WORKING 

 PAPERS

THE VALUE OF A SECOND BITE AT THE APPLE:

THE EFFECT OF PATENT DISPUTE SETTLEMENTS

 ON ENTRY AND CONSUMER WELFARE

Joel Schrag

WORKING PAPER NO. 281

January 2006

___________________________________________________________________________

FTC Bureau of Economics working papers are preliminary materials circulated to stimulate discussion

and critical comment. The analyses and conclusions set forth are those of the authors and do not

necessarily reflect the views of other members of the Bureau of Economics, other Commission staff, or

the Commission itself. Upon request, single copies of the paper will be provided. References in

publications to FTC Bureau of Economics working papers by FTC economists (other than

acknowledgment by a writer that he has access to such unpublished materials) should be cleared with the

author to protect the tentative character of these papers.

______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
The Value of a Second Bite at the Apple: 

The Effect of Patent Dispute Settlements on Entry and Consumer 

Welfare 

Joel Schrag*

Original Draft: June 2001 

This Draft: January 2006 

Abstract: I analyze the effect on consumer welfare of settlements of patent infringement 

lawsuits that consist of a royalty-free license for delayed entry by a potentially 

infringing horizontal competitor of the incumbent patent-holder. Settlements that 

split the remaining patent life in a way that reflects the expected outcome of the 

trial do not in general improve consumer welfare compared to the litigation 

alternative. This result arises because such settlements can undermine potential 

entrants’ incentives to challenge the incumbent’s monopoly. If settlements of 

patent infringement lawsuits cause a reduction in the investment in development 

of competing products, consumers may prefer that the parties to such disputes 

litigate rather than settle. 

Keywords: patents, settlement, antitrust, intellectual property 

JEL Codes: K21, L4, O34 

 

*

 Economist, Bureau of Economics, Federal Trade Commission, Washington, DC 20580. The author 

thanks David Balan, Michael Kades, and Dan O’Brien for comments on an earlier draft. The author can be 

reached by email at jschrag@ftc.gov, by phone at (202) 326-3588, and by fax at (202) 326-3443. The 

views expressed in this paper do not necessarily reflect the views of the Federal Trade Commission or any 

individual Commissioner. 
1

1. Introduction

Intellectual property disputes between actual or potential horizontal competitors are an 

unavoidable consequence of the uncertain nature of the property right that a patent represents.1

 

The parties involved in such disputes can choose to litigate their cases to a final conclusion, but 

they may also resolve their disagreements with settlements. Such settlements can produce a 

variety of benefits, including lower social and private litigation costs, faster entry by new 

producers, and the reduction of risk. Yet such settlements can also raise antitrust concerns, since 

they are agreements between firms that are, at least with some probability, direct competitors. 

Some kinds of patent dispute settlements clearly raise more concerns than others. A cash 

payment from an incumbent firm to a potentially infringing entrant in exchange for the entrant’s 

commitment to abandon or delay the marketing of its product would clearly be worrisome; 

consumers would probably prefer the firms to litigate rather than reach such a settlement.2

 A 

royalty-bearing license that enabled an entrant to immediately market its product might raise 

fewer red flags; such a settlement could conceivably benefit both consumers and the parties to the 

settlement agreement. In a related paper (Schrag (2004)), I demonstrate some of the difficulties 

that can arise in an analysis of the competitive effects of this kind of agreement. 

In this paper, I analyze the effects of a particular kind of patent dispute settlement 

between potential horizontal competitors, namely a royalty-free license in exchange for delayed 

 

1

 See Shapiro and Lemley (2005) for a discussion of the “probabilistic” nature of intellectual property 

rights. As they point out, a patent is not an iron-clad right to exclude a competitor. It is instead a right to 

try to exclude a competitor. 

2

 The Federal Trade Commission has challenged patent settlements between Schering-Plough and two 

potential generic competitors, Upsher-Smith Laboratories and the ESI Lederle unit of American Home 

Products, on the grounds that Schering had essentially paid its rivals not to compete. See 

http://www.ftc.gov/os/2001/04/scheringpart3cmp.pdf. In December, 2003, the Commission released its 

final decision in this case, finding that the agreements were anticompetitive. See In the Matter of Schering 

Plough Corporation, et al., Dkt No. 9297 (December 18, 2003) (final decision of the Commission). In 

March 2005 the 11th Circuit Court of Appeals reversed the FTC’s decision. For related examples in the 

pharmaceutical industry, see also Abbott Labs., Dkt. No. C-3945 (May 22, 2000) (consent order); Geneva 

Pharm., Inc., Dkt. No. C-3946 (May 22, 2000) (consent order) and Hoechst Marion Roussel, Inc., Dkt. No 

9293 (May 8, 2001) (consent order). 
2

entry by the potentially infringing firm. I assume that, aside from the license, the incumbent 

cannot transfer to the entrant any other net consideration, e.g. cash. Under this assumption, the 

Federal Trade Commission’s concern about an incumbent paying for delayed entry that was the 

focus of its recent Schering case cannot arise.3

 The central question that I address is whether such 

settlements for “time off the patent” serve consumers’ interests. Given a choice, would 

consumers accept such settlements, or would they prefer that the parties litigate their cases? My 

main finding is that royalty-free licenses for delayed entry do not necessarily serve consumers’ 

interests, even if the entrants have all of the bargaining power in their negotiations with 

incumbent patent-holders and can therefore obtain relatively early entry dates through their 

settlements. 

It may seem that a patent settlement that licensed the entrant to come into the market after 

a mutually agreeable delay would tend to be competitively neutral, as long as the litigants’ 

bargaining was not distorted by a cash payment from the incumbent to the entrant. If litigation 

costs are small, it is plausible that such a settlement would more or less reflect the expected 

outcome of the trial, and consumers would therefore be approximately indifferent between 

litigation and settlement, at least as long as their discount rate was not very different from the 

litigants’ discount rates. Suppose, for instance, that a patent-holder’s chance of winning an 

infringement case against a potential competitor is fifty percent. If the remaining life of the 

patent were ten years and litigation costs were small, an agreement that licensed the potentially 

infringing firm to enter in approximately five years would essentially reflect the expected 

outcome of the trial. Setting aside the issue of discounting, such a settlement at first glance seems 

both reasonable and likely. If the entrant tried to obtain a significantly earlier entry date through 

the settlement, the incumbent should have an incentive to litigate rather than settle. If the 

incumbent tried to obtain a significantly later entry date through the settlement, the entrant would 

 

3

 See the discussion in note 2. 
3

have an incentive to litigate rather than settle. Under both litigation and the hypothesized 

settlement for time off the relevant patent’s life, then, the entrant would expect to be in the market 

— and consumers would expect to benefit from the entrant’s presence — for approximately five 

years. 

