Hitotsubashi University
Institute of Innovation Research

Reverse payments and generic entry competition
Jiangyun(Yunyun) Wan

IIR Working Paper WP#16-09

Aug.

2016

Institute of Innovation Research
Hitotsubashi University
Tokyo, Japan
http://www.iir.hit-u.ac.jp

Reverse payments and generic entry competition

Yunyun Wan1
This revision: August 16, 2016

Abstract
In the United States, brand-name drug manufacturers often pay generic companies to delay marketingof their generic products. In this paper we develop an analytical framework to examine the implicationsof banning reverse payment settlements. We first find that reverse payment settlements occur whengeneric firms face relatively high entry cost but do not when entry costs are sufficiently low. We next
show cases in which reverse payment settlements are harmful to brands. We also consider thecounterfactual case when 180-day marketing exclusivity rights are removed from Hatch-Waxman andfind that the absence of marketing exclusivity rights encourages brands to proceed with reverse
payment settlements.
Keywords: reverse payment settlements, generic entry competition, Hatch-Waxman, marketingexclusivity
JEL Classification Codes: I18, K23, L13

Institute of Innovation Research, Hitotsubashi University University, Kunitachi, Tokyo, Japan.
Email address: jiangyun.wan@gmail.com

1

Institute of Innovation Research, Hitotsubashi University, Japan1. Introduction
The Hatch-Waxman Act was enacted in 1984 to promote generic entry competition with aneye to slowing down the rising costs of medicines in the United States. To encourage generic entry,
HW requires that generic drug manufacturers demonstrate only the bioequivalence of their genericproducts with the original brands, and also rewards the generic firm that successfully challenges thepatent pertaining to the brand with the 180-day period of marketing exclusivity, during which noother generics are allowed to compete in the market.1
Brand-name manufacturers have responded to such entry-promoting measures by making
arrangements for generic challengers to delay entry, usually in exchange for payments. Two
features of Hatch-Waxman helps brands maintain monopolies. One is the fact when a genericchallenges the brand’s patent, the latter has the option of filing an infringement suit, which results in
an automatic 30 month stay of FDA approval, prolonging the brand’s monopoly. However, this isroughly how long a court takes before announcing its finding as to the validity of the brand’s patent.
Thus, as long as the FDA maintains the policy of not approving generics while they are litigated,removing this automatic stay has little effect on the monopoly. Thus, in our study we focus on thesecond feature, which is the 180-day marketing exclusivity right granted to the first challenger ofthe brand’s patent. Before 2003, the brand and the generic could use this right to keep other generics
from entering for additional 180 days to further prolong the brand’s monopoly. The 2003
Amendments to Hatch-Waxman (so called the Medicare bill) addressed this abuse by making it arequirement that the marketing exclusivity right be forfeited if the generic fails to market the drug inquestion within 75 days since the granting of the exclusivity right.
The marketing exclusivity however is a rather controversial feature of Hatch-Waxman as it
has both the pro-competitive (encourages entry competition among generics) and the anticompetitive (only one generic is allowed to market for the exclusivity period) effect so that its full
effect on consumer welfare is not clear without further analysis. In this paper, we therefore explore

1

See Guidance for Industry: 180-Day Generic Drug Exclusivity Under the Hatch-Waxman Amendments to the Federal
Food, Drug, and Cosmetic Act.

2
the implications of removing marketing exclusivity rights on incentives for brands to propose
reverse payment settlements with generics.
It is time to outline our model. It is a multi-period model with one brand (incumbent) andtwo potential entrants (generics). The incumbent is an innovation drug company that produces thebranded drug with the patent. Two entrants are generic drug manufacturers that must win marketing
approval before entering the market. To make the multi-period model analytically tractable, some
simplifying assumptions are made. One such assumption is that the brand’s patent expires at the endof period 3. This is a simple way to capture the fact that generic entry usually occurs towards theend of the branded drug’s patent life. One explanation is that “data exclusivity” prohibits genericfirms to use the innovation drug’s test data to prove the safety and efficacy of the generic drugs.2
Since preparing own test data is extremely costly, generic firms wait till data exclusivity expires tosubmit applications for marketing approval.
If generic firms challenge the patent, they are likely to be embroiled in patent infringement
litigation. In fact, patent infringement litigation is a key ingredient of our analysis. We highlight two
features of litigation. First, litigation is stochastic. This is much emphasized in the economic andlegal studies literature. For example, as Lemley and Shapiro (2005) put it, “When the patent holder
asserts the patent against an alleged infringer, the patent holder is throwing the dice. If the patenthas been found invalid, the property right has been evaporated” (p. 75). To model this feature of
litigation, we follow Choi (1998) and assume that with exogenous probability the court finds thepatent valid.
The other feature of litigation we highlight is its length. Lengthy litigation is a fact of lifeand especially pertinent to the pharmaceutical industry. Since FDA does not approve generic drugs
while infringement is disputed, the branded drug manufacturer has the incentive to take thechallenger to court to strategically delay its entry. To model the time-consuming nature of litigation
2

Data exclusivity refers to protection of the clinical test data of a new drug submitted to FDA. It prevents generic drug
manufactures from relying on this data in their own applications. Data exclusivity is granted for 5 years for new chemical
entities but in cases can be extended for three additional years. For more details, see
http://www.fda.gov/Drugs/DevelopmentApprovalProcess/SmallBusinessAssistance/ucm069962.htm.

