumbent and the entrant. Importantly, the following lemma greatly simplies the analysis by showing that only two types of settlement agreements can occur in equilibrium. Lemma 1. There are only two types of settlements in equilibrium: 1. Licensing agreements with an entry date t = l and a licensing fee π (2) p = (1 l) θ π (2) π (3) if delay 0 if litigate if litigate + c otherwise if license (7) from the entrant to the incumbent. 2. Pay-for-delay agreements with an entry date t = 1 and a reverse payment π (2) p = (1 l) (1 θ) π (3) π (3) if delay 0 if litigate if litigate c otherwise if license (8) from the incumbent to the entrant. Proof. There are no settlements if θ > θ (Proposition 1). Assume θ θ. Let us rst characterize best responses in stage two of the game. An entrant's best response to litigate is settle if S W and wait 12

13 otherwise. The inequality S W is equivalent to (t l) π (2) + (1 l) θπ (2) if t < l p (1 t) θπ (2) (t l) (1 θ) π (3) if t l An entrant's best response to settle is settle if S L and litigate otherwise. The inequality S L is equivalent to (x t) π (2) + (1 x) π (3) if t < x (1 l) π (3) if x < l p c + (1 θ) (1 t) π (3) if t x (x l) π (2) + (1 x) π (3) if x l Consider now the rst stage of the game. If there is one settlement in equilibrium, the incumbent's payo writes I = C + p + tπ (1) + (1 t) Π (2) (1 l) (1 θ) [Π (2) Π (3)] It is never optimal for the incumbent to leave an entrant strictly better o from a settlement, as otherwise she could deviate by strictly increasing p while still ensuring that the entrant accepts the settlement oer. Thus an entrant who settles must be indierent between accepting or rejecting the settlement oer. Using this indierence, in equilibrium (l t) π (2) + (1 l) θπ (2) if t < l p = (1 t) θπ (2) (t l) (1 θ) π (3) if t l must hold. Suppose t < l. Then by increasing t innitesimally, the incumbent gains Π (1) Π (2) π (2) 0 since industry prots are weakly decreasing. Thus t l. Again, by increasing t innitesimally, the incumbent gains Π (1) Π (2) θπ (2) (1 θ) π (3) 0 Thus t = 1. If there are two settlements in equilibrium, the incumbent has the payo I = P + min {t, x} Π (1) + (max {t, x} min {t, x}) Π (2) + (1 max {t, x}) Π (3) 13

14 where P denotes the sum of the two individual payments. Using a similar argument as above, in equilibrium, each entrant must be indierent between accepting or rejecting the settlement oer, so (x t) π (2) + (1 x) π (3) if t < x (1 l) π (3) if x < l p = c + (1 θ) (1 t) π (3) if t x (x l) π (2) + (1 x) π (3) if x l Summing the two payments yields (x t) π (2) + (1 x) 2π (3) if t < x (1 l) π (3) if x < l P =2c + (1 θ) (t x) π (2) + (1 t) 2π (3) if t x (x l) π (2) + (1 x) π (3) if x l (1 l) π (3) if t < l (1 θ) (t l) π (2) + (1 t) π (3) if t l By increasing min {t, x} innitesimally, the incumbent gains 0 if min {t, x} < l Π (1) Π (2) π (2) (1 θ) π (2) π (3) if min {t, x} l By increasing max {t, x} innitesimally, the incumbent gains 0 if max {t, x} < l Π (2) + π (2) Π (3) 2π (3) (1 θ) π (2) π (3) if max {t, x} l Since industry prots are weakly decreasing, min {t, x} l. Furthermore, since the changes are constant in time, we have a corner solution: t, x {l, 1}. The payments follow by inserting these entry dates to the expressions for the payments. Lemma 1 shows that there are only two types of settlements in equilibrium. A licensing agreement allows the entrant to enter the market without infringing the patent, but the entrant must pay a licensing fee in return. The licensing fee accounts for the prots the entrant earns before the expected entry date of litigation. A pay-for-delay agreement involves a commitment from the entrant to stay out of the market even if the patent has been declared invalid in the court of law. In return, the incumbent makes a reverse payment to compensate for the lost prots after the expected entry date 14