In order to test this argument, I develop a formal model in which two entrants each 

decide whether or not to develop a substitute product in order to challenge an incumbent firm’s 

patent-protected monopoly in some market. After an entrant successfully develops a product, the 

incumbent can sue for patent infringement, and the firms can either litigate their case or settle for 

a royalty-free license that permits the entrant to sell its product after some delay. Even though I 

assume that litigation is costless, I show that a settlement between the incumbent and the entrant 

that develops its product first creates a non-negative surplus that they can divide. This surplus 

arises because their settlement discourages the trailing entrant’s product development, increasing 

the profits that the incumbent and the leading entrant can share. The incumbent and the entrant 

that develops a product first therefore strictly prefer settlement to litigation, even in the absence 

of direct litigation costs. In order to identify the effects of the firms’ settlements, I analyze 

consumer welfare and the entrants’ product development decisions both when the firms can settle 

their cases and when the firms always litigate any patent infringement cases. 

In the model, the relevant market is a natural duopoly, so at most one entrant completes 

its project. Under this assumption, I find that settlements for time off the patent generally leave 

consumers worse off than they would be if the firms litigated their cases. This conclusion does 

not change even if the terms of settlement are very favorable to the potential entrants, whose 

interests during settlement negotiations are to some degree aligned with consumers’ interests; 

both consumers and entrants prefer earlier entry, ceteris paribus. My formal assumption about 

settlement bargaining is that the incumbent captures none of the surplus from avoiding trial, so 

any entry occurs at the earliest possible date that is consistent with the incumbent being willing to 

settle rather than litigate. 
4

My analysis reveals two reasons that settlements can harm consumers’ interests. First, 

the time that consumers expect to benefit from a particular entrant represents a lower bound on 

the expected time that consumers would benefit from some entrant. For example, a particular 

entrant may have a fifty-fifty chance of winning an infringement case, but a settlement that 

enables the entrant to sell its product halfway through the remaining patent life could shortchange 

consumers, because another entrant may emerge if the first loses its infringement case. Given 

this possibility, consumers would have a greater than fifty-fifty chance of benefiting from some

entrant. I develop this argument more fully in the example in the next section. 

Second, the form of patent settlement that I analyze can undermine the entrants’ 

incentives to invent around the incumbent’s patent. If the entrant that completes its product 

development first always settles with the incumbent, a slower entrant would likely never have a 

chance to earn duopoly profits.4

 If the entrant that completes its product development first always 

litigates, meanwhile, a slower entrant would possibly have an opportunity to earn duopoly profits, 

because the first entrant may lose its patent infringement case. The prospect of settlement thus 

increases the relative importance to an entrant of being the first to develop a competing product 

and, therefore, discourages an entrant from undertaking a project that it believes will take a long 

time to complete. 

It would be wrong to conclude from the results that the settlement of intellectual property 

disputes generally harm consumer welfare. First, the analysis considers only one kind of 

settlement that parties to such a dispute could reach. Second, in order to expose the basic 

arguments more clearly, the analysis abstracts away from key factors, such as the private and 

social costs of litigation. Incorporating these costs into the model would tend to make settlement 

look more socially desirable. Of course, the analysis also abstracts away from some of the social 

 

4

 The first entrant and the incumbent could always guarantee that the later entrant did not receive duopoly 

profits by including in their settlement agreement a provision for the first entrant’s immediate entry if any 

other firm could enter. Then the second entrant would not earn duopoly profits even if it won an 

infringement case before the first entrant’s negotiated entry date. 
5

benefits of litigation. For example, litigating a patent infringement or invalidity case reveals 

valuable information about the true scope or even existence of the patent-holder’s property right. 

Incorporating such benefits into the model would tend to make litigation look more socially 

desirable. 

The formal analysis does, however, support two broad conclusions. First, the model 

highlights the importance of analyzing the effects of any patent settlement on the incentives of the 

relevant third parties before drawing any conclusions about the settlement’s effect on consumers’ 

interests. If an incumbent monopolist and the first entrant to challenge the incumbent’s 

monopoly craft an agreement that, intentionally or not, undermines other firms’ incentives to 

develop competing products, consumers may be worse off than they would be if the firms 

litigated their case. I develop this idea further in Schrag (2004), in which I examine the 

competitive effects of a patent dispute settlement in which the incumbent grants the entrant an 

immediate-entry, royalty-bearing license. 

Second, because the model reveals that patent settlements that license entry at a date that 

is consistent with the expected outcome of the trial are not necessarily beneficial to consumers, it 

suggests that other settlement terms that help parties reach agreement on a delayed entry license 

cannot be assumed to be ancillary to a pro-competitive outcome. If these other terms raise 

independent competition concerns, a settlement is even less likely to benefit consumers and 

should therefore be subject to even greater scrutiny. For example, suppose that two firms settled 

for a royalty-free delayed entry license, along with a side deal that transferred intellectual 

property from the entrant to the incumbent in exchange for cash. An outside observer might 

worry that the incumbent was tempted to overpay for the intellectual property in order to 

convince the entrant to accept a relatively late entry date.5

 The parties might argue that such a 

side deal was necessary in order to achieve any agreement at all, and that, furthermore, the 

 

5

 This was the FTC’s contention in its Schering case; see note 2, supra. 
6

negotiated entry date simply reflected the expected outcome of the trial that they avoided, 

meaning that the entrant would compete for the same amount of time, in expectation. For a 

variety of reasons, third parties may not be in a position to evaluate whether the negotiated entry 

date actually was consistent with the expected outcome of the case.6

 My findings suggest that, 

even if the negotiated entry date actually did reflect the expected outcome of the case, consumers 

might very well have been better off anyway if the parties had litigated. 

There is a small economic literature on the antitrust issues that patent settlements raise. 