3
we assume that a court takes one period to deliver its verdict. Thus, the incumbent can delay
generic entry for one period by filing infringement suit against a patent challenger. If theincumbent’s patent is found invalid, generic entry is approved. Otherwise, generic entry occurs after
patent expiration.3
Lastly, we assume that marketing exclusivity lasts for one period, to keep things simple. In
reality, litigation lasts much longer than 180 days during which entry by other generics is checked.4
Thus, with this assumption we may appear to be overstating the value of marketing exclusivity in
our analysis. However, this overstatement is balanced, at least in part, by the fact that, contrary to
our symmetry assumption, the first generic entrant in reality reaps greater profits relative to later
entrants due to the presence of “substantial switching costs in pharmaceutical markets” (Crawford
and Shum 2005).
In such a model environment we first present a model in which reverse payment
settlements are ruled out. We then allow reverse payment settlements. A comparison of the resultsfrom these models gives us insight as to when reverse payment settlements are arranged and what
their implications are on competition and social welfare. We next consider the counterfactual
scenario in which marketing exclusivity is removed from hatch-Waxman provisions.
Our main findings are as follows. With marketing exclusivity, equilibria with reverse
payment settlements occur when the generic entry costs are in the intermediate range. If the entry
costs are too low there are no equilibria with reverse payment settlements because a forfeiture of themarketing exclusivity induces a second generic challenge, destroying the monopolistic equilibrium.
If the entry costs are too high, of course, there is no generic entry before patent expiration. Even insuch cases, there is a curious possibility that the prospect of a reverse payment settlement induces ageneric to challenge the patent although generics have no incentive to do so when reverse payments
are banned. In such cases brands and generics are better off when reverse payments are banned. As
for the welfare effect, we find that banning reverse payment settlements improves social welfare
3
4

We assume as in Choi (1998) that, when declared valid, the patent remains valid for the remainder of its life.
An automatic 30-month stay will be given if infringement suit is filed against a patent challenger.

4
when the entry costs are in the intermediate range but otherwise has no effect on welfare. Finally,
we show that removing marketing exclusivity rights results in more cases of reverse payment
settlements.
The remainder of this paper is organized as follows. Section 2 describes the model
environment. Section 3 presents the model without the possibility of reverse payment settlements,
while section 4 examines the case with reverse payment settlements. Section 5 considers thecounterfactual scenario when there is no granting of marketing exclusivity to the first generic patentchallenger. The final section concludes.

2. Model environment
We consider a multi-period model with three firms: an incumbent and two potential
entrants. Periods run from 1 to infinity. All actions take place at the beginning of periods. Let δ (< 1)denote the common discount factor. The incumbent is an established branded drug manufacturer
and the patent holder. Two potential entrants are generic drug manufacturers that must file formarketing approval before entering the market. Obtaining marketing approval requires the one-time
fixed entry cost F (> 0). The incumbent’s patent expires at the beginning of the third period, so entry
occurring in period 3 or later does not entail patent infringement. In contrast, entry in period 1 or
period 2 must begin with a patent challenge, which may result in infringement litigation.
With two potential generic entrants, there can be three market structures: monopoly (M),duopoly (D) and triopoly (T). Let ΠJ denote the incumbent’s (equilibrium) per-period profit whenthe market structure is J (= M, D, T). We assume that Π M > Π D > ΠT ; the incumbent’s profit
decreases as generic competition intensifies. Similarly, let πJ be the profit to a generic firm when themarket structure is J (= D, T). Naturally, we have that πD > πT. It is well known that even though thegenerics are known to be fully equivalent to the branded drug consumers tend to prefer the latterdrug largely because of their familiarity with it through previous use.5 In reflection of this fact we
5This is explored further in Wan (2016), who develops a two-period model to study brand loyalty in the pharmaceuticalindustry.

