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					 “An Economic Analysis of Relitigation
Rules in Intellectual Property Litigation”



              Bruce H. Kobayashi
         George Mason University School of Law




FINDING THE BALANCE BETWEEN BENEFIT AND COST:
      A PUBLIC POLICY ROUNDTABLE ON THE
       FEDERAL RULES OF CIVIL PROCEDURE

 Wednesday, April 21st, 2010—Thursday, April 22nd, 2010
      An Economic Analysis of Relitigation Rules in Intellectual Property Litigation

                                     Bruce H. Kobayashi         •



                                      Professor of Law
                              George Mason University Law School

                                                Abstract

     While a large literature has examined the economics of litigation and settlement in a
single plaintiff/single defendant context, the existence of multiple parties often presents
distinct and important issues regarding the effect of procedural rules on the incentives of
litigants. This paper explicitly examines two rules that operate significantly in the
multiple litigant case - the rules of issue preclusion - which asymmetrically prevent
relitigation of claims or issues - and vacatur – which has been used in the past to avoid
issue preclusion in future cases.

    This paper provides an economic analysis of how the rules of preclusion affect
intellectual property litigants' incentives to litigate and settle disputes. We examine these
incentives under the Supreme Court’s Triplett rule that allowed relitigation of patent
issues, and under the Court’s holding in Blonder-Tongue which overruled Triplett and
allowed the defensive use of collateral estoppel by non parties. We also examine the
effect of allowing courts to vacate prior judgments based on the voluntary settlement of
the parties, a practice widely used by intellectual property plaintiffs to escape the effect
of Blonder-Tongue, and limited by the Supreme Court in U.S. Bancorp v. Bonner Mall.
We show that both rules serve to control the extent to which plaintiffs and defendants
capitalize the value of potential future litigation into the current case. This capitalization
of litigation in turn controls the litigation expenditures of the parties, and their incentive
to settle or litigate cases. This analysis has implications regarding litigants’ incentive and
ability to relitigate erroneous decisions, and provides an further explanation for why
parties agree to reverse settlements that result in payments to the entrant that exceed his
expected judgment value of the case.




•
 Professor of Law, George Mason University School of Law. This paper was prepared for the Searle
Center Public Policy Roundtable on Finding the Balance between Benefit and Cost: A Public Policy
Roundtable on the Federal Rules of Civil Procedure, April 21st-22nd, 2010. The author would like to thank
the participants at the Searle Center on Law, Regulation, and Economic Growth’s Public Policy Roundtable
on the Federal Rules of Civil Procedure, and the Searle Center for financial support. Any remaining errors
are the author’s.
I.      Introduction

    The standard economic models of litigation have focused on litigation and settlement
in a single plaintiff/single defendant setting. In the standard model, disputes are modeled
as private disputes between two opposed parties, and trials either because of a failure of
prediction or a failure of bargaining.1 In this private law setting, settlements are
encouraged, as trials are viewed as failures to come to a Pareto preferred settlement.2

     This view of settlement has been disputed. Critics of settlement have noted that
settlement, even in the single litigant/single defendant model, can detract from social
welfare by reducing the accuracy of legal outcomes.3 Moreover, in the context of
litigation with external effects, settlement can eliminate opportunities to produce valuable
judgments that can influence future litigation through the effects of precedent or
persuastion.4 In addition, resolution of legal or factual issues can have a preclusive
effect, and can serve to reduce the overall costs of litigation by reducing future litigation.
Thus, when judgments have value external to the case at hand, the resource cost savings
associated with settlement of a single case may not be preferred to litigation that produces
a judgment.5

    These external effects are particularly relevant in intellectual property litigation.6 The
courts and commentators have recognized the public benefits of patent litigation
associated with the invalidation of “bad” patents.7 The public benefits of invalidating
patents in litigant have led to calls for implementing procedures or laws that restrict
patent settlements. These include proposals to broadly apply the antitrust laws to
scrutinize patent settlements, and to deter post-judgment settlements by preventing
patentees from using vacatur to escape the effects of earlier judgments that held their
patent invalid or unenforceable. While concerns over enforcing bad patents are
legitimate and are an integral part of any error-cost analysis of patent litigation, they are
only one part of such an analysis. A complete analysis would also consider how such
changes would affect the costs of invalidating “good” patents and the direct costs of more
patent litigation.

    Despite the importance of the external effects of patent litigation, few have analyzed
these effects in any detail. The primary purpose of this paper is to provide such an
analysis by comparing the litigation and settlement of patent disputes under various rules
1
  See generally, R. D. Cooter and D. L. Rubinfeld, Economic Analysis of Legal Disputes and their
Resolution, 27 J. ECON. LIT. 1076 (1989) (surveying literature).
2
  For a statement of this view, see S. R. Gross and K. D. Syverud, Getting to No: A Study of Settlement
Negotiations and the Selection of Cases for Trial, 90 MICH. L. REV. 319 (1991).
3
  Ezra Friedman and Abraham L. Wickelgen, Chilling, Settlement, and the Accuracy of the Legal Process,
26 J. L. ECON. & ORG. 144 (2010); Owen M. Fiss, Against Settlement, 93 YALE L. J. 1073 (1984).
4
  Bruce H. Kobayashi, Case Selection, External Effects, and the Trial/Settlement Decision, 17 in DISPUTE
RESOLUTION, D. A. Anderson, ed., JAI Press (1996).
5
  See, e.g., Leandra Lederman, Precedent Lost: Why Encourage Settlement, and Why Permit Non-party
Involvement in Settlements? 75 N. D. L. REV. 221 (1999).
6
  See, generally Mark Crane & Malcolm R. Pfunder, Antitrust and Res Judicata Considerations in the
Settlement of Patent Litigation, 62 ANTITRUST L. J. 151 (1993-4).
7
  See text accompanying notes _ and _, infra.


                                                    2
governing the ability to re-litigate and to vacate earlier judgments. The analysis in this
paper shows that challenges to patents in conjunction with the effects of non-mutual non-
party collateral estoppel cause distortions in the litigation process that generate strong
incentives for patentees to settle cases, and also cause patentees to disproportionately
spend resources on litigation in those cases that are not settled. In this setting, vacatur is
used as a mechanism to moderate both of these effects, especially in cases involving
determinations of factual issues or mixed questions of law and fact that would be
reviewed under an unfavorable “clearly erroneous” standard on appeal.

     The analysis suggests that a regime where patentees can relitigate the validity of
previously invalidated patents may be preferred to either a regime of non-mutual non-
party collateral estoppel that prevents patentees from re-litigating the validity of invalided
patents, or a regime that also allows patentees to re-litigate invalidated patents through
the use of vacatur. We show that the regimes of non-mutual non-party estoppel with and
without vacatur represent extreme solutions to the tradeoff between type I and type II
errors in patent litigation. In contrast, this paper shows that a system of re-litigation can
be a more effective way to sort between correct and incorrect prior decisions. This will be
the case if the parties’ incentives cause the latter and not the former to be relitigated, so
that earlier errors can be corrected while correct decisions are allowed to stand. Because
such a system presents a more rational tradeoff between type I and type II errors in patent
litigation, it may be preferred to a system that attempts to save resources by preventing
re-litigation or a system.