15 of litigation. Furthermore, when the incumbent settles with both entrants, she is able to capture the litigation cost of both entrants. If there is only one settlement, no litigation costs are saved. To glean intuition for the proof of the lemma, recall that an entrant has a best response to settle if and only if S max {L, W }. This means that, in equilibrium, any entrant who settles must receive at least her deviation payo of rejecting the settlement oer and going to court or waiting instead. However, the incumbent will never leave an entrant strictly better o from a settlement: otherwise, the incumbent has a protable deviation to strictly increase the payment in the settlement oer, equal to the amount p = S max {L, W } > 0 (9) while still ensuring that the entrant accepts the settlement oer. Thus, an entrant who settles in equilibrium must be indierent between accepting or rejecting the settlement oer: S = max {L, W } (10) This indierence pins down equilibrium payments given the entry dates. There is no reason for the incumbent to allow entry during the litigation period. By refusing to settle, an entrant stays out of the market for sure during the litigation period, and obtains zero prots. Therefore, the incumbent can ask an entrant to pay the prot she makes and gets the entire industry prot from the litigation period. Since industry prot is weakly decreasing in the number of rms, the incumbent monopolizes the market during the litigation period. After the litigation period, there is a possibility of entry through litigation and the incumbent cannot monopolize the market with zero cost. On one hand, an entrant must be compensated for missed opportunities in the market due to entry delay after the expected entry date of litigation. On the other hand, an entrant is willing to pay only the prot she makes before the expected entry date of litigation. Furthermore, the innitesimal net benet of entry delay is constant in time. Therefore, if an entrant is delayed slightly beyond the litigation period, it is optimal for the incumbent to delay her until patent expiration. 15

16 Litigation for Intermediate Patents Using Lemma 1 to account for the payments, the incumbent has the following net payo in equilibrium with two settlements: Π (1) 2 (1 θ) π (2) I = 2c + lπ (1) + (1 l) Π (2) + θπ (2) (1 θ) π (3) Π (3) + 2θπ (3) if (delay,delay) if (licence,delay) if (licence,license) (11) A licensee is willing to pay a lower licensing fee when the other entrant obtains a license: there is a negative settlement externality between the licensees that reduces individual licensing fees, harming the incumbent. Similarly, a delayed entrant must be compensated more when the other entrant is delayed as well: there is a positive settlement externality between the delayed entrants that increases the individual reverse payments, again harming the incumbent. However, litigation has the benet of eliminating these settlement externalities: the incumbent's payo under litigation writes θπ (1) + (1 θ) Π (2) (1 θ) π (3) I = C + lπ (1) + (1 l) θπ (2) + (1 θ) Π (3) + θπ (2) θπ (1) + (1 θ) Π (3) if (litigate,delay) if (litigate,license) if (litigate,wait) (12) A licensee is still willing to pay a high licensing fee when the other entrant litigates, because the litigator does not enter the market when the patent is upheld in court. Still, the incumbent gets away with a small reverse payment, as the waiting payo equals the expected triopoly prot. The optimal settlement design compares the benets of litigation to the cost of litigation, because the incumbent eectively loses the total litigation costs 2c + C in court. We have the following result. Proposition 2. For any patent strength θ ˆθ, the equilibrium of the game is (delay,delay) if the gain from monopolization is suciently high, Otherwise, there exists an interval Θ Π (1) Π 2π (2) + max {Π (3), Π (2) π (3)} (13) [ 0, ˆθ ] of patent strength such that there is litigation in equilibrium if θ Θ and no litigation otherwise. The interval shrinks in total litigation costs C + 2c and is empty for costs large enough. In particular, for zero litigation costs, Θ = [0, 1]. Proof. See the Appendix. 16