5
posit that Π D ≥ π D and ΠT ≥ π T . Finally, we suppose that πD/2 < πT < 3πD/4. This assumption ismore of a technical nature, which keeps the probability that the incumbent wins infringement suit
between 0 and 1, and is satisfied in Cournot oligopoly with linear demand and constant marginalcost.
Let Ω denote the discounted sum of the triopoly profit for the incumbent; i.e., Ω ≡ ΠT/(1δ). Define ω = πT/(1- δ) for the generics similarly. For the remainder of the analysis, we assume that
ω – F > 0, implying that both generic firms enter after patent expiration, if they have not done so
earlier. This assumption allows us to focus on the central question of this paper: generic entry
competition before patent expiration.
If the generic firms challenge the patent, the incumbent decides whether to file patent
infringement suit. We suppose that, if it chooses to file suit, a court takes one period to deliberate.
Let α ∈(0, 1) denote the probability that the patent is found valid. We further assume the following,as in Choi (1998). First, the probability α is exogenous.6 Second, if one generic firm challenges andthe patent is found invalid, then the other generic firm can also enter without infringing the patent.
On the other hand, if the patent is found valid, the validity is respected for the rest of the patent life
so generic entry occurs only after patent expiration. Third, when there are two simultaneous
challengers, the court deliberates their cases jointly. Lastly, legal fees are negligibly small.
Consider next what happens if the incumbent accommodates entry in period 1. Then, FDA
grants marketing approval in period 1, allowing the generic firm(s) to enter immediately.7 In thiscase, however, the incumbent still reserves the right to file infringement suit later. If the incumbent
files suit later and the patent is found infringed, the infringers are ordered to fully compensate theincumbent for all the losses it suffered from patent infringement.

3. Hatch-Waxman without reverse payment settlements
6

According to a 2002 FTC study entitled Generic Drug entry Prior to Patent Expiration, generic applicants prevailed 73
per cent of the cases in which a court has resolved the patent dispute. This suggests a relatively small value for α.
7
In reality, FDA takes about two years to review and approve a generic drug application (Mossinghoff 1999). To focus
on patent challenges, however, we assume immediate FDA approval.

6
In this section we consider the model without possibilities of reverse payments. The game
begins with two generic producers simultaneously deciding, in period 1, whether to challenge theincumbent’s patent (action C) or not (action ~C). The generic firms’ first-period actions gives rise tofour subgames: two with symmetric actionss, (C, C) and (~C, ~C) and two more with asymmetricactions, (C, ~C) and (~C, C). Let v00 and v11 denote, respectively, the (symmetric) generic firm’s
profit from the subgames (~C, ~C) and (C, C). For the asymmetric subgames, let v10 denote thechallenger's profit and v01 the non-challenger’s profit. We solve each subgame first and then solve
the whole game for the subgame-perfect Nash equilibrium.

3.1: Subgame (C, C): Two challengers in period 1
Suppose that two generic firms challenge the patent, both incurring the entry cost F in period 1. If
the incumbent files suit and a court finds the patent invalid, only one generic firm enters in period 2;
the other firm waits till period 3. Note that the second entrant need not incur the cost F in period 3
because FDA stayed marketing approval for it in period 1 but did not deny its application.
When both generic firms challenge the patent, filing suit is the dominant strategy for theincumbent. To see this, observe that filing suit delays generic entry for one period due to lengthy
litigation. Thus, the incumbent receives the monopoly profit ΠM in period 1 and either ΠM withprobability α or ΠD with probability 1 – α in period 2. In period 3 the other generic firm enters,
regardless of a court decision. Thus, the incumbent's expected profit from filing suit is(1)ΠM + δ[αΠM + (1 – α)ΠD] + δ2Ω

where Ω ≡ ΠT/(1- δ). On the other hand, if the incumbent does not file suit, FDA approves bothgenerics but grants marketing exclusivity to only one firm. In period 2, marketing exclusivity
expires and the other generic firm enters. However, the patent has not expired yet. At this point, theincumbent chooses to file suit because otherwise it would forgo the compensations for patent
infringement (with probability α). As we assume full compensation when the patent is upheld, theincumbent’s profit from accommodating entry in period 1 and then filing suit in period 2 is

7
ΠD + δΠT + δ2Ω + α(ΠM + δΠM - ΠD - δΠT)
= αΠM (1+ δ) + (1 - α)(ΠD + δΠT) + δ2Ω.
Note that the term in parentheses on the left-hand side of the equality represents the compensation
the incumbent receives when its patent is found infringed. However, the above profit is less than the
profit (1), so the incumbent files suit against both challengers in period 1.
Given the incumbent’s optimal response to challenging the patent, we calculate the genericfirms’ profits. In period 1, they earn zero profit because FDA does not generally grant marketing
approval while there is litigation. In period 2, if the patent is found invalid one generic firm enters
under marketing exclusivity while the other enters in period 3. If the patent is found valid, bothgeneric firms wait till period 3 to enter. Assuming that each generic firm is equally likely to be
granted marketing exclusivity, we obtain the following equilibrium profit for a generic firm(2)

v11 = - F + δ(1- α )πD/2 + δ2ω,

where ω ≡ πT/(1- δ). The incumbent’s equilibrium profit is given by (1).