    The direct implication of the analysis in this paper is that relitigation may be
beneficial in cases where the costs of error are high and correction through appellate
review is limited. Our focus on intellectual property litigation is intended to illustrate
such a situation where relitigation can have beneficial effects. In examining how
judgments in one case affect future cases, the paper is related to the literature on the
economic analysis of precedent. Indeed, much of this literature examines the evolution
of rules assuming relitigation.8 It is also related to the economic analysis of the doctrine
of stare decisis and court error,9 and the optimal vertical and horizontal structure of
courts.10

     The organization of the paper is as follows. Section II illustrates the issue of
relitigation by examining the patent litigation involving the Taxmoxifen patents, as well
8
  See, e.g., William M. Landes & Richard A. Posner, Adjudication as a Private Good, 8 J. LEG. STUD. 51
(1979), Paul H. Rubin, Why is the Common Law Efficient?, 6 J. LEG. STUD. 51 (1977); George L. Priest,
The Common Law Process and the Selection of Efficient Rules, 6 J. LEG. STUD. 65 (1977).
9
  See, e.g., I. J. Good & Gordon Tullock, Judicial Errors and A Proposal for Reform, 13 J. LEG. STUD. 289
(1984).
10
   See, e.g., Erin O’Hara, Social Constraint or Implicit Collusion?: Toward A Game Theoretic Analysis of
Stare Decisis, 24 SETON HALL L. REV. 736 (1993), Steven Shavell, On the Design of the Appeals Process:
The Optimal Use of Discretionary Review versus Direct Appeal, 39 J. LEG. STUD. 63 (2010), Steven
Shavell, The Appeals Process as a Means of Error Correction, 24 J. LEG. STUD. 379 (1995), Lewis
Kornhauser, Adjudication by a Resource-Constrained Team: Hierarchy and Precedent in a Judicial
System. 69 S. CAL. L. REV. 1605 (1995).




                                                    3
as the subsequent litigation over use of reverse payments and vacatur in intellectual
property litigation. Section III sets out the economic model of litigation and analyzes in
detail patent litigation with one potential entrant/infringer. Section IV extends the model
to allows for more than one potential entrant and relitigation of issues decided in the first
case. Section V uses the model set out in Section IV to examine how the rules governing
the application of collateral estoppel and vacatur alter litigation incentives on the margin.
Section VI concludes.


II.    An Example of the Relitigation of Patents: The Tamoxifen Patent and
Antitrust Litigation

        A.       The Tamoxifen Patent Litigation

     The issues of relitigation in patent litigation are illustrated by the Tamoxifen patent
litigation. Figure 1 illustrates the timeline in the Tamoxifen patent litigation. In August
of 1985 ICI obtained a patent for Tamoxifen, the most widely prescribed drug for the
treatment of breast cancer. Four months later, Barr Laboratories filed an Abbreviated
New Drug Application (ANDA) with the FDA to market a generic version of Tamoxifen.
The ANDA procedure, part of the Hatch-Waxman Act, was designed to speed entry of
generic drugs into the market place.11 The Act allows generic drug makers to make use
of brand name drugs for purposes of FDA testing, and to make use of the lower
regulatory burdens of the ANDA procedure. That Act also provided that patentees can be
granted a patent term extension of up to seven years to compensate for delays caused by
the FDA during the New Drug Application process.

     [INSERT FIGURE 1 HERE]

     ANDA filers must include one of the following certifications: A “paragraph I”
certification that no patent was filed for the listed drug; a “paragraph II” certification that
the patent has expired; a “paragraph III” certification that the patent will expire on a
specified date and the ANDA filer will not market the drug until that date; or a
“paragraph IV” certification that the patent is invalid or would not be infringed by the
manufacture, use, or sale of the new drug.12 Barr’s initial ANDA included a paragraph
III certification that would have allowed Barr to enter the market with a generic version
of Tamoxifen when the ICI patent expired in 2002. In September 1987, however, Barr
amended its ANDA to include a paragraph IV certification. The filing of a Paragraph IV
ANDA creates an act of infringement that allows the patentee to file an infringement suit.
If this is done within forty-five days, further FDA action on the entrant’s ANDA is stayed
for thirty months.13 In effect, the thirty-month stay operates like a preliminary injunction,
and generally allows for the adjudication of the validity of the patent prior to the
11
   See Drug Price Competition and Patent Term Restoration Act of 1984, PUB. L. NO. 98-417, as modified
by the Medicare Prescription Drug, Improvement, and Modernization Act of 2003, PUB. L. NO. 108-173
§1102(b).
12
   21 U.S.C. § 355(j)(2)(A)(vii).
13
   If no action is taken by the patentee, the Hatch-Waxman Act provides that the entrant can file a
declaratory judgment action to declare the patent not-infringed, invalid or unenforceable.


                                                   4
expiration of the stay. Because the generic entrant generally has not sold his competing
product at the time that the district court renders its decision, damages are not an issue in
these cases.14

     ICI filed a timely suit in response the Barr’s paragraph IV certification. The case
went to trial, and in April 1992, the district court held that the patent was unenforceable
because ICI had engaged in misconduct by deliberately withholding “crucial
information” from the Patent and Trademark office.15 The district court’s holding that
the patent was unenforceable presented serious issues for ICI. Under the Court’s holding
in Blonder-Tongue v. University of Illinois Foundation,16 ICI would be estopped from re-
litigating the factual finding that ICI engaged in misconduct before the PTO and the
conclusion of law that the patent was “invalid and unenforceable”.17 Moreover, under the
Court’s holding in Blonder-Tongue, the estoppel could be asserted by non-parties. Thus,
unless reversed or vacated, the district court’s findings and judgment would bar ICI from
asserting Tamoxifen patent in any future litigation.