Shapiro (2003) proposes that a settlement of an intellectual property dispute, including a 

settlement for a license that permits delayed entry by a potential entrant, should satisfy a simple 

rule to pass antitrust muster, namely that expected consumer surplus must be at least as large 

under the settlement as under continued litigation. In practice, such a standard would often be 

difficult to implement, because it would often involve a highly subjective analysis of the likely 

outcome of the parties’ litigation. Shapiro argues that there always exists a settlement that leaves 

both the parties and consumers better off than they would be with litigation, but he does not 

analyze the effect of patent settlements on third parties’ incentives to develop products.7

Meurer (1989) studies the effect of antitrust policy on patent settlements when the patent 

holder has private information about its patent’s validity and can make a take-it-or-leave-it offer 

to a competitor. In his model, antitrust policy falls on a continuum between what he terms a 

laissez-faire and a lump sum policy. A laissez-faire policy enables the two parties to split 

monopoly profits, while a lump-sum policy limits the parties to a split of the Cournot-Nash 

profits in any settlement they reach. He finds that antitrust policy has no effect on the probability 

 

6

 In such a situation, the defendants in the antitrust case would have a natural incentive to exaggerate the 

strength of the incumbent’s case in the underlying patent case, since that would tend to reduce their 

antitrust liability. See the discussion in O’Rourke and Brodley (2003). Evidence that could overcome this 

exaggeration may often be protected by attorney-client privilege. 

7

 Shapiro does, however, endorse the FTC’s concern about delayed entry patent settlements that include 

cash payments from the incumbent to the alleged infringer. See also Shapiro and Lemley (2004) and 

Hovenkamp et al. (2003). 
7

that the parties settle. In the equilibrium of his signaling model, a patent holder that holds a valid 

patent always refuses to settle, and a patent holder with an invalid patent must also refuse to settle 

with a high enough probability that the competitor is willing to litigate in the event that the patent 

holder refuses to settle. The competitor’s payoff from litigation is unaffected by antitrust policy, 

because if it loses its case it earns nothing, while it enters as a duopolist if it wins. But then the 

patent holder’s settlement behavior must also be unaffected by antitrust policy, in order to satisfy 

the equilibrium condition that the competitor is indifferent between settling and litigating, 

regardless of the antitrust policy. Meurer focuses only on the issue of patent invalidity, so he 

does not consider the effect of settlement on a potential competitor’s incentive to invent around 

the incumbent’s patent. 

In a related paper that examines potential entrants’ investment incentives, Choi (1998) 

analyzes the effects of litigation over a patent’s validity when there are multiple potential 

entrants. He shows that the information externalities associated with litigation can cause the 

entrants to play a waiting game, in which each entrant may delay their entry (and the ensuing 

patent litigation) in order to increase the chance that its rival goes first and bears the cost of 

testing the validity of the incumbent firm’s patent. He also shows that the patent holder may have 

an incentive to delay a patent suit against the first entrant to present itself as a potential infringer, 

since doing so eliminates the possibility that the second entrant could benefit from information 

revealed by the first entrant’s litigation. Choi does not consider the possibility that the entrants 

will settle their patent litigation. 

In the next section I present a simple example that illustrates the basic idea that underlies 

the formal model, which I introduce in section three. Section four concludes. 
8

2. An Example

Consider a market that will last for ten years, and assume that there is no discounting. 

One risk neutral incumbent is already selling in the market, and there are two risk neutral and 

identical potential entrants. The first entrant’s product is ready for immediate sale, but the second 

entrant’s product will not be available for two years, either because it requires additional 

development or because it must obtain regulatory approval. I assume that the second entrant’s 

incremental cost of bringing its product to market is sufficiently high that it finds entry as the 

third supplier to be unprofitable. If the first entrant successfully launches its product, therefore, 

the second entrant stops work on its product and does not enter. 

Each entrant’s product potentially infringes a patent that the incumbent holds. Suppose 

that each entrant has a fifty percent chance of prevailing in court if the incumbent sues for 

infringement, and suppose further that the entrants’ cases are independent. To simplify the 

example and expose the basic argument, I assume that both patent litigation and any settlement 

negotiations are instantaneous and costless. It follows from these assumptions that the incumbent 

will immediately sue for patent infringement if an entrant launches its product, and the parties 

will either settle their case or litigate. 

 Rather than imposing a particular structure to the settlement bargaining, I analyze 

how the expected outcome of the litigation influences the range of possible settlements that could 

arise. I assume that a settlement consists of an entry date and, in the case of the first entrant, a 

provision that it can enter the market in the event that the second entrant is able to sell its product. 

Such a provision would always serve the interests of both the incumbent and the first entrant, 

since it would discourage the second entrant from continuing its product development following a 

settlement between the incumbent and the first entrant. 
9

Under the model’s assumptions, the incumbent and the second entrant are indifferent 

between settling and litigating.8

 In the absence of either litigation costs or risk aversion, a 

settlement between the incumbent and the second entrant creates no surplus to divide, so the 

terms of any agreement would exactly reflect the expected outcome of their litigation. When the 

incumbent and the first entrant settle, however, they do create and therefore may divide a nonnegative surplus. The source of this surplus is the entry-deterring effect of the settlement on the 

second entrant’s investment. Define πE > 0 as the yearly profit that the entrant earns from selling 

its product. Define πM and πD as the incumbent’s yearly profit as a monopolist and a duopolist, 

respectively, and assume that πM > πD > 0. If the first entrant and the incumbent fail to settle their 

dispute before trial, then their payoffs are determined by the expected outcome of their litigation: 

First Entrant’s Litigation Payoff = LE = 0.5(10)πE = 5πE, 

 Incumbent’s Litigation Payoff = LI 

 = 0.5(10)πD + 0.5[0.5(10)πM + 0.5(2πM + 8πD)] 

 = 3πM + 7πD. 

The entrant’s payoff reflects the fact that it has a fifty percent chance of winning a 10- year 

duopoly and a fifty percent chance of winning nothing. The incumbent’s payoff reflects the fact 

that it has a fifty percent chance of prevailing in its litigation against the first incumbent, in which 

case it still faces the prospect of possible entry from the second incumbent. 

Given these litigation payoffs, it is clear that, irrespective of the exact nature of 

settlement bargaining, the incumbent will not agree to a settlement that enables the entrant to 

compete for more than seven years, and the first entrant will not agree to a settlement that allows 

it to compete for less than five years. Both parties strictly prefer a settlement that permits 

competition for between five and seven years over the alternative of litigating. The exact terms 

 

8

 This would not necessarily be true if the litigants could settle for an immediate entry, royalty bearing 

license. 
10

of any settlement in this range would presumably depend on the parties’ relative bargaining 

power. 