17 If the gain from monopolizing the market is suciently high, Π (1) Π, the incumbent will always delay both entrants, regardless of patent strength. Otherwise patent strength plays a role in determining the equilibrium strategies: there exists an interval of patent strength such that benets from litigation exceed the total cost of going to court; in particular, for zero litigation costs, this is true for any patent strength. The intuition why litigation occurs for intermediate patent strength is that, by going to court, the incumbent has the chance of monopolizing the market, but spends money in litigation. For a suciently weak patent, the chance of winning in court and monopolizing the market is too low compared to the litigation cost. For a suciently strong patent, the cost of litigation is too high compared to the small reverse payments needed to delay entry with settlements. Patent Strength vs. Pay-for-Delay An interesting question is how patent strength aects the equilibrium number of delayed entrants. Since a reverse payment accounts for a share 1 θ of the prots a delayed entrant loses after the litigation period, the cost of entry delay decreases in patent strength. Thus, intuitively, entry delay is more likely to occur when the patent is strong. However, the licensing revenue also increases in patent strength, because the incumbent is able to charge a share θ of the prots a licensee makes in the market. When there are two settlements in equilibrium, (delay,delay) provides the highest (settle,settle) payo for an incumbent with a suciently strong patent, θ > θ 1 min { Π (1) Π (2) π (2), 1 2 [Π (1) Π (3) 2π (3)]} π (2) π (3) (14) By contrast, the incumbent has the highest payo in (license,license) when the patent is suciently weak, θ θ 1 max { 1 2 [Π (1) Π (3) 2π (3)], Π (2) + π (2) Π (3) 2π (3)} π (2) π (3) (15) Both thresholds of patent strength are decreasing in the gain from monopolization and increasing in the dierence between duopoly and triopoly entry prot, which captures the intensity of the settlement externality between the two entrants. If the gain from monopolization is high and entry prot decreases little in subsequent entry, even a weak patent can be enough to monopolize the market. Finally, the divide and conquer strategy of (license,delay) provides the highest payo for the incumbent when the patent has intermediate strength: θ < θ θ. In particular, when subsequent entry decreases industry 17

18 prot less than the rs entrant, there is no scope of such a divide and conquer strategy: Π (1) Π (2) π (2) Π (2) + π (2) Π (3) 2π (3) = θ = θ (16) Thus the divide and conquer strategy (license,delay) is an equilibrium strategy for intermediate patent strength only if subsequent entry reduces industry prot more than initial entry. The following result summarizes how patent strength aects entry delay in equilibrium without litigation. Proposition 3. Suppose Π (1) < Π, θ / Θ and θ ˆθ. Then, the equilibrium of the game is (delay,delay) if θ > θ, (license,delay) if θ < θ θ and (license,license) if θ θ. Furthermore, θ = θ if the the change in industry prot weakly decreases in entry and θ < θ otherwise. Proof. Suppose Π (1) < Π, θ / Θ and θ ˆθ. Then, there is no litigation in equilibrium (Proposition 2). Suppose the incumbent oers two pay-for-delay agreements if θ > θ, one pay-for-delay agreement and one licensing agreement if θ < θ θ and two licensing agreements if θ θ. Then each entrant has a best response to settle if the other entrant settles or waits. Since litigate is never a best response to litigate, there exists a unique subgame perfect equilibrium in which both entrants settle. Looking at the equilibrium with litigation more closely, we observe that licensing and litigation are substitutes for the incumbent. Comparing the payos between (litigate,license) and (litigate,wait) we immediately see that (litigate,license) is never an equilibrium. Since monopoly maximizes industry prot, the incumbent is always better o by not oering a licensing agreement. Then both entrants will enter the market only if the incumbent loses in court. If the incumbent wins, she monopolizes the market. This means that in equilibrium with litigation, a settlement is always a pay-for-delay agreement. Proposition 4. Suppose Π (1) < Π and θ Θ. Then, the equilibrium of the game is (litigate,delay) if Π (2) Π (3) + π (3) (17) and (litigate,wait) otherwise. Proof. Suppose Π (1) < Π and θ Θ. Then, there is litigation in equilibrium (Proposition 2). Suppose 17 holds and the incumbent oers t = 1 to both entrants, but one entrant is oered a reverse payment p = (1 l) (1 θ) π (3) while the other entrant is charged p > 0. Then, the entrant who is oered the 18