    ICI appealed the district court’s decision to the Court of Appeals for the Federal
Circuit. While the appeal was pending, the parties entered into a settlement agreement.
Under the agreement, Barr would receive a $21 million “reverse” payment and a license
to sell Tamoxifen produced by Zeneca (who now owned the patent rights) under Barr’s
own label. Zeneca also agreed to pay Barr’s raw material supplier, Heumann over $45
million over a ten-year period. In exchange, Barr agreed to change its paragraph IV
certification to a paragraph III certification, which would not authorize manufacture or
sale of Barr’s own generic version of Tamoxifen until the patent expired in 2002.18 In
addition, in order to restore the enforceability of the patent, Barr and Zeneca filed a joint
motion to dismiss the appeal as moot and to vacate the district court’s judgment. The
Federal Circuit granted the motion and vacated the judgment below.19

   Between June of 1994 and February 1996, three other generic manufacturers,
Novopharm Ltd., Mylan Pharmaceuticals, and Pharmachemie B.V., filed paragraph IV
ANDAs for Tamoxifen. Zeneca responded by filing timely infringement suits against all

14
   Similarly, damages are not an issue when a potential entrant or current licensee files a declaratory
judgment action. See The Declaratory Judgment Act, 28 U.S.C. §2201 (providing that “[i]n a case of
actual controversy within its jurisdiction…any court of the United States, upon the filing of an appropriate
pleading, may declare the rights and other legal relations of any interested party seeking such
declaration.”). The mathematics of the settlement litigation is identical to the case of the pharmaceutical
patent litigation, except that the negative payment M is now a “forward” payment from the
defendant/patentee to the plaintiff/entrant.
15
   Imperial Chem. Indus., PLC v. Barr Labs., Inc., 795 F.Supp. 619, (S.D.N.Y.1992). The court found that
ICI deliberately failed to disclose to the PTO test results on mice that showed effects opposite from those
found in human and other reported animal studies. The court held that this adversely impacted
“enablement” and “best mode” disclosure requirements, and that the deliberate failure to disclose these
studies required invalidation of patent.” Id.
16
   402 U.S. 313 (1971).
17
   Id.
18
   In re Tamoxifen Citrate Antitrust Litig., 277 F.Supp.2d 121, 125-26 (E.D.N.Y.2003)
19
   Imperial Chem. Indus., PLC v. Heumann Pharma GmbH & Co., 991 F.2d 811 (Fed. Cir. 1993)
(unpublished opinion).


                                                      5
three firms. In all three cases, the district courts hearing the cases rejected the generic
entrants’ attempt to rely on the vacated decision holding the Tamoxifen patent
unenforceable. In addition, all three courts held the patents valid and enforceable, and
concluded that Zeneca had not engaged in inequitable conduct while prosecuting the
patent.20 The Federal Circuit affirmed.21

    The case above illustrates how the patent holder, ICI/Zeneca, using a reverse
settlement conditioned on vacatur, can relitigate the validity or enforceability of their
invalidated or unenforceable patents despite the rule of non-mutual non-party collateral
estoppel set out by the Court in Blonder-Tongue. It also illustrates one potential benefit
of allowing patent relitigation, the ability to correct factual errors. The history of the
Tamoxifen litigation following the vacatur indicates that by coming to the opposite
conclusion, three district courts did not find the decision or reasoning of the Barr court’s
determination of misconduct by the patentee persuasive. Under the assumption that the
Barr court’s determination was an error, the use of vacatur to prevent the application of
estoppel allowed the patentee a viable chance to prevent the effects of an erroneous
judgment from being locked-in.

     Indeed, preserving the ability of patentees to relitigate erroneous decisions was an
important consideration behind the Court’s holding in Triplett v. Lowell.22 In Triplett, the
Court considered litigants’ ability to relitigate the validity of patent claims, even when a
prior decision held the patent claim invalid. The Court accepted the doctrine of mutuality
of estoppel, requiring that parties asserting preclusion must be bound by the judgment in
the original case. The Court’s Triplett rule was in part based on the availability of
relitigation as an “essential safeguard against improvident judgments of invalidity.”23
The Court held that:

         Neither reason nor authority supports the contention that an adjudication
     adverse to any or all the claims of a patent precludes another suit upon the same
     claims against a different defendant. While the earlier decision may by comity be
     given great weight in a later litigation and thus persuade the court to render a like
     decree, it is not res adjudicate and may not be pleaded as a defense.24


20
    Zeneca Ltd. v. Pharmachemie B.V., 2000 WL 34335805 (D.Mass. 2000) (concluding that Zeneca had
not engaged in inequitable conduct and that the patent was valid); AstraZeneca UK Ltd. v. Mylan Pharms.,
Inc., No. 00-2239, slip op. at 2-3 (W.D.Pa. Nov. 30, 2000) (entering stipulated consent order that FDA
approval for Mylan would not be effective before the expiration of the Tamoxifen patent); Zeneca Ltd. v.
Novopharm Ltd., 111 F.3d 144, (Fed.Cir. 1997).
21
   See Zeneca Ltd. v. Novopharm Ltd., 111 F.3d 144, (Fed.Cir. 1997).
22
   Triplett v. Lowell, 297 U.S. 638 (1936). See also Ronald P. Kananen, Comments and Observations on
Res Judicata and Patent Law, 18 W. RES. L. REV. 103 (1966-1967) (discussing historical approach to
patent law, collateral estoppel and mutuality).
23
   See Blonder-Tongue, supra note _ at 330 (noting, but rejecting as un-persuasive, error-correction as
reason to allow relitigation). But see Technograph Printed Circuits, 372 F.2d at 977-78 (“for patent
litigation, there is a special reason why relitigation is not automatically banned as needless or redundant,
and why error should not be perpetuated without inquiry. … Because of the intrinsic nature of the subject,
the first decision can be quite wrong, or derived from an insufficient record or presentation.”)
24
   Triplett, supra note 22 at 642.


                                                      6
         The court whose jurisdiction is invoked by such a suit must determine for
     itself validity and ownership of the claims asserted, notwithstanding a prior
     adjudication of invalidity of some of them, unless those issues have become res
     adjudicate, by reason of the fact that both suits are between the same parties or
     their privies.25

    The Court’s Triplett rule allowing patentees to relitigate the validity of their
invalidated patents was overturned in Blonder-Tongue.26 As noted above, under the
Triplett rule, a holding regarding the validity of a patent was preclusive only between the
parties litigating that case. Patentees that had their patents invalidated could assert them
against infringers that were not parties and were not bound by the prior judgment.
Infringers that were not parties and were not bound by a prior judgment holding the
patent valid could challenge the patents validity in a later action.

    In Blonder-Tongue, the Court overturned the Triplett rule and eliminated the
mutuality requirement. The Court did so despite the fact that the issue was not raised in
the petition for review, and the fact that both parties in the case apparently opposed
overturning Triplett. In overturning Triplett, the Court allowed non-parties to invoke
collateral estoppel defensively against a repeat litigant. The repeat litigant, however,
could not assert preclusion offensively against non-parties, because doing so would deny
these non-parties their day in court.27

    Note that the ability to relitigate is made even more important given that the
alternative path for overturning an erroneous judgment in this case, an appeal of the
decision to the Federal Circuit, may not be a viable option due to the strict standard
applied to appeals of factual determinations.28 In order to overturn a finding of fact
supporting the district court’s ruling that the patent is unenforceable, the appellant must
establish that the finding is “clearly erroneous”.29

    Patentees’ ability to enable relitigation through the use of reverse settlements
conditioned upon vacatur has not been without controversy. Indeed, there have been
legal challenges to both of the principal aspects of these patent settlements. First, use of
reverse settlements in Hatch-Waxman litigation, including the settlement discussed
above, has been attacked on antitrust grounds. Part B of this section discusses this issue.