The example illustrates how, even in the absence of risk aversion or litigation costs, 

settlement can still be advantageous for the incumbent and the first entrant. By causing the 

second entrant to abandon its entry plans, the settlement between the incumbent and the first 

entrant increases the total profits that they can split. If the first entrant receives any of the surplus 

that the settlement creates, its entry date under settlement will be earlier than its expected entry 

date under litigation, possibly leading to the conclusion that the settlement benefits consumers. 

Such a conclusion may not be valid, as the following analysis of consumers’ interests illustrates. 

Were settlement between the incumbent and the entrants impossible, consumers would 

face a fifty percent chance of ten years of duopoly (the first entrant wins its infringement case), a 

twenty-five percent chance of ten years of monopoly (both entrants lose their cases), and a 

twenty-five percent chance of two years of monopoly followed by eight years of duopoly (the 

first entrant loses and the second entrant wins). Define CSn as the (time-invariant) yearly 

consumer surplus when n ∈ {1, 2} firms are selling in the market. Consumers’ expected surplus 

if the entrants always litigate their cases is: 

ECSlit = 0.5(10CS2) + 0.25(10CS1) + 0.25(2CS1 + 8CS2) = 3CS1 + 7CS2.

Consumers’ expected surplus under a settlement that permits the first entrant to compete for t* 

years is 

ECSsettle = (10 - t*)CS1 + t*CS2. 

Because CS2 > CS1, consumers strictly prefer settlement to litigation if and only if t* > 7, but the 

preceding analysis of the litigants’ incentives indicates that the incumbent would not be willing to 

accept such a settlement. If the incumbent has any bargaining power at all, i.e. if it captures any 

of the bargaining surplus, then under a settlement the first entrant would compete for less than 
11

seven years and consumers would then be strictly worse off if the entrants and the incumbent 

settle rather than litigate. 

The example illustrates how the settlement of patent litigation between the incumbent 

firm and an entrant can harm consumers’ interests, even if the settlement allows the entrant to 

enter the market sooner than the date that would reflect the strength of its infringement case. A 

simple rule of thumb that consumers will be indifferent between litigation and a settlement that 

reflects the expected outcome of the trial fails to recognize that, if the settling entrant were to lose 

its infringement case, another entrant may replace it.9

 From the perspective of consumers, the 

probability that the first entrant prevails in its infringement case is a lower bound on the 

probability that they will benefit from some entrant. If the incumbent and the first entrant can 

craft a settlement that discourages subsequent entrants from developing and offering a product, 

consumers may strongly prefer litigation to settlement. 

The first entrant clearly benefits when it receives a share of the surplus created by 

deterring the second entrant’s possible entry. This increase in the first entrant’s profits may 

strengthen its ex ante incentive to develop a product and challenge the incumbent’s monopoly. 

On the other hand, the second entrant is clearly hurt by the settlement between the incumbent and 

the first entrant, and the decrease in the second entrant’s profits may weaken the early incentive 

to develop a product. The net effect of settlement on the entrants’ initial incentives to develop 

products (before it is known which will be first and which will be second) is not immediately 

obvious. I explore this issue in more detail in the formal model in the next section. 

 

 

9

 Willig and Bigelow (2002, p. 2) seem to suggest just such a rule of thumb. Their paper does not address 

the effect of patent settlements on third party investment behavior. 
12

3. A Model of Patent Litigation Settlement

 Consider a market in which an incumbent firm is currently selling a product. Because it 

holds a patent that claims its product, the incumbent initially faces no competition. I normalize 

the patent life to unity and assume for simplicity that there is no discounting.10 I also assume that 

free entry immediately drives profits to zero after the patent expires. Before that occurs, two 

potential entrants can each attempt to invent around the incumbent’s patent and enter early. I 

index the entrants by i ∈ {a, b}. In order to model the entrants’ product development decisions, I 

assume that each entrant can begin a development project at time t = 0. To simplify the model, I 

assume that this is the only time at which an entrant can start a project.11 Associated with entrant 

i’s project is a parameter zi that represents the amount of time the entrant would need to complete 

the project. I assume that za and zb are random variables that are independently and identically 

distributed on the support [0, ∞) according to the continuous probability distribution function f(⋅). 

Entrant i knows how long its own project will take, i.e. entrant i observes zi at time 0, but neither 

entrant can observe how long the other entrant’s project will take. While each entrant knows 

when its rival has completed its project, neither entrant can observe whether its rival is working 

on an unfinished project. Each entrant must therefore decide whether to continue investing in its 

project without knowing what its rival is doing. If an entrant decides to pursue a project, it must 

pay a flow cost c > 0 until it either completes or abandons the project. 

To streamline the exposition that follows, I often refer to the “first entrant” and the 

“second entrant.” By definition, the first entrant’s project has the earlier completion date, and the 

second entrant’s project has the later completion date. Of course, the identities of the first and 

 

10 Incorporating discounting into the model is straightforward, but it complicates the presentation without 

adding additional insights. 

11 Relaxing this assumption would enable an entrant to choose a more complicated investment strategy, 

since it could defer a decision about whether to start a project until after it knew whether its rival would 

quickly complete its project. I conjecture that the main qualitative conclusions of the paper would continue 

to hold even if this sort of behavior were possible. 
13

second entrant are not known ex ante; either entrant a or entrant b could have the fastest project. 

The distributions of the first and second entrants’ project completion dates are the well-known 

distributions of the first and second order statistics. 

The firms’ flow profits at any point in time depend on the number of firms that are in the 

market. If there are n ∈ {1, 2, ...} firms in the market, the incumbent earns πI(n), and any entrant 

that is selling earns πE(n). It is reasonable to assume that πx(n) > πx(n + 1), x ∈ {I, E}; additional 

entry reduces the firms’ flow profits. I initially simplify the model by assuming that πE(2) > πE(3) 

= 0. This assumption means that the second entrant will abandon its product development if the 

first entrant to complete a project successfully enters. The second entrant has no incentive to 

incur development costs if it anticipates earning no profit from selling its product.12 

After an entrant completes a project, the incumbent can sue for patent infringement, in 

which case the parties either litigate the case or settle. Each entrant wins its case with probability 

α > 0, and the two entrants’ cases are independent. As in the example, I assume that both 

litigation and settlement are instantaneous and costless, in which case the incumbent always sues 

when an entrant completes its project. While strong, this assumption permits me to focus on the 

incumbent and first entrant’s ability to extract rents from the second entrant. In the conclusion I 

discuss the potential effect of relaxing this assumption. A settlement of any infringement 

litigation between the incumbent and an entrant consists of an entry date and, in the case of the 

first entrant to complete its project, a provision that it can enter the market in the event that the 

second entrant is able to sell its product. As explained in the previous section, such a provision 

discourages the remaining entrant from developing a product once one of the entrants has finished 

its product and settled with the incumbent, so such a provision would always serve the joint 

interests of the incumbent and the first entrant. 