3.2. Subgames (C, ~C) and (~C, C): One challenger in period 1
As in the previous case, filing infringement suit guarantees the monopoly profit ΠM in period 1 forthe incumbent. If the patent is found valid, the incumbent also earns ΠM in period 2. On the other
hand, if the patent is found invalid, the challenger enters so the incumbent’s profit is ΠD. Regardlessof a court decision, the second generic firm does not enter till period 3. Therefore, the incumbent’s
expected profit is the same as the one in (1).
On the other hand, if the incumbent accommodates entry, there is duopoly in period 1. In
period 2, the market exclusivity expires but the patent does not. If the second generic firm
challenges the patent in period 2, the incumbent files suit against both generic firms, which delays
entry of the second generic. The incumbent is also entitled to the compensations from the first
entrant with probability α. Thus, accommodation in period 1 (followed by litigation against bothgenerics in period 2, if the second enters) yields the expected profit to the incumbent:8(3)

ΠD (1 + δ) + δ2Ω + α[(ΠM - ΠD)(1 + δ)]

where the last term in brackets represents the compensation. In contrast, also accommodating thesecond generic firm in period 2 yields ΠD + δ ΠT + δ2Ω. As this profit is clearly smaller than the onein (3). Thus, the incumbent files suit if the second generic firm enters in period 2. Therefore, inperiod 2’s values, the second generic firm’s expected profit will be – F + δω if it enters and δ(ω - F)
if it waits till period 3. Clearly, the second firm chooses not to enter. However, the incumbent still
files suit against the first entrant, because it yields the profit in (3) while filing suit against the first
generic firm yields ΠD (1 + δ) + δ2Ω, a smaller profit.
We have shown that the incumbent obtains the profit in (3) by accommodating a challenger
in period 1 and then filing suit against that firm in period 2. However, this profit is still smaller thanthe one in (1). Thus, the incumbent files suit against the challenger in period 1. The incumbent’s
equilibrium profit is given in (1). The challenger’s profit is(4)

v10 = −F + δ (1− α )π D + δ 2ω

while that of the non-challenger is(5)v01 = δ 2 (ω − F) > 0.

3.3 (~C, ~C): No challengers in period 1
If the generic firms do not challenge the patent in period 1, then they again simultaneously decide
whether to challenge the patent or not in period 2. We show, in Appendix A, that not to challenge
the patent in period 2 is the dominant strategy. Therefore, the generic firms do not enter before
patent expires, and hence the equilibrium profit is

v00 = δ 2 (ω − F) .

3.4 Equilibrium in period 1
Having solved all the subgames, we can move back to the first-period game, in which twogeneric firms simultaneously choose C or ~C. We present the equilibrium outcomes in the next

9
proposition while relegating the proof to Appendix B. We begin by defining the function

Φ :(0,1) → ! + :Φ(α) ≡ δ(1- α)ΠD/(1- δ2).8
From the preceding subsections, if only one generic firm enters in period 1, the other generic firm
delays entry till period 3, earning the expected profit v01. If instead the latter also enters in period 1,
it pays the cost F upfront and faces the expected profit (1 - α)πD/2 in period 2, given equal chancesof getting granted marketing exclusivity. Paying the cost F upfront as opposed to in period 3 costs
the firm (1 - δ2)F additionally. If this extra cost equals the firm’s expected gain in profit, δπD(1 α)/2, then the firm is indifferent between challenging the patent in period 1 and delaying entry till
period 3, provided that the rival challenges the patent. Arranging the equality (1 - δ2)F = δπD(1 α)/2, we obtain F = Φ(α)/2, which is equivalent to v11 = v01. If F = Φ(α)/2, v11 > v01 and hence thefirm challenges the patent in period one.
Now consider the case in which neither firm challenges the patent in period 1. Then we canshow that they both delay entry until period 3 (see Appendix B). In this case, if instead one firm
decides to challenge the patent in period 1, its expected profit is raised by (1 - α)δπD, since it is the
only challenger. Thus, when the rival does not challenge the patent in period 1, the firm is
indifferent between challenging the patent and not doing so if (1 - δ2)F = δπD(1 - α). Solving for F
yields the other key condition F = Φ(α), which is equivalent to the equality v10 = v00.
Now, if the entry cost is low enough to satisfy F < Φ(α)/2, then F < Φ(α). Thus, we havethat v11 > v01 and v10 > v00; patent challenging is the dominant strategy. If F is higher so that Φ(α)/2< F < Φ(α), then v11 < v01 and v10 > v00, implying that a firm challenges the patent if and only if therival does not. As a result, there is one challenger in this range of F. Finally, if F is so high that F >Φ(α), not entering is the dominant strategy. We summarize these results in

Proposition 1: Fix α.

8Φ(α) is the value of F that satisfies the equality v10 = v00 (= δ2(ω - F)); see Appendix B for details.