25
   Id. at 645.
26
   Blonder-Tongue Laboratories, Inc. v. University of Illinois Foundation, et al. 402 U.S. 313 (1971).
27
   Robert G. Bone, Rethinking the “Day in Court” Ideal and Nonparty Preclusion, 67 N. Y. U. L. REV. 193
(1992) (arguing for expansion of non-party preclusion to non-repeat litigation based on the concept of
“virtual representation”.) However, the Court has recently ruled against the expansion of non-party
estoppel to apply to litigants that have not had their “day in court”. See Taylor v. Sturgell, 553 U.S. 880
(2008) (disapproving virtual representation theory in claim preclusion case).
28
   F.R.C.P. Rule 52(a)(6) provides that “[f]indings of fact, whether based on oral or other evidence, must
not be set aside unless clearly erroneous, and the reviewing court must give due regard to the trial court’s
opportunity to judge the witnesses’ credibility.”
29
   See Zeneca Ltd. v. Novopharm Ltd., supra note _ at _; Hoffmann-La Roche, Inc. v. Promega Corp. See
also Lisa A. Dolak, Inequitable Conduct: A Flawed Doctrine Worth Saving (March 17, 2010). Available at
SSRN: http://ssrn.com/abstract=1588916 (discussing problems with the inequitable conduct doctrine and
suggesting reforms).


                                                     7
Moreover, the Court, in U.S. Bancorp v. Bonner Mall, placed strict limits on the ability of
courts to grant motions for vacatur based on the voluntary settlement of the parties.
These issues are discussed in Part C.

         B.       Antitrust and Patent Settlements

     The patent settlement in the Tamoxifen case spawned antitrust litigation that
challenged the inclusion of reverse payments as part of the settlement of the patent
litigation.30 These reverse settlements are common in patent settlements between patentee
plaintiffs with patents covering brand name pharmaceutical facing entry by generic
entrant that has filed a Paragraph IV Abbreviated New Drug Application (ANDA).
However, because such settlements preserve the monopoly status of the patentee,
settlements that include payments flowing from the plaintiff/patentee to the defendant/
entrant have been the subject of antitrust scrutiny as well as the subject of academic
commentary and proposed legislation that would make such payments per se illegal
under the antitrust laws. Antitrust concerns focus on the settlements in which patentees
with suspect patents enter into agreements where the entrants delays entry in exchange
for a payment from the patentee. Some academics31 and lawmakers32 have argued that
such reverse settlements should be per se illegal.

    Table 1 lists the potential outcomes of a patent challenge. Those that advocate the
antitrust condemnation of entry delaying reverse settlements focus on the case of type II
error. Allowing such settlements increases the rate of type II errors (Table 1, Row 2).
Critics also focus on the role these settlements play in allowing patentees to maintain and
extend the effect of invalid patents, frustrating the strong public policy interest in
invalidating such patents.33



30
   See In re Tamoxifen Citrate Antitrust Litigation, 429 F.3d 370 (2005).
31
   Carrier, supra note _ at 47; Thomas F. Cotter, Antitrust Implications of Patent Settlements Involving
Reverse Payments: Defending a Rebuttable Presumption of Illegality in Light of Some Recent Scholarship,
71 ANTITRUST L.J. 1069 (2003-2004) (discussing vast literature on the antitrust of reverse settlements).
32
   See Geoffrey A. Manne & Joshua D. Wright, Reverse Payment Settlements and Upcoming Congressional
Action, The Federalist Society for Law and Public Policy Studies, available at www.fed-soc.org (discussing
recently proposed federal legislation to make reverse settlements per se illegal).
33
   The invalidation of “bad” patents creates a public good that allows greater use of the ideas formerly
protected by the invalidated patent. See Lear, Inc. v. Adkins, 395 U.S. 653 (1969) (stressing the importance
of challenges to a patent’s validity because of the “public interest in permitting full and free competition in
the use of ideas which are in reality a part of the public domain.”); Christopher R. Leslie, The
Anticompetitive Effects of Unenforced Invalid Patents, 91 MINN. L. REV. 101 (2006); Joseph Farrell &
Robert P. Merges, Incentives to Challenge and Defend Patents: Why Litigation Won’t Reliably Fix Patent
Office Errors and Why Administrative Patent Review Might Help, 19 Berkeley Tech. L.J. 943 (2004). The
Court in MedImmune, supra note _, recently expanded the ability of patent licensees to bring declaratory
judgment actions challenging the validity of a patent, holding that current licensees are not required to
terminate or materially breach their existing licenses in order to sue the patentee. See also Megan M. La
Belle, Patent Litigation, Personal Jurisdiction, and The Public Good, Working Paper, Catholic Univeristy
Columbus School of Law, available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1563487
(arguing for changes to jurisdictional rules to allow the expanded use of declaratory judgment action in
patent cases).


                                                      8
     However, payments from the patentee to the potential infringer in exchange for the
potential infringer’s recognition of the patent can be the normal outcome of patent
litigation apart from any antitrust concerns.34 A settlement that delays entry until the
patent expires results in the same market performance (monopoly profits) as when there
is a judgment in which the patent is held valid and infringed. If the patent is valid, this
outcome yields the correct outcome, and avoids the possibility of a type I error (see Table
1, Row 1). The costs of type I error would be the reduced incentives for innovation that
might result from a reduction in the number of valid patents held valid and enforceable.35
Moreover, such settlements also serve the standard function of settlement in litigation,
that is, the reduction of direct litigation costs. So far, the courts faced with evaluating
reverse settlement under the antitrust laws generally have not condemned such payments,
noting that an agreement to delay entry until the expiration of the patent is one of the
rights associated with a valid patent. Several circuit courts have rejected use a per se
approach to patent settlements.36

    Indeed, whether or not one would want to allow or disallow such settlements will
depend on the relative rates and costs of type I and type II errors as well as the costs of
administering the system.37 Moreover, a per se approach is generally reserved for cases
where the costs of type I error are de minimus. Given the likely negative effect of such a
rule on valid patents, an assumption of de minimus type I error seems unwarranted.
Moreover, under a strict per se anti-reverse settlement rule, an adverse selection of cases