 

12 The assumption that πE(2) > πE(3) = 0 is consistent with a model in which the entrants’ products are 

perfect substitutes for each other, and they engage in Bertrand price competition. In such a model, neither 

entrant would earn a positive flow profit if they both entered. 
14

In order to establish a benchmark, I first analyze the entrants’ product development 

decisions when the incumbent and the entrants are not permitted to settle their legal disputes and 

instead must litigate. The timing of the model is as follows. First, each entrant i chooses a 

“cutoff” project, say  ̄zi, i ∈ {a, b}. Next, each entrant learns the amount of time it would take to 

complete its project, i.e. entrant i observes the realization of zi. Entrant i then pursues any project 

with a completion date zi ≤  ̄zi until either it completes the project or its rival prevails in patent 

infringement litigation with the incumbent, whichever is earlier. A pure strategy Nash 

equilibrium is a pair of cutoff projects, say ( ̄za

*

,  ̄zb

*

), such that each entrant’s choice of a cutoff 

project maximizes its expected profits given the other entrant’s strategy. In the following 

Proposition, I describe the unique pure strategy Nash equilibrium of this version of the model.13

PROPOSITION 1: Suppose that the entrants and the incumbent are not permitted to settle their 

legal disputes and instead must litigate. Then the unique pure strategy Nash equilibrium 

of the model is a pair of cutoff projects ( ̄za

*

 =  ̄zl,  ̄zb

*

 =  ̄zl), where  ̄zl satisfies: 

(1) ∫ =α−−α−α−π l z

E l l dxxFczFz

0

0))(1())(1()1)(2( .

In the Nash equilibrium of the model without settlement, each entrant pursues any project 

that yields non-negative expected profits. Equation (1) in the proposition is the condition that 

defines the equilibrium cutoff project  ̄zl. In the equilibrium, the entrants expect to earn nonnegative profits only from projects with completion times that are less than or equal to  ̄zl. I notice 

that, in this version of the model, there is some value to being the second entrant to complete its 

project, even though πE(3) = 0. An entrant does not necessarily need to complete its project first 

in order to profitably enter, since the entrant that completes its project first may lose its 

infringement case. 

 

13 The proofs of Proposition 1 and all other formal results are located in the Appendix. 
15

Using the entrants’ Nash equilibrium strategies, it is straightforward to calculate expected 

consumer surplus when the incumbent and the entrants cannot settle their legal disputes. Define 

CSn as consumer surplus when there are n ∈ {1, 2, ...} firms selling in the market. It is 

reasonable to assume that CS(n + 1) > CSn, and I normalize CS1 to be equal to zero. Then expected 

consumer surplus in the Nash equilibrium given in Proposition 1, say ECSl, is: 

 (2) ∫ ∫ ⎥

⎦

⎤ ⎢

⎣

⎡ − − = α−α+−α− l l z z

x l dxdyy xF

yf xxFxfCSECS

0

2 )1()(1

)( )1()1())(1)((2 . 

In expression (2), the integral represents the expected amount of time that consumers will benefit 

from an entrant’s presence. The bracketed term in the integrand is proportional to the expected 

surplus that consumers receive when the first entrant to complete its project does so at time x ≤  ̄zl. 

This term reflects both the α probability that the first entrant wins its infringement case, in which 

case consumers benefit from the entrant for 1 – x periods, and the 1 - α probability that the first 

entrant loses in court, in which case consumers benefit from entry only if the second entrant also 

found it worthwhile to start a project. The expectation is taken with respect to the first entrant’s 

completion date, which is distributed according to the probability density function 2f(x)(1 – F(x)). 

Entry benefits consumers only if at least one of the entrants initially has a project that it could 

complete before  ̄zl. If not, neither entrant starts a project, and there is no entry until the 

incumbent’s patent expires. 

I now suppose that the incumbent and the entrants can settle their legal disputes before 

trial. Permitting settlement bargaining between the firms introduces a degree of indeterminacy 

into the model, since it is typically not possible to predict the exact division of the surplus that the 

firms create through an agreement, at least without making somewhat hard-to-justify assumptions 

about the nature of their bargaining. In this model, any settlement bargaining between the 

incumbent and the second entrant is an exception to this general rule, since the lack of litigation 

costs and risk aversion means that a settlement between them creates no surplus to divide. The 

incumbent and the second entrant are therefore both indifferent between litigating and settling for 
16

an entry date at time t2* = 1 – α + αz2, where z2 is the date on which the second entrant completes 

its project.14

A settlement between the first entrant and the incumbent does potentially create surplus 

that the litigants can divide, and the division of this surplus affects consumer welfare. The 

surplus arises in this case because a settlement between the first entrant and the incumbent 

induces the second entrant to abandon any project it has begun. I begin by identifying the range 

of possible settlements between the first entrant and the incumbent. To do this, it is necessary to 

determine the firms’ threat points in their settlement bargaining, which depend on their expected 

payoffs from litigation. Neither the incumbent nor the first entrant would accept a settlement that 

yielded lower expected profits than it would receive from litigation. 

If the first entrant completes its project at time z1, its expected payoff from litigation is LE

= απE(2)(1 – z1). This payoff reflects the fact that the entrant wins in court with probability α, in 

which case it earns duopoly profits for 1 – z1 periods. 