10(A) If F ∈(0,Φ(α ) / 2) , both generic firms challenge the patent in period 1.
(B) If F ∈(Φ(α ) / 2,Φ(α )) , only one generic firm challenges the patent in period 1.
(C) If F ∈(Φ(α ),∞) , neither firm challenges the patent in period 1.

Proposition 1 is illustrated in figure 1. In region labeled 1, both generics challenge the patent; inregion 2, only one generic does so, and there is no patent challenging in region 3.
As we saw in proposition 1 and figure 1, the equilibrium outcome crucially hinges on theentry cost F. Prior to Hatch-Waxman, entry costs were probably very high, because “there were 150
drugs that went off-patent (after 1962), but for which there were no generics because genericcompanies simply would not spend the time and money doing the clinical trials to get to themarket” (Mossinghoff 1999). 9 Hatch-Waxman has introduced the Abbreviated New Drug
Application (ANDA) process, which exempts generics from both pre-clinical and clinical trials andrequires only the bioequivalence tests to be satisfied for FDA approval (Mossinghoff 1999).
Furthermore, as noted earlier, test data of the branded drug, previously kept as trade secrets, aremade available to generic drug manufacturers after five years of data exclusivity.10 The fact that
there are many generic versions of the branded drugs today implies that Hatch-Waxman has beenquite successful in reducing entry costs for generics.11
We end this section with the welfare calculations. We first introduce notation anddefinitions. Social surplus is defined as the sum of consumer surplus and industry profits less entry
costs in each period. Social welfare is the discounted sum of social surpluses evaluated at the
beginning of period 1. CSi (i = M, D, T) denotes the per-period consumer surpluses undermonopoly, duoply and triopoly, respectively. Si denotes the social surplus under the market

9

DiMasi et al. (1991) estimated the average cost to develop and win marketing approval for a new drug was $231
million (in 1987 dollars).
10
Refer to Footnote 5 for the definition of data exclusivity.
11
Empirical work shows remarkable growth of generic sales in the U.S. pharmaceutical markets since the 1980s; see, forexample, Frank and Salkever (2004).

11
structures i = M, D, T. Social surplus is assumed to increase as the market becomes morecompetitive; i.e.,
SM (= ΠM + CSM) < SD (= ΠD + πD + CSD) < ST (= ΠT + 2πT + CST).
Write S T / (1− δ ) ≡ Σ .
We now compute the equilibrium social welfare in the four regimes under marketingexclusivity. In regime 1, there are two challengers in period 1. The incumbent files suit and remains
a monopoly. In period 2 there is duopoly with probability (1 – α) and monopoly otherwise. In
period 3 there is triopoly. Thus, the equilibrium social welfare is given by:(6)

W (1) = S M + δ [α S M + (1− α )S D ] + δ 2 Σ − 2F

In regimes 2 and 3, there is only one challenger in period 1. In period 2, there is duopoly withprobability (1 – α) and monopoly otherwise. The equilibrium social welfare is given by:

W (2, 3) = S M + δ [α S M + (1− α )S D ] + δ 2 Σ − F − δ 2 F .
In regime 4 there is no entry until period 3. The social welfare equals(7)

W (4) = (1+ δ )S M + δ 2 (Σ − 2F) .

4. Reverse payment settlements
We now extend our baseline model to allow reverse payments and examine theimplications. In the extension we assume that the incumbent cannot arrange for reverse payment
settlements after the patent expires. This assumption rules out the possibility that the incumbent
remains a monopoly forever by buying out all generic competitors and still earns a greater profit
than when there is generic entry.
The extended model adds a new stage to the baseline game, in which the incumbent
chooses whether to offer a reverse payment to the generic firm that has been granted marketingexclusivity. If such a proposal is made, the parties involved choose the amount of a reverse
payment, which we denote by R. In the extended analysis, then the first period begins with twogeneric firms deciding whether to challenge the incumbent’s patent or not. If the patent is12challenged and the notice is received that a paragraph IV certification was filed, the incumbent thenchooses to file suit or not. If it files suit, the rest of the game proceeds as in the baseline model. On
the other hand, if it chooses not to file suit so that a generic firm is granted marketing exclusivity,
then the incumbent decides whether to accommodate entry in the manner described in section 3 or
to proceed for a reverse payment settlement with the generic firm. In case of the latter choice theincumbent pays the generic firm the settlement payment R and the latter postpones entry until thepatent expires.
Below we first solve the scenario in which the incumbent proceeds for a reverse payment
settlement. We then move back to earlier stages to obtain the subgame-perfect Nash equilibrium of
the extended model. We thus begin by examining the four period-one subgames that are initiated by
the generic firms’ decisions. Suppose that the first-period decision outcome is (C, C) but theincumbent does not file suit so that one firm is granted marketing exclusivity. If a reverse payment
settlement agreement is reached, the generic firm chooses not to market its generic drug till period
3, which results in an automatic forfeiture of marketing exclusivity and the subsequent introductionof the other generic drug. Assume for now that the incumbent does not propose a reverse payment
settlement with this firm, but instead files suit against the second generic firm, thereby delaying its
entry till period 2, when the court decides whether the incumbent’s patent is invalid. This meansthat the incumbent’s expected profit equals ΠM + δ[αΠM + (1 – α)ΠD] – R. Since this profit is, for
ant R, less than the profit in (1) the incumbent would receive if it filed suit in the first place, theincumbent never enters into a reverse payment settlement agreement when both generic firms
challenge the patent in period 1. Thus, the expected profit to each generic firm is the same as ingiven in (2), that is, v11R = v11 = - F + δ(1- α )πD/2 + δ2ω.
In the preceding case we assumed that the incumbent does not consider a reverse payment
settlement with the second generic firm. Suppose now that it does. Then, if this negotiation fails theincumbent’s profit would as in the proceeding paragraph. A successful reverse payment settlement