34
   Keith N. Hylton and Sungjoon Cho, The Economics of Injunctive and Reverse Settlements, 12 AM. L. &
ECON. REV. _ (forthcoming 2010), Injunctive and Reverse Settlements in Competition-Blocking Litigation,
B.U. SCHOOL OF LAW WORKING PAPER NO. 09-47 (2009), available online at
http://ssrn.com/abstract=1490013.
35
   Indeed, this is a complex issue. See generally, Hylton & Cho, supra note _; Robert D. Willig & John P.
Bigelow, Antitrust Policy Toward Agreements that Settle Patent Litigation, 49 ANTITRUST BULL. 655
(2004). For examine, if patentees are overcompensated or if patents rents are dissipated at a high rate,
invalidating valid patents may increase welfare. For a general discussion of rent dissipation issues, see,
e.g., Edmund W. Kitch, The Nature and Function of the Patent System, 20 J. L. & ECON. 265 (1977); Mark
F. Grady & Jay I. Alexander, Patent Law and Rent Dissipation, 78 VA. L. REV. 305 (1992). Moreover,
patents also serve to promote efficiency apart from their role in providing optimal incentives for creation of
new ideas. See, e.g., Henry E. Smith, Intellectual Property as Property: Delineating Entitlements in
Information, 116 YALE L. J. 1742 (2007)).
36
   See, e.g., Schering-Plough v. FTC, 402 F.3d 1056 (11th Cir. 2005) (rejecting both per se and rule of
reason antitrust analysis as “ill suited for cases involving patents.”); Valley Drug v. Geneva
Pharmaceuticals, Inc., 344 F.3d 1294 (11th Cir. 2003) (rejecting use of per se approach); In re Tamoxifen
Citrate Antitrust Litigation, 466 F.3d (2d Cir. 2006 (rejecting use of per se approach, and allowing vacatur
of district court judgment holding patent non-enforceable); In re Ciprofloxacin Hydorchloride Antirust
Litigation, 544 F. 3d 3123 (Fed. Cir. 2008) (rejecting a per se approach, and applying strict standard to
antitrust plaintiffs). Note that in the one case that the court followed a per se illegality approach, the
settlement in question involved a delay in triggering the 180-day period of marketing exclusivity under the
Hatch-Waxman Act, effectively delaying all generic entry. See In re Cardizem CD Antitrust Litigation,
332 F.3d 896 (6th Cir. 2003). Such tactics were addressed in the 2003 revisions to the Hatch-Waxman Act,
which established forfeiture events that cause the first ANDA IV filer to lose the 180-day marketing
exclusivity. See also C. Scott Hemphill, Paying for Delay: Pharmaceutical Patent Settlement as a
Regulatory Reform Design Problem, 81 N. Y. U. L. REV.1553 (2006).
37
   For and explicit analysis of the social and private incentives to sue in such a setting, see Hylton and Cho,
supra note _. See also, Mark A. Lemley, Rational Ignorance at the Patent Office, 95 NW. U. L. REV. 1495
(2001) (discussing social costs of enforcing bad patents).


                                                       9
for litigation will be generated, where only strong patents will be litigated, and weak
patents will settle for relatively small payments in exchange for a license. In such a
regime, weak patents will not be invalidated through litigation, while strong patents that
are challenged will be litigated.

    One approach would be to have the probability that a settlement will be challenged be
inversely related to the likelihood that patent is valid. While direct measure of the true
validity of a patent are at best elusive,38 some have used the size of the reverse settlement,
which will be a function of the ex-ante probability that the patentee will prevail, as a
proxy for the strength of a patent.39 For strong patents, ceteris paribus, the expected
losses to the patentee will be small, and so rational reverse settlement payments will be
small. Weak patents, ceteris paribus, will result in larger potential payments.

    Use of the size of settlement as a proxy for the ex-ante probability a patent will be
held valid, and thus as a proxy for the strength or validity of a patent, may be a
theoretically useful construct in the context of the single patentee/single infringer model.
However, this model does not take into account the effects of multiple infringers, and the
effects of non-mutual collateral estoppel. As will be shown in the following sections,
once these considerations are included, the issues become much more complex, and will
depend heavily upon the rules controlling litigants ability to relitigate issues.

         C.       Restrictions on Vacatur

    In addition to the potential for antitrust litigation and liability, the extent to which
patentees with invalidated patents can rely on the use of post-judgment vacatur to
facilitate relitigation of the validity of the patent is not clear. The settlement conditioned
on vacatur in the Tamoxifen Citrate Antitrust Litigation was granted just before the
Supreme Court decided U.S. Bancorp Mortgage Co. v. Bonner Mall Partnership.40 In
that case, the Court severely limited lower courts’ ability to grant post-judgment vacatur
based on mootness generated by the voluntary settlement of the parties.

    U.S. Bancorp involved litigation over whether the new value exception to the
absolute priority rule in bankruptcy survived enactment of the Federal Bankruptcy Code.
The bankruptcy court held that the new value exception was unavailable, but the district
court reversed, and the 9th Circuit affirmed. The creditor, U.S. Bancorp, filed for
certiorari, and the Court granted the petition. Subsequent to the Court’s granting the
petition for certiorari, a reorganization plan was approved and accepted by the parties.
U.S. Bancorp moved to vacate the decisions below because the settlement of the case
mooted the appeal to the Court. Bonner Mall opposed vacatur, and the Court set the
vacatur issue for briefing and argument.



38
   See e.g., Valley Drug v. Geneva, supra note _ at 1306-9 (rejecting use of outcome of litigation as a proxy
for ex-ante knowledge of invalidity).
39
   There are also administrability issues with this test. Id. at 1309-10.
40
   513 U.S. 18 (1994).


                                                     10
    In its decision, the Court recognized that vacatur of a existing judgment was proper
when the controversy presented for review becomes moot due to circumstances
unattributable to any of the parties or when mootness results from the unilateral actions of
the party who prevailed in the lower court. However, the Court held that vacatur was not
generally proper where mootness results from a voluntary settlement of the parties. In
the latter case, the judgment below was not unreviewable, but simply unreviewed by
choice of the parties. The Court found mootness by settlement was insufficient to
overcome opposing considerations that favor denying vacatur. These include the
advancement of “the public interest” in preserving judicial precedent and the proper
course of appellate procedure.41 As a result, “the losing party has voluntarily forfeited his
legal remedy by the ordinary processes of appeal or certiorari, thereby surrendering his
claim to the equitable remedy of vacatur”.42 The court held that when a case is mooted by
the voluntary settlement of the parties, vacatur was now an “extraordinary remedy” to be
granted only in “exceptional circumstances”.43

    The extent to which relitigation can occur under U.S. Bancorp will be determined by
how courts interpret whether or not “exceptional circumstances” exist. The Court’s
opinion suggests limited circumstances in which vacatur based on voluntary settlement
should be allowed. Indeed, the Second Circuit Court of Appeals decision in the
Tamoxifen antitrust case noted that a “[s]ettlement [a]greement which [is] contingent on
the vacatur of [a prior] district court judgment” such as the one used in the Tamoxifen
case would now be “held to be invalid in nearly all circumstances by the Supreme Court
[in U.S. Bancorp ].”44