19 reverse payment has a best response to settle unless the other entrant settles. But the other entrant never settles, because S < 0 W, and her best response to settle is litigate, since θ ˆθ. Consequently, there is a unique subgame perfect equilibrium in which one entrant accepts a pay-for-delay agreement while the other entrant litigates. Suppose 17 does not hold and the incumbent oers t = 1 and p > 0 to both entrants. Then S < 0 W for both entrants and there are two subgame perfect equilibria; in both of these equilibria one entrant litigates while the other one waits. Proposition 4 shows that entry delay is independent of patent strength when there is litigation in equilibrium. Given that there is litigation, the incumbent monopolizes the market with probability θ. Otherwise there is entry to the market, and the incumbent can either compete in a triopoly or duopoly, but needs to compensate the delayed entrant with a reverse payment that is proportional to 1 θ. Therefore, the incumbent chooses to delay one of the entrants independently of patent strength. Only the mode of competition matters. If the triopoly prot of an entrant is less than the change in incumbent's prot when moving from duopoly to triopoly, the incumbent delays the entrant. Example 1 To provide an illustration, suppose that the instantaneous prot functions are determined by a textbook Cournot quantity-setting game with a simple inverse demand 1 Q, where Q denotes the industry output. All rms are symmetric and marginal costs are normalized to zero. The equilibrium rm-level outputs are q (1) = 1 2, q (2) = 1 3 and q (3) = 1 4, resulting in equilibrium prots π (1) = 1 4, π (2) = 1 9 and π (3) = The thresholds of patent strength are θ = 2 7 and θ = 3 7 (industry prot decreases more in subsequent entry). Furthermore, π (2) 2π (3) = < 0 so the equilibrium with litigation is (litigate,wait). 4 A Model with n Entrants Let us now consider a more general environment with n symmetric entrants to the market. The aim is to show how the optimal settlement design changes when there are more potential entrants to the market. As in the model with two entrants, for a suciently strong patent, there is no credible litigation threat from the entrants. Proposition 5. All entrants wait in equilibrium if and only if θ > ˆθ (n) 1 c (1 l) π (1 + n) (18) 19

20 Proof. The proof follows similar steps as in the proof of Proposition 1. For the details, see the Appendix. Observe that the relevant threshold ˆθ (n) is weakly decreasing in the number n of potential entrants to the market. Even a weak patent may shield the incumbent from entry if competition between the entrants is intensive enough. For a suciently weak patent, though, the litigation threat is credible and the incumbent cannot monopolize the market with zero cost. Indeed, θ ˆθ (n) implies that the litigation payo is always positive. Thus wait can only be a best response if at least one other entrant litigates. But if at least one other entrant litigates, waiting saves on the litigation cost. There is never more than one entrant who litigates in equilibrium, because otherwise each litigator has a protable deviation to wait, keeping the strategies of the other entrants xed. There is always one entrant who litigates, unless the incumbent settles with everybody. Therefore strategies where all entrants wait, more than one entrant litigates or all entrants either wait or settle can be ruled out from the equilibrium path. There is no litigation if and only if all entrants settle. Otherwise, under litigation there is one entrant who litigates while the others either settle or wait. Licensing and Pay-for-Delay As in two entrants model, the indierence condition pins down the payments in equilibrium. The following lemma is a generalization of Lemma 1 to the environment of n entrants. Lemma 2. There are only two types of settlements in equilibrium: 1. Licensing agreements with an entry date t = l and a licensing fee c if all settle p = (1 l) θπ (1 + e) + 0 otherwise (19) from the entrant to the incumbent, where e is the number of licensees. 2. Pay-for-delay agreements with an entry date t = 1 and a reverse payment 10 c if all settle p = (1 l) (1 θ) π (2 + n d) 0 otherwise (20) 10 Notice that the number two in the reverse payment accounts for the increase in the number of players in the market when the pay-for-delay agreement is rejected. 20