13with the second generic firm further reduces the incumbent’s expected profit and hence theincumbent prefers to file suit in the first place.
Consider next the subgame in which only one firm challenges the patent in period 1. A
reverse payment settlement with this firm makes the incumbent a monopoly in period 1 for sure. In
period 2, if the other generic firm challenges the patent, the incumbent can file suit to delays its
entry till period 3. Anticipating this reaction on the part of the incumbent, the second generic firm isbetter off waiting till period 3 to enter. Therefore, when there is one firm challenging the patent inperiod 1, the incumbent’s expected profit from proceeding for a reverse payment settlement will beΠM (1 + δ)ΠM – R, which can exceed the profit in (1), depending on the value R.
In determining the amount of reverse payment, we suppose that the two firms determine R
through Nash bargaining, that is, they choose R to maximize the Nash product [ΠM (1 + δ) – R –B](R – b), where B and b are the profits the incumbent and the generic firm would, respectively,
receive in case bargaining fails. We compute B and b as follows. If negotiations fail, we supposethat the incumbent files suit against the generic firm immediately. If the patent is found invalid inperiod 2, the generic firm markets its produce under marketing exclusivity; otherwise, theincumbent remains a monopoly. Thus, the incumbent’s profit would be
B = ΠM + δ[αΠM + (1 – α)ΠD].
For the generic firm, the above action on the part of the incumbent implies that the generic firm
gains only if the patent is found invalid; that is,b = δ(1 – α)πD.
Note that this expression does not contain F because it is sunk before the firms negotiate for areverse payment settlement. Substituting these values, we can compute the equilibrium R:

R! = δ (1− α )(Π M – Π D + π D ) / 2 > 0 .
Substituting this value of R, we can compute the incumbent’s expected profit:ΠM (1 + δ) – δ(1 - α)(ΠM – ΠD + πD)/2,

14This profit exceeds the profit in (1) by δ(1 - α)(ΠM –πD – ΠD)/2 > 0, implying that the reverse
payment settlement dominates litigation. The patent challenger’s profit isv10R = - F + δ(1 - α)(ΠM – ΠD + πD)/2 .
Since the non-challenger enters in period 3, its profit in period 1 equals
Rv01= δ 2 (ω − F)

When neither generic firm enters in period 1, then as shown earlier, there is no introductionof generic drugs until period 3 and hence no reverse payment settlement. The generic firm’sR
expected profit is symmetric and equals v00= v00 = δ 2 (ω − F) .

Now we can solve the first-stage game. Before proceeding, defineδ (1− α )(Π M − Π D + π D )Γ(α ) ≡.
1− δ 2
RR
We have (C, C) if v10R ≥ v00
and v11R ≥ v01. But the second inequality implies the first. Thus, we have

(C, C) if F ≤ Φ(α ) / 2 as in the baseline model. In this case, there are no reverse payment
RR
settlements. Next, we have (C, ~C) if v10R ≥ v00
and v11R < v01, which translate into the inequalities:F ≤ Γ(α ) / 2 and F > Φ(α ) / 2 . As we showed in this case there is a reverse payment settlement.
Lastly, we have (~C, ~C) if F > Γ(α ) / 2 . In this case there are perforce no reverse payment
settlements.

Proposition 2.
(A) The incumbent proceeds for a reverse payment settlement with a generic challenger if and only
if F ∈(Φ(α ) / 2,Γ(α ) / 2] .
(B) For F ∈(Φ(α ),Γ(α ) / 2] , the prospect of a reverse payment settlement prompts generic firms
to challenge the patent although they would not without a reverse payment settlement.

Figure 2 illustrates thee above cases, where the broken line represents the function Γ(α)/2. Reverse
payment settlements occur only in the regions labeled 2 and 3A. In region 3A there was no generic

15
entry without reverse payments but now generics enter to take advantage of being party to reverse
payment settlements. Note that (ΠM – ΠD + πD)/2 > πD, which implies that Γ(α ) / 2 > Φ(α ) as
shown in the figure. This fact also implies that the intervals (Φ(α ) / 2,Γ(α ) / 2] are not empty; thatis, there is an F satisfying the condition in proposition 2.