     However, courts, including the Second Circuit, have not strictly applied the Court’s
“exceptional circumstances” standard. In practice, courts have found “exceptional
circumstances” in post U.S. Bancorp cases similar to that faced in the Tamoxifen
litigation. In Major League Baseball Properties,45 the Second Circuit accepted a
trademark owner’s argument that exceptional circumstances for vacatur existed because
accepting a settlement and forgoing an appeal that left an adverse judgment standing
could make its marks vulnerable in future litigation. The court, noted that “the only
damage to the public interest from such a vacatur would be that the validity of [the]
marks would be left to future litigation” and found exceptional circumstances exist where
“vacatur of the district court's order and opinion was a necessary condition of
settlement”. And in Microsoft Corp. v. Bristol Technology, Inc., the Second Circuit
found that exceptional circumstances existed, in part, because a vacatur of a federal
41
   The Court, citing Justice Stevens dissent in Izumi, 513 U.S. 18 (1994), noted that “Judicial precedents are
presumptively correct and should stand unless a court concludes that the public interest would be served by
a vacatur”.
42
   U.S. Bancorp, supra note _ at 25,
43
   Id. at 26, 29. The Court also addressed the policy argument that vacatur facilitated settlement. The Court
found this argument incomplete, noting that vacatur would facilitate settlement at the appellate stage but
may deter settlement at an earlier stage. See also Jill E. Fisch, Rewriting History: The Propriety of
Eradicating Prior Decisional Law Through Settlement and Vacatur,76 CORNELL L. REV. 589 (1990-1991).
44
   In re Tamoxifen Citrate Antitrust Litig., 466 F.3d 187, 194 (2d Cir. 2006). The court did not revisit the
vacatur in that case, as the rule in announced in U.S. Bancorp does not apply retroactively. See U.S.
Phillips Corp. v. Sears Roebuck & Co., 55 F.3d 592, 598 (Fed.Cir. 1994).
45
   Major League Baseball Properties v. Pacific Trading Cards, Inc., 150 F.3d 149 (2d Cir. 1998)


                                                     11
court’s interpretative opinion of a state statute was “perhaps dispensable” from a
precedential perspective. Moreover, motions for vacatur following the voluntary
settlement of the parties have been granted in several recent patent cases.46

    Given that some courts have allowed parties to use vacatur to escape the effects of
non-mutual collateral estoppel, an important question is whether a discernable standard
for the finding of “exceptional circumstances” has emerged from these cases. Indeed, the
Court’s focus on the effect of precedent suggests one might broadly distinguish between
vacating decisions of an appeals court, which was the setting in U.S. Bancorp, and the
setting in Tamoxifen where the vacatur is applied to a district court decision. The
Second Circuit noted this distinction in ATSI Communications, observing that the value
of precedent, “an important consideration when a case becomes moot before the Supreme
Court,” is “less compelling” when, as here, the judgment to be vacated is one of a federal
district court.47 “District court decisions, unlike the decisions of States' highest courts
and federal courts of appeals, are not precedential in the technical sense: they have
collateral estoppel, res judicata, and “law of the case” effects, but create no rule of law
binding on other courts.”48 However, it concluded that no such distinction was warranted
under U.S. Bancorp v. Bonner Mall since the Court held that their decision applied to
courts of appeals. The ATSI panel also considered whether “exceptional circumstances”
existed based on the parties argument that “[t]he district court's decision does not purport
to make new law; it merely applies existing law to the unique facts of this case. Thus, the
public has no interest in the [district court's] Judgment and [its] Orders in terms of the
development of the decisional law.” However, the court did not find the parties’ law/fact
distinction persuasive. 49

    One way to interpret the cases is through use of a narrower law/fact distinction than
the one proposed by the appellant in ATSI. Such a distinction would not be made on the
basis of an inherent distinction between issues of law and issues of fact, but perhaps
based on one suggested by Allen & Pardo where the decision to label and issue as one of
“law” or “fact” is best viewed as a functional one based on who should decide the issue
under what standard.50 This distinction could be the basis for a positive theory of
allowing vacatur conditioned on settlement under the Court’s “exceptional
circumstances” test. Thus, exceptional circumstances can exist when the risk and costs of
type I error are high, the right of review is limited to review under a clearly erroneous
standard, and where vacated decision has little precedential value. Thus, the grant of
vacatur in trademark cases where type I errors are costly, that are of little precedential
46
   See http://www.patentlyo.com/patent/2010/03/settlement-vacatur-whitewashing-an-invalidated-
patent.html, discussing Gracenote Inc. v. MusicMatch, 2004 U.S. Dist. Lexis 17617 (2d. Cir 2005),
http://www.patentlyo.com/patent/2010/03/vacating-an-invalidity-rulings-as-a-condition-of-a-negotiated-
settlement.html, discussing Block Financial v. Lending Tree (W.D. Mo. 2010) and other recent cases.
47
   Russman v. Bd. of Educ., 260 F.3d 114, 122 n. 2 (2d Cir. 2001).
48
   ATSI Communications, Inc, v. The SHAAR Fund, Ltd, et al., 547 F.3d 109 (2008) (considering, but
rejecting such a distinction.
49
   See generally, Geoffrey C. Hazard, Jr., Preclusion as to Issues of Law: The Legal System’s Interest, 70
IOWA L. REV. 81 (1984-1985) (discussion the law/fact distinction and preclusion).
50
   Ronald J. Allen and Michael S. Pardo, The Myth of the Law-Fact Distinction, 97 N. W. U. L. REV. 1771
(2003). See also Thomas G. Field, Jr., Law and Fact in Patent Litigation: Form versus Function, 27 IDEA
153 (1987).


                                                    12
value, and where the mixed issues of law and fact involved are reviewed under a clearly
erroneous standard would be consistent with this theory. The same would hold for
Hatch-Waxman patent cases similar to the Tamoxifen Citrate Antitrust case.51 Other
cases in which the risk of factual error or the cost of type I error were small would not
trigger an “exceptional circumstances” exception to the Court’s U.S. Bancorp rule.

    A further question arises once the de facto decision to create a broad “exceptional
circumstances” exception to U.S. Bancorp in intellectual property cases has been made –
that is, whether is would be better to directly revisit the Court’s earlier decision in
Blonder-Tongue. That is, if the “exceptional circumstances” test is used as a relitigation
gatekeeper, is there any advantage or disadvantage to such a test relative to an explicit
rule that allows patentees to relitigate their invalidated patents. In the following sections,
we use the economic model of litigation and settlement to explore this question.