21 from the incumbent to the entrant, where d is the number of delayed entrants. Proof. See the Appendix. The licensing fee paid by an individual licensee is decreasing in the number of other licensees, whereas an individual reverse payment is increasing in the number of delayed entrants. The general model shows that these settlement externalities are more pronounced when there are many potential entrants to the market. If the incumbent settles with all entrants, she obtains the following payo: I = nc + lπ (1) + (1 l) Π (1 + n d) + (n d) θπ (1 + n d) d (1 θ) π (2 + n d) }{{}}{{} (21) licensing revenue cost of entry delay Using a similar argument as in the baseline model, we can show that there is no licensing under litigation, yielding the following payo of the incumbent under litigation: I = C + lπ (1) + (1 l) θπ (1) + (1 θ) Π (1 + n d) d (1 θ) π (2 + n d) }{{} cost of entry delay (22) Importantly, the cost of entry delay grows quickly in the number of delayed entrants d, since each individual reverse payment as well as the number of reverse payments is increased. In particular, when d = n, the incumbent needs to compensate each entrant with the expected duopoly prot from litigation, amounting to a large total reverse payment: pn = n (1 l) (1 θ) π (2) nc (23) We have the following result, which generalizes Proposition 2. Proposition 6. For any patent strength θ ˆθ (n), there are n delayed entrants in equilibrium if the gain from monopolization is suciently high, Π (1) Π (n) nπ (2) + max d<n Otherwise, there exists an interval Θ Π (1 + n d) dπ (2 + n d) }{{} cost of entry delay [ 0, ˆθ ] of patent strength such that there is litigation in equilibrium when θ Θ and no litigation otherwise. The interval shrinks in total litigation costs and is empty for costs large enough. In particular, for zero litigation costs, Θ = [0, 1]. 21

22 Proof. See the Appendix. The underlying economic intuition behind Proposition 6 is the same as in the model with two entrants. We shall oer an intuition for the proof here. The proof of the result has the following steps. We rst show that the equilibrium payo of an incumbent who settles with everybody is increasing and convex in patent strength, whereas the incumbent's payo in equilibrium with litigation is linear and increasing in patent strength. Therefore, the dierence between the litigation and no litigation equilibrium payos is concave in patent strength. Furthermore, when the incumbent settles with everyone, she saves on the litigation costs, which means that for costs high enough, litigation will not occur in equilibrium. At the other extreme, when total litigation costs go to zero, there will always be litigation in equilibrium. The main take-away from the general result is that the gain from monopolization must be very large for n pay-for-delay agreements to be concluded in equilibrium. For suciently large n, the cost of entry delay is too high and the incumbent accommodates entry to the market, either through licensing or litigation. The following result shows how the number of delayed entrants depend on patent strength when the incumbent settles with all entrants. Proposition 7. Suppose Π (1) < Π, θ / Θ and θ ˆθ. Then, in equilibrium, there are n d (θ) licensees and d (θ) arg max d Π (1 + n d) + (n d) θπ (1 + n d) d (1 θ) π (2 + n d) }{{}}{{} licensing fees reverse payments (24) delayed entrants, where d (θ) is weakly increasing in patent strength θ. Proof. See the proof of Proposition 6. Proposition 7 generalizes Proposition 3 to the case of n entrants. The settlement externalities are pronounced when the number of potential entrants to the market is large. This means that the extreme strategies of licensing to all or delaying everyone are less likely to constitute an equilibrium. On one hand, the incumbent needs to pay a high total reverse payment for delaying many entrants, because more entrants need to be compensated and individual reverse payments go up when there is less competition in the market. On the other hand, licensing becomes more protable when the 22