The welfare consequence of reverse

payment settlements is straightforward. When low enough entry costs (i.e., F ≤ Φ(α ) / 2 ) induce
both generic firms to challenge the patent, there are no reverse payment settlements, so theequilibrium welfare equals W(1) given in (6) Similarly, if F > Γ(α ) / 2 there are no patentchallenges so the welfare equals W(4) given in (7). In the complementary cases, i.e.,F ∈(Φ(α ) / 2,Γ(α ) / 2] , reverse payment settlements occur and hence there is no generic entry in
the first two periods. Since there is one patent challenger, the welfare level is given by(8)

W R = (1+ δ )S M + δ 2 Σ − F(1+ δ 2 ) .

Note that this welfare level is lower than when there are no patent challengers, i.e., W(4), because
here one firm incurs the entry cost F in period 1 instead of period 3 and yet there is no generic entry
until period 3. Thus,

Proposition 3. Prohibiting reverse payment settlements increases social welfare forF ∈(Φ(α ) / 2,Γ(α ) / 2] , and has no welfare effects otherwise.

5. The effect of removing marketing exclusivity on reverse payments
Now we consider the counterfactual case: no marketing exclusivity in Hatch-Waxman. If
both generic firms enter in period 1, we suppose that the incumbent enters into an agreement withboth. To keep things simple, also assume that the three-party negotiations fail unless all three cometo an agreement. Then the settlement payments Rj to firm j (= 1, 2) maximizes the Nash product[ΠM (1 + δ) – R1 – R2 – B](R1 – b1)(R2 – b2), where B and bi are the expected profits to the16
incumbent and to each generic firm i, respectively. If negotiations fail, the game reverts to thebaseline model, where the incumbent chooses whether to file suit or not. Hence,
B = ΠM + δ[αΠM + (1 – α)ΠT]
whileb = δ (1− α )π T .
Thus, we have that b1 = b2 = b. Substituting these values, we can rewrite the Nash product as[δ(1 – α)(ΠM – ΠT) – R1 – R2][R1 – δ(1 – α)πT] ][R2 – δ(1 – α)πT].
Maximization yields
R̂i = R̂ = δ (1 – α ) (Π M – ΠT + π T ) / 3 .

The incumbent’s profit is therefore equal to(1 + δ)ΠM – 2δ(1 – α)(ΠM – ΠT + πT)/3.
This profit exceeds the profit in (6) by δ(1 - α)(ΠM – 2ΠT + πT)/3 > 0, implying that a reverse
payment settlement dominates litigation. The generic firm’s profit is thereforev̂11R = δ(1 – α)(ΠM – ΠT + πT)/3 – F.
On the other hand, if one firm challenges the patent in period 1, the result is exactly the same aswith marketing exclusivity. If there is no patent challenging, the outcome is the same as in thebaseline model; there are no reverse payment settlements.
With all the subgames solved, we proceed to the first-stage game. To that end, first defineδ (1− α )(Π M − ΠT + π T )Λ(α ) ≡.
1− δ 2
RR
We have (C, C) if v̂11R ≥ v01
and v10R ≥ v00, which implies the bounds on F:

F ≤ Min{ Λ(α ) /3 , Γ(α ) /2}.
Since (ΠM – ΠT + πT)/3 < (ΠM – ΠD + πD)/2, we haveΛ(α ) /3 < Γ(α ) /2.
R
R
Hence, we have (C, C) if F ≤ Λ(α ) /3. Next, we have (C, ~C) if v̂11R < v01
and v10R ≥ v00. Theseconditions implies that Λ(α ) /3 < F ≤ Γ(α ) /2. Lastly, we have no patent challenges if F > Γ(α ) /2,
as in the previous section. The next proposition puts together the above findings.

17

Proposition 4: (A) If F ≤ Λ(α ) /3, both generic firms challenge the patent and the incumbent
proceeds for a reverse payment settlement with both firms.
(B) If Λ(α ) /3 < F ≤ Γ(α ) /2, one firm challenge the patent, with which the incumbent proceeds fora reverse payment settlement.
(C) If F > Γ(α ) /2, there is no patent challenging.