III.     An Economic Model of Litigation and Settlement

         A.       The General Model

     In this section, we set out a model of litigants’ incentives to litigate and settle cases.
Our model deviates from the standard two party model in several ways. First, we
examine the case where there is a common patentee (Firm p) facing multiple potential
infringers in sequence (Firms i, j, … , N). We purposely do not use the terms plaintiff and
defendant as the principal distinction here is between the repeat litigant (in this case, the
patentee) and the non-repeat litigant (the infringing firms). Moreover, the patentee can
be the plaintiff or defendant depending upon whether or not he initiates the action as an
infringement action, or whether the infringer initiates the action when seeking a
declaratory judgment regarding the validity or enforceability of a patent. In addition our
model takes into account the persuasive, preclusive and precedential effect the first
litigation has on the outcome of subsequent litigation. Third, while the standard model
focuses on differences in the litigants’ estimates of the probability that the plaintiff
prevails, we abstract from that issue and assume that there is general agreement over
these probabilities. Fourth, while most economic models examine a setting where
parties are litigating over damages, in our setting, damages are not a primary concern. In
declaratory judgment actions involving patents, for example, a resolution of the status of
the patent is sought before any damages have occurred.52 Likewise, as noted in Section
II, in patent actions involving generic and brand name pharmaceutical companies under
the Hatch-Waxman Act, litigation over the validity or enforceability of a patent generally



51
   Another way in which error correction can be facilitated would be to change the standard of review
applicable to particular factual issues or mixed issues of law and fact. See Allen & Pardo, supra note 50, at
_, suggesting that in recent decisions, including Cooper Industries v. Leatherman Tool Group, Inc, 532
U.S. 424 (2001) and Markman v. Westview Instruments, 517 U.S. 370 (1996), the Court has determined
issues to be questions of “law” in cases that are difficult to explain based on history or tradition.
52
   The federal courts have recently expanded the ability of potential infringers to bring declaratory
judgment actions. See MedImmune Inc., v Genentech, Inc., 549 U.S. 118 (2007).


                                                     13
takes place before damages have occurred.53 Thus, in these cases, the primary effect of
the litigation is to determine whether or not a valid and enforceable intellectual property
right exists, so the effect of injunctive relief both as part of a judgment and as part of a
settlement is the primary concern.

   To derive the settlement range in such a setting, we must examine the litigant’s trial
payoffs. The maximum entrant i is willing to pay is determined by his expected cost of
going to trial:

(1)      Ti = pi (Di + Li) - (1 - pi)Gi + Ci,

where pi is Firm i’s estimate that the patentee will prevail, Di are the damages involved in
the cases, and Gi and Li are the net external gains and losses for litigant i imposed upon
judgment, and Ci is the marginal cost of going to trial over settling. An acceptable
settlement would be any offer in which the monetary payment M plus the “injunctive”
costs of a settlement relative to the status quo, Ii, are less than the entrant’s cost of going
to trial:54

(2)      S = M + Ii ≤ T i

Similarly, the minimum the patentee is willing to accept is determined by his trial payoff:

(3)      Tp = pp (Dp + Gp) - (1 - pp)Lp – Cp,

so acceptable settlements for the patentee would include settlements where the monetary
settlement M plus the non-monetary benefits of a settlement relative to the status quo,
Ip,55 are greater than the benefits of going to trial:

(4)       S = M + Ip ≥ T p .

A sufficient, but not necessary, condition for litigation is the absence of a bargaining
range. A bargaining range will be absent when Tp – Ip > Ti – Ii, or when:

(5)      pp(Dp + Gp) - (1 - pp)Lp - Cp - Ip > pi (Di + Li) - (1 - pi)Gi - Ii + Ci.

or equivalently,

53
   Under the Hatch Waxman act, entry by generics is conditioned upon FDA approval of an Abbreviated
New Drug Application (ANDA). When generics attempt to enter prior to the expiration of a patent
covering the drug, the patentee has 45 days to sue for infringement. If this occurs, automatic 30-month stay
on FDA approval of the ANDA is triggered. As a result, patent litigation generally takes place during the
30-month stay on FDA action imposed under the Hatch-Waxman Act. For a description of the ANDA
process and litigation under this act, see Michael, A. Carrier, Unsettling Drug Patent Settlements: A
Framework for Presumptive Illegality, 108 MICH. L. REV. 37 (2009), and the discussion in Section III,
infra.
54
   Note that if the settlement generates benefits to the firm over and above the status quo, Ii < 0.
55
   If the settlement does not alter the outcome relative to the case where the suit is terminated, this term will
be zero.


                                                       14
(6)        pp(Dp + Gp) - pi (Di + Li) - (1 - pp)Lp + (1 - pi)Gi + Ii – Ip > Ci +Cp.

    Equation (6) shows that the sufficient condition for litigation is more likely to be
satisfied, ceteris paribus, if the litigants are relatively optimistic (pp > pi), if the patentee
has relatively large damages or high external benefits from a favorable judgment, if the
infringer has relatively large external gains from a judgment favorable to him, or if the
infringer’s non-monetary costs from a settlement are larger than the patentee’s non-
monetary gains.

     Note that optimism is not required to generate litigation, as is the case in the standard
model of litigation and settlement. Intuitively, judgments can have intrinsic value to the
litigants, thus creating a demand for a judgment when these effects are positive, and
litigation aversion when they are not. Examples of such judgment specific benefits
would be the precedential or persuasive effects of a favorable judgment. Such effects
produce external gains for the patentee by lowering the probability that the patent will be
successfully challenged in the future. Another example of a judgment specific external
effect is the negative effect of non-party preclusion, which will prevent the patentee from
relitigating the validity of the patent held invalid in the first case.

    To see this, consider the case where there are symmetric stakes, and no disagreement
on the probability the plaintiff will prevail, Dp = Di = D and pp = pi = p. This yields the
following sufficient condition for litigation:

(7)        p (Gp - Li) + (1 - p)(Gi - Lp) + Ii – Ip > Ci +Cp.

Equation (7) shows that even in the absence of disagreement over p, litigation will be
encouraged, ceteris paribus, if the patentee’s expected external gain from a favorable
judgment is greater than the infringer’s expected external loss from such a judgment,
when the infringer’s expected external gain from a favorable judgment is greater than the
patentee’s loss from such a judgment, and when the infringer’s non monetary costs of a
settlement are greater than the patentee’s non monetary gains from a settlement.

           B.      Injunctive Settlements & Reverse Settlements in Litigation between
                   Two Parties

     In a recent set of papers, Hylton & Cho examine a variant of the model in Section
II.56 They model litigation and settlement when non-monetary or injunctive relief is an
important part of the effects of settlement. Hylton & Cho apply this model to examine the
properties and effects of competition blocking injunctive settlements such a entry
blocking reverse patent settlements. These papers, and the expansion of the litigation and
settlement model to include the effects of non-monetary settlements, are an important
contribution to the literature.