The incumbent’s payoff from going to court against the first entrant depends on whether 

it anticipates that the second entrant might continue developing a project if the first entrant loses 

in court. If the incumbent believes that the second entrant will not pursue its project, regardless 

of the outcome of the first entrant’s litigation, then the incumbent’s payoff from litigation is LI = 

(απI(2) + (1 - α)πI(1))(1 – z1). It is easy to verify that, in this situation, settlement between the 

first entrant and the second entrant creates no surplus, and so any settlement would permit entry 

by the first entrant at time t1* = 1 - α + αz1. The more interesting case arises when the incumbent 

believes that, if the first entrant loses in court, the second entrant will continue developing any 

project that it can complete before some cutoff date, say  ̄z2 > z1. Then the incumbent’s expected 

payoff from litigation against the first entrant is: 

 

14 This settlement reflects the fact that the second entrant has a 1 - α chance of losing in court, in which 

case it can enter after the patent expires at time 1, and an α chance of winning in court, in which case it can 

enter immediately at time z2.
17

LI =

2

1

1

2

11 1

1 1

(1 ) (2)

(1 ( )) ( ) (1 ) (1 ) (1) ( (( ) (1) (1 ) (2)) (1 )(1 ) (1) (1 ( )) (1 ( ))

I

z

I II I z

z

F z f x z x z x z dx

Fz Fz

α π

α π α π π απ

− +

⎡ − ⎤

− −+ −+ ⎢ − + − − ⎥ ⎣ − − ⎦ ∫

= ⎥

⎦

⎤ ⎢

⎣

⎡

π−π−α − −π−α−+π−α ∫

2

1

))2()1()(1(( ))(1(

)( )1()1()1()2()1(

1

1 1

z

z I I x II dx

zF

xf

z z . 

A settlement between the incumbent and the first entrant specifies a date, say t1* ∈ [z1, 

1], on which the entrant can first sell its product. The entrant’s payoff from a settlement is 

SE = (1 – t1*)πE(2), 

and the incumbent’s payoff is: 

SI = (1 – t1*)πI(2) + (t1* - z1)πI(1). 

Using the two parties’ payoffs from litigation and settlement, it is straightforward to 

determine the range of possible settlements that the incumbent and the entrant could reach.15 If, 

as is the case in the Nash equilibrium of the model, both entrants pursue any project that can be 

completed before a common cutoff, say  ̄zs, then under a settlement the first entrant to complete its 

project, say at time z1, will enter the market at a time t1* ∈ [1 - α + αz1 - ∫ −

− α−α s z

z

dx

zF

xxf

1 )(1

)1)(( )1( , 

1 - α + αz1].

Because my goal is to identify the potentially negative effects of patent settlements on 

consumers, I assume that the incumbent and the first entrant that completes its project reach the 

settlement that is most favorable to consumers, subject to the constraint that each firm (at least 

weakly) prefers the settlement to litigation. If consumers prefer litigation to such a settlement, 

then, a fortiori, they prefer litigation to settlements that are less favorable to their interests. From 

the perspective of consumers, the best possible settlement involves the earliest possible entry by 

 

15 To find the latest possible entry date that the entrant would accept, set SE = LE and solve for t1*. To find 

the earliest possible entry date that the incumbent would accept, set SI = LI and again solve for t1*. 
18

one of the two entrants and leaves the incumbent just indifferent between litigating and settling. 

There are two reasons for consumers’ preference for early entry. First, when entry occurs sooner, 

consumers receive the incremental consumer surplus that an additional competitor produces for a 

longer period of time. Second, earlier entry dates enable the entrants to earn greater expected 

profits, increasing the entrants’ incentives to challenge the incumbent’s monopoly.16

Given the assumption on settlement bargaining, the Nash equilibrium of the model can 

again be described by a pair of cutoff projects, say (z ̄a**, z ̄b**), such that each entrant’s choice of 

a cutoff project maximizes its expected profits given the other entrant’s strategy. In the following 

Proposition, I describe the unique pure strategy Nash equilibrium of this version of the model. 

PROPOSITION 2: Suppose that the entrants and the incumbent always settle on the most 

favorable possible terms for consumers. Then the unique pure strategy Nash equilibrium 

of the model is a pair of cutoff projects (z ̄a** =  ̄zs, z ̄b** =  ̄zs), where  ̄zs satisfies: 

(3) ∫ =−−−α−π s z

E s s dxxFczFz

0

0))(1())(1()1)(2( .

As in the version of the model without settlement, each entrant pursues any project that 

yields non-negative expected profits, i.e. any project with a completion time that is less than or 

equal to  ̄zs. A key difference between the two versions of the model, however, is that, with 

settlement, there is no value to being the second entrant to complete its project. Because the first 

entrant and the incumbent always settle on terms that eventually allow the first entrant to sell its 

product, the second entrant always stops work on its project after the first entrant settles with the 

incumbent. 

 

16 This discussion reflects consumers’ interests with respect to entry by the two hypothesized entrants only. 

It specifically sets aside consumers’ interest with respect to providing the incumbent with an incentive to 

develop its patented good in the first place. 
19

Using the entrants’ Nash equilibrium strategies, it is straightforward to calculate expected 

consumer surplus when the incumbent and the entrants settle their legal disputes on the terms that 

are most favorable to consumers. Expected consumer surplus, say ECSs, is: 

 (4) ∫ ∫ ⎥

⎦

⎤ ⎢

⎣

⎡ − − = α−α+−α− s s z z

x s dxdyy xF

yf xxFxfCSECS

0

2 )1( )(1

)( )1()1())(1)((2 .

In expression (4), the integral represents the expected amount of time that consumers will 

benefit from an entrant. If an entrant completes its project at a time x ≤  ̄zs, the earliest entry date 

that the incumbent will accept is t*(x) = 1 - α + αx - ∫ −

− α−α s z

x

dy xF

yyf

)(1

)1)(( )1( , so under the 

assumption about bargaining, consumers benefit from the entrant for 1 – t*(x) periods. I notice 

that, except for the entrants’ cutoff project ( ̄zs rather than  ̄zl), the expression for expected 

consumer surplus given in (4) is identical to the expression for expected consumer surplus when 

the firms always litigate, given in (2). 

The following lemma helps to address the issue of how settlement affects consumers. It 

establishes that the entrants are less likely to start developing a product when settlement is 

possible, compared to when they always litigate their cases. 

LEMMA 1: Each entrant is less likely to start a project when settlement is possible, compared to 

when they must litigate their cases, i.e.  ̄zs ≤  ̄zl. 