The relative location of Λ(α ) and Φ(α ) depends on the difference (ΠM – ΠT + πT)/3 - πD.
If the incumbent’s product does not have much brand loyalty so that ΠT ≈ πT and ΠD ≈ πD, then (ΠM– ΠT + πT)/3 - πD < 0, implying that Λ(α ) /3 < Φ(α ) . We show this case in figure 4, where thedotted line represents Λ(α ) /3. In region 1 and region 2A both generics challenge the patent,
resulting in reverse payment settlements. In regions 2B and 3A one generic challenges the patent,
resulting in reverse payment settlements. Finally, if the incumbent’s branded drug commands
greater brand loyalty so that πD is sufficiently small, then the above inequality may be reversed, i.e.,(ΠM – ΠT + πT)/3 - πD > 0 so Λ(α ) /3 > Φ(α ) .
A comparison between figures 2 and 3 yields the following results, which is independent of
the relative magnitude between Λ(α ) /3 and Φ(α ) . On the one hand, since Λ(α ) /3 < Γ(α ) / 2 ,removing marketing exclusivity encourages both generic firms to challenge the patent even if theentry costs are higher. On the other hand, removing marketing exclusivity intensifies generic entry
competition and as a result weakens generic firms’ negotiation positions. Thus, with marketingexclusivity, when both generic firms challenge the patent, the incumbent does not offer a reverse
payment settlement, whereas without marketing exclusivity a brand finds it more profitable topropose reverse payment settlements with both generics. In other words, removing marketingexclusivity facilitates reverse payment settlements.

18
Proposition 5. Removing of marketing exclusivity increases the incentive for reverse payment
settlements, that is, without marketing exclusivity the incumbent proceeds for a reverse payment
settlement whenever there is generic entry (which occurs for all F ≤ Γ(α ) / 2 ).

Proposition 5 has a dire welfare consequence. The equilibrium welfare isŴ11R = (1 + δ )S M + δ 2 Σ – 2F

when both generic firms challenge and WR given in (8) when one firm challenges. Clearly Ŵ11R is
the worse since entry costs are incurred upfront in period 1 without generic penetration into themarket. We thus conclude that in the presence of reverse payment settlements, removing marketingexclusivity from Hatch-Waxman reduces social welfare.

6. Concluding remarks
In this paper we develop a formal analytical framework to examine the implications ofbanning reverse payment settlements. We find that reverse payment settlements occur when genericfirms face relatively high entry costs while reverse payments are not profitable when entry costs are
sufficiently low. We also identify cases in which reverse payment settlements are harmful to brands.
Such cases occur when generic firms have no incentives to challenge brands’ patents without
reverse payment possibilities, but generics are induced to challenge the brands’ patents by theprospect of sharing the monopoly profits through reverse payments.
We also consider the counterfactual case when marketing exclusivity rights are removed
from Hatch-Waxman and find that the absence of marketing exclusivity rights encourages brands toproceed with reverse payment settlements. This marketing exclusivity rights serve as checks tospreading of reverse payment settlements.

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Appendices
Appendix A: We analyze the period-2 subgames with marketing exclusivity, when there are nochallengers in period 1. We consider each subgame.
A1. Two challengers in period 2
In this subgame, filing suit in period 2 delays entry till period 3. In period 3, the patent
expires, so there is no longer granting of marketing exclusivity. Therefore, regardless of what court
determines, both generic firms enter, yielding ΠT to the incumbent. Thus, if the incumbent files suit,its expected profit (evaluated at the beginning of period 2 and exclusive of the first-period profit)
equals(A1)

ΠM + δΠT + δ2Ω.12

In contrast, with accommodation, only one generic firm enters in period 2 under marketingexclusivity, yielding to the incumbent(A2)

ΠD + δΠT + δ2Ω.

This is less than the profit in (A1) and hence the incumbent files suit against both challengers.
Given the preceding discussion, each challenger’s expected profit in period 2 is e11 = −F + δω .

A2. One challenger in period 2This case is similar to the previous subcase. By filing suit, the incumbent receives the same profit asin (A1). By accommodating, the incumbent receives ΠD in period 2 and ΠT in all later periods, so its
profit is given by (A2). Thus, the incumbent files suit against the challenger in period 2. The
challenger’s profit is e10 = −F + δω while the non-challenger’s profit is e01 = δ (ω − F) > e10.

A3. No challenger in period 2
If both generic firms wait till period 3 to enter, each firm expects the profit e00 = δ (ω − F) .

12

Originally, market exclusivity was not forfeited by patent expiration. In such a case, the incumbent’s profit from filingsuit is greater and equals ΠD + δ[αΠT + (1 – α)ΠD] + δ2Ω.. This therefore does not change the remainder of the analysis.

20
These profits to the generic firms imply that not challenging is the strictly dominant strategy.
Hence, the generic firm’s equilibrium profit is
v00 = δ 2 (ω − F)and the incumbent’s equilibrium profit is ΠM(1+ δΠ) + δ2Ω.

21
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22

F
3

2
φ(α)
φ(α)/21α01Figure 1: Generic entry without reverse payment

23

F
3B
3A
Γ(α)/22φ(α)φ(α)/21

0

1

Figure 2: Generic entry with reverse payment

α

24

F
3B
3A

2B

Γ(α)/2φ(α)Λ(α)/32A

1
αφ(α)/20
1

Figure 3: Generic entry without marketing exclusivity