When settlement is not possible, an entrant need not be the first to finish its project in order to 

enter, even though it would never enter as a triopolist. The firm that is second to finish its project 

may enter the market because the firm that is first to finish may lose its infringement case. When 

the incumbent and the first entrant can settle their infringement case, on the other hand, there is 

no value to being the second entrant, because the first entrant will always settle and (eventually) 

enter the market. When settlement is possible, it is not profitable to start a project that will take a 

relatively long time to finish, because the odds of being the first to finish are relatively low. 
20

Obviously, this result depends to some extent on the assumption that litigation costs are zero. If 

litigation costs are significant and settlement is not possible, an entrant may have little incentive 

to try to invent around the incumbent’s patent. But the maintained assumption that the entrant 

captures the entire surplus under settlement bargaining is extreme as well, and it serves to 

increase the incentive to invent around the incumbent’s patent when settlement is possible. A 

more realistic division of the bargaining surplus between the incumbent and the entrant would 

further depress the entrants’ incentives to invest when settlement is possible. 

The following proposition contains the main result. 

PROPOSITION 3: Expected consumer surplus is lower when the incumbent and the entrants can 

settle their patent infringement cases, compared to when they must litigate, i.e. ECSs < 

ECSl. 

The proposition establishes that, even when settlements between the incumbent and the entrants 

are on terms that are most favorable to consumers, consumers are still better off if the firms 

litigate their cases rather than settle. This result stems from the fact that, in this model, the 

entrants are less likely to develop a competing product and challenge the incumbent’s monopoly 

when they can settle an infringement case. Consumers would be even worse off under a 

settlement if the incumbent and the entrants agreed to terms that enabled the incumbent to capture 

part of the surplus that a settlement with the first entrant creates.

4. Discussion and Conclusions 

My analysis employs several simplifying assumptions. Because they may not always be 

satisfied, I conclude by discussing how my conclusions might depend on some of them. The 

assumption that litigation is costless is clearly not realistic. Litigation imposes direct costs on the 

parties (e.g. attorney fees, the opportunity cost of time spent on case preparation, etc.), and, if the 
21

parties are risk averse, the uncertainty of the trial’s outcome also imposes a cost. There are two 

ways that such litigation costs could influence the analysis. First, they could affect the terms of 

any settlement. If, for example, incumbents typically bear far greater litigation costs than 

entrants, including litigation costs in the analysis could possibly swing the terms of settlement 

more in the entrants’ (and consumers’) favor, offsetting the conclusion that, at least in the natural 

duopoly model, consumers are harmed by settlements. 

Second, to the extent that litigation costs are avoided with settlement and not avoided if 

the parties litigate their cases, ignoring them tends to bias the comparison of a settlement regime 

and a litigation regime in favor of the litigation regime, unless the incumbent captures the lion’s 

share of the surplus created by settlement. The reason is that litigation costs increase a potential 

entrant’s cost of bringing a product to market, reducing the incentive to try to invent around the 

incumbent’s patent. Whether this effect is great enough to reverse the conclusions given in the 

paper depends on how significant litigation costs are relative to the expected profits that an 

entrant expects to earn. In situations where these costs are relatively small, or if the entrant 

receives a sufficiently small fraction of the surplus created by bargaining, the conclusion that 

consumers prefer for the firms to litigate will still hold. 

My model also reflects an assumption that the two entrants’ cases are statistically 

independent. There may be circumstances where it would be more appropriate to assume that the 

entrants’ cases are correlated. For example, the entrants may have adopted similar strategies to 

invent around the incumbent’s patent.17 Suppose that the entrants’ cases were perfectly 

correlated. Then settlement between the incumbent and the first entrant deprives the second 

entrant of information about its case. Because the second entrant would enter at best as a 

triopolist, it might not continue its project without knowing whether it would win. If a settlement 

between the first entrant and the incumbent deters entry that would follow a win by the first 

 

17 If the entrants alleged that the incumbent’s patent were invalid, rather than merely not infringed by their 

products, then their cases would be correlated. 
22

entrant in court, both benefit from the external effect of settlement. On the other hand, if 

settlement is not possible, the entrants’ cases are correlated, and litigation costs are significant, 

both entrants may wish to delay their entry and litigation in order to free ride on the information 

that its rival’s litigation would reveal. In this case the entrants’ rivalry could lead to a waiting 

game, as in Choi (1999), and settlement could speed entry. This sort of effect would be 

particularly pronounced if the entrants litigated the validity of the incumbent’s patent, rather than 

merely asserting that their products did not infringe. 

My model also reflects an assumption that the entrants’ product development options are 

exogenous. In some situations, they may be able to choose how to try to invent around the 

incumbent’s patent. For instance, an entrant may have some control over how “close” in the 

relevant characteristic space to develop a product.18 By developing a “closer” product, the entrant 

can presumably complete its work faster and at lower cost, but it also presumably faces a higher 

probability of being found to infringe the incumbent’s patent. The entrants may approach this 

tradeoff differently depending on whether they can settle any patent infringement suits or instead 

must litigate. If the ability to settle their legal disputes encourages entrants to develop substitute 

products faster and at lower cost, then consumers may prefer settlement to litigation. 

 Finally, I observe that it would be inappropriate to interpret the results of the formal 

model as implying that settlements of patent disputes routinely harm consumer interests. Rather, 

the analysis indicates that simple rules of thumb about what kinds of settlements will harm or 

promote consumer interests may sometimes, or even often, be misleading. Of course, a 

conceptually simple rule of thumb, e.g. that a patent dispute settlement should reflect the expect 

outcome of the litigation in question, may be difficult to implement in practice because of the 

unavailability of the necessary evidence. The analysis in this paper shows that such simple rules 

may also be wrong. 

 

18 For an example of a model in which entrants must choose where to locate in a product space, see 

Waterson (1990). 
23

This paper represents at best a first step in the analysis of the antitrust issues that 

surround the settlement of patent disputes, but it is a first step on an important road. Because 

settlement is such a key part of any litigation, antitrust policy towards patent settlements has a 

significant effect on the nature of the property right that a patent represents. The development of 

a sound basis for this policy is of great importance. 
24

APPENDIX 

Proof of Proposition 1: I first notice that ∫ α−−α−α−π= z

E zH dxxFczFz

0

))(1())(1()1)(2()(

is a continuous, monotone decreasing function of z, and H(0) > 0 > H(1). Therefore, there exists 

a unique  ̄zl satisfying H( ̄zl) = 0. Suppose that entrant i believes that j is choosing a cutoff z ̄. l

Entrant i pursues any project that yields non-negative profit, and its net profit from pursuing a 

project with z ≤  ̄zl is H(z); the first term in H(ÿ) reflects the fact that the entrant earns duopoly 

profits for (1 – z) periods if both it wins its patent litigation and the other entrant has not already 

completed its project and prevailed in its patent litigation, and the second term reflects the 

entrant’s expected cost of pursuing the project, adjusted to reflect the possibility that its rival will 

finish first. But then entrant i’s best reply to entrant j choosing a cutoff  ̄zl is to choose the same 

cutoff itself, and there is a unique symmetric pure strategy Nash Equilibrium in which both 

entrants choose  ̄zl. It remains to show that there does not exist an asymmetric pure strategy Nash 

Equilibrium. Assume without loss of generality that  ̄z1 <  ̄z2. Because entrant 1’s payoff from a 

project with z ≤  ̄z2 is H(z), it follows immediately that  ̄z1 =  ̄zl. But entrant 2’s payoff from a 

project with z >  ̄zl is ∫ α−−α−α−π z

E l dxxFczFz

0

))(1())(1()1)(2( < H( ̄zl) = 0, so it is not optimal for 

entrant 2 to choose a cutoff  ̄z2 >  ̄zl, and there exists no asymmetric pure strategy Nash 

Equilibrium. QED 

Proof of Proposition 2: Suppose that entrant i believes that entrant j is choosing a cutoff 

 ̄zs. Then arguments identical to those in the proof of Proposition 1 establish that  ̄zs is also entrant 

i’s best reply, substituting ∫ −−−α−π= z

E zG dxxFczFz

0

))(1())(1()1)(2()( for H(z) and recognizing 

that the settlement that the incumbent and first entrant reach at time z1 =  ̄zs is for the first entrant 

to enter at 1 - α + α ̄zs. It remains to show that there does not exist an asymmetric pure strategy 

Nash equilibrium. Assume without loss of generality that  ̄za <  ̄zb. In an asymmetric equilibrium, 

the settlement between the incumbent and the entrant will depend on the identity of the entrant. 

Under the assumption that the entrant captures all of the surplus from bargaining, the incumbent’s 

settlement with entrant a permits entry at time ta*(x) = 1 - α + αza - ∫ −

− α−α b

a

z

z

dy xF

yyf

)(1

)1)(( )1( , za ≤

 ̄za. The incumbent’s settlement with entrant b permits entry at time: 

⎪

⎩

⎪

⎨

⎧

>α+α−

≤ −

− α−α−α+α− = ∫

abb

z

z ab

b

b

bb

zzz

zzdy zF

yyf

z

zt

a

b

,1

, )(1

)1)(( 1 )1( )(* . 

For  ̄za to be a best reply for entrant a, its payoff from a project with a completion date 

exactly equal to  ̄za must be equal to zero, i.e. 

(A1) 0))(1())(1)( )(1

)1)(( )1()1()(2(

0

=−−− −

− α−α+−απ ∫ ∫ b a

a

z z

z a

a

E a dxxFczFdx

zF

xxf

z . 

But entrant b’s payoff from pursuing any project with a completion date z >  ̄za is: 

 (A2) 0 (2) (1 )(1 ( )) ( (1 ( )) (1 ( ))( )) az

E a aa π α − − − − +− − z F z c F x dx F z z z ∫

which is strictly less than entrant a’s payoff in (A1) and is therefore negative. It immediately 

follows that entrant b does not wish to choose a cutoff  ̄zb >  ̄za, and there exists no asymmetric 

pure strategy Nash equilibrium. QED 
25

Proof of Lemma 1: Define ∫ −−−α−π= z

E zmI dxxmFczmFz

0

))(1())(1()1)(2(),( . I(m,z) ≡ 0 

implicitly defines a function z(m) on the domain [0, 1]. I notice that z(α) =  ̄zl, and z(1) =  ̄zs. 

Because α < 1, it is sufficient to show that z′ < 0. Using the Implicit Function Theorem, I have: 

 (A3) ))(1)()2((

)()1)(2()(

/

/ 0

zmFc

zF dxxFcz

zI

mI

z

E

z

E

−+απ

+−απ−

= ∂∂

∂∂− ′ = ∫ . 

Because the denominator in (A3) is greater than zero on the relevant domain, z′ < 0 if and only if 

0)()1)(2()(

0

+−απ− < ∫

z

E zF dxxFcz . Because F(x) < F(z) for x ≤ z, it is sufficient to show that 

απE(2)(1 – z) > cz. Because I(m,z) ≡ 0, it follows that ∫ > −

− =−απ z

E czdx

zmF

xmF

cz

0 )(1

)(1 )1)(2( , which 

establishes the result. QED 

Proof of Proposition 3: Define 

∫ ∫ ⎥

⎦

⎤ ⎢

⎣

⎡ − − = α−α+−α− z z

x

dxdyy xF

yf xxFxfCSzECS

0

2 )1( )(1

)( )1()1())(1)((2)( . 

Simple differentiation establishes that dECS/dz > 0, and the result follows immediately from the 

Lemma, which establishes that  ̄zs ≤  ̄zl. QED 
26

REFERENCES 

Choi, Jay Pil (1998). “Patent Litigation as an Information-Transmission Mechanism,” American 

Economic Review, 88: 1249 – 1263. 

Hovenkamp, Herbert et al. (2003). “Anticompetitive Settlement of Intellectual Property 

Disputes,” Minnesota Law Review, 87:1719. 

Meurer, Michael J. (1989). “The Settlement of Patent Litigation,” RAND Journal of Economics, 

20: 77 – 91. 

O’Rourke, Maureen and Joseph Brodley (2003). “Antitrust Implications of Patent Settlements: 

An Incentives Modifying Approach,” Minnesota Law Review, 87: 101. 

Schrag, Joel (2004). “An Antitrust Gordian Knot: Analyzing the Competitive Effects of Patent 

Settlements,” unpublished manuscript. 

Shapiro, Carl (2003). “Antitrust Limits to Patent Settlements,” RAND Journal of Economics, 

34:391. 

Shapiro, Carl and Mark Lemley (2005). “Probabilistic Patents,” Journal of Economic 

Perspectives, 19: 75 - 98. 

Waterson, Michael (1990), “The Economics of Product Patents,” American Economic Review, 

80:860 – 869.