56
     See Hylton & Cho, supra note _.


                                                 15
     However, one limitation of their analysis is that their model does not consider the
negative external effects of a judgment against the patentee. Specifically, their model
examines the case where Gi = Lp = 0. Because of this assumption, the Hylton & Cho
model best captures the litigants’ incentives in a setting with a single potential entrant
into the patentee’s market (N = 1) who challenges the patent. In concentrating on this
setting, their model abstracts from and does not capture the effects a judgment has on
future litigation. This assumption also implies that the entrant will enter in the absence of
a judgment for the patentee. Part B.1 of this Section examines their model. Part B.2
examines the alternative assumption where the single entrant does not enter unless there
is a judgment that the patent is invalid.

       1.      Entrant Enters in the Absence of a Judgment for the Patentee.

    Hylton & Cho consider settlements that alternatively allow and preclude entry post
settlement. Hylton & Cho label settlement agreements as “non-injunctive” settlements
when the settlement preserves the status quo. Their model implicitly assumes that entry
occurs post settlement if it is not explicitly precluded in the settlement, so the status quo
is entry. In this setting, a non-injunctive settlement results in the patentee agreeing not to
enforce the patent against the entrant and acquiescing to entry. Ii = Ip = 0, and litigation
occurs when:

(8)    p (Gp - Li) > Ci +Cp

    Under these conditions, litigation can occur when the external gain to the patentee is
greater than the external loss to the entrant. In the case of a single potential entrant
challenging the patent, this condition will hold given normal assumptions regarding the
nature of competition in the market. To see this, suppose the patentee and a successful
entrant/challenger will make duopoly profits, πpd and πid respectively, during the life of
the patent. If we assume that the entrant will enter if the patentee does not file suit in
response to entry, both will make duopoly profits in the absence of a suit.

    If there is judgment for the plaintiff patentee, the patentee will make monopoly profits
 m
π , and his marginal gain from a favorable judgment will equal Gp = πm - πpd. The
entrant challenger will be excluded from the market for the remaining life of the patent,
so his marginal loss is Li = πid. Since the patentee’s monopoly profits will be greater
than the sum of duopoly profits, πm > πpd + πid, Gp - Li =πm – (πpd + πid) >0. Moreover,
the condition for litigation is more likely to be satisfied when there is a high probability p
that the patent will be held valid and enforceable.

    In addition, they also consider the case where the settlement implements the outcome
of a judgment for the plaintiff (where the defendant recognizes the validity of the patent
and delays entry until the expiration of the patent). With such an entry blocking
settlement, Ii = Li and Ip = Gp. Note that this particular entry blocking “injunctive
settlement” results in Ii < Ip, which increases the settlement range relative to the “non-
injunctive” settlement. The condition for litigation becomes:



                                              16
(9)      (p – 1)(Gp - Li) > Ci +Cp

Indeed, because Gp - Li > 0, (9) is never satisfied. Thus, in all cases where there is no
disagreement regarding the probability that patentee will prevail, a feasible “injunctive
settlement” that precludes post-settlement entry exists.57

    In the case of a settlement that allows post-settlement entry, payments flow from the
entrant to the patentee. In contrast, an entry-blocking settlement will include the
possibility of payment from the patentee to the entrant in the absence of large damages.
To see this, settlement payment must satisfy the following:

(10)      pp (Dp + Gp) – Ip - Cp ≤ M ≤ pi (Di + Li) - Ii +Ci.

If entry occurs after settlement, Ii = Ip = 0, and D = 0, (10) becomes

pGp – Cp ≤ ME ≤ pLi +Ci.

If the settlement delays entry until after the patent expires, Ii = Li, Ip = Gp, and D = 0,
(10) becomes:

(11)     (p – 1)Gp – Cp ≤ MB ≤ (p – 1)Li +Ci.

For positive expected value challenges to the patent, MB < 0.

         2.       Entry Does Not Occur Absent a Judgment for the Entrant

    The Hylton & Cho analysis assumes that entry will occur in the event of an
unlitigated patent. However, in patent litigation, this assumption may not hold. Patent
damages, especially those for willful infringement, can include enhanced (trebled)
damages and the award of costs and attorneys’ fees.58 Thus, in many cases, potential
licensees and others who may be accused of infringing patents may be deterred from
entering or induced to take out licenses, even in cases where they doubt the validity of a
patent.59



57
   Hylton & Cho, supra note _ at _.
58
   See 35 U.S.C. §284-5, awarding “damages adequate to compensate for the infringement, but in no event
less than a reasonable royalty … together with interests and costs as fixed by the court. In addition, the
statute provides that “the court may increase the damages up to three times the amount found or assessed”
and that the court “in exceptional cases may award reasonable attorney fees to the prevailing party.” See,
e.g., Rochelle Cooper Dreyfuss, Dethroning Lear: Licensee Estoppel and the Incentive to Innovate, 72 VA.
L. REV. 677 (1986) (discussing the deterrent effects of patents).
59
   For an economic analysis of this issue, see Michael Risch, Patent Challenges and Royalty Inflation, 85
IND. L. J. _ (forthcoming 2010) (Noting that the size of the royalty payment will reflect the uncertain status
of the patent, discussing the effect of covenants not to sue on the size of royalty payments, and discussing
how the federal courts’ longstanding failure to enforce such covenants and related contracts will inflate the
size of such royalty payments).


                                                      17
    The analysis when the entrant would not enter absent of a favorable judgment that
invalidated the patent or made the patent unenforceable is similar to that presented in part
B.1 of this Section. When entry will not occur absent a judgment invalidating the patent,
Gp = Li = 0, and the condition for litigation (7) becomes:

(12)   (1 - p)(Gi - Lp) + Ii – Ip > Ci +Cp

Under these conditions, Lp = πm - πpd and Gi = πid so Gi - Lp < 0. Thus, when the
settlement implements the outcome of a judgment for the patentee, Ii = Ip = 0, all cases
will settle, as (12) will never be satisfied. For positive expected value challenges to the
patent, these entry-blocking settlements will result in a negative or reverse payment MB <
0, as

(13)   (p – 1)Lp – Cp ≤ MB ≤ (p – 1)Gi +Ci < 0.

    If we consider settlements that implements the outcome of a judgment for the entrant
by allowing post settlement entry, Ii = -Gi, Ip = -Lp. When settlement allows entry, the
patentee can prefer judgment over settlement, as judgment is the only way to prevent
entry. The condition for litigation becomes:

(14)   p(Lp - Gi) > Ci +Cp

     Given that Lp - Gi = πm – (πpd + πid) > 0, condition (14) can be satisfied when p is
large and when the difference between the monopoly profits and the joint duopoly profits
is large relative to the joint costs of litigation.

    In such cases where an entry allowing settlement is possible, the monetary portion of
the entry accommodating settlement ME will be bound by:

(15)   pLp – Cp ≤ ME ≤ pGi +Ci.

ME will be positive as long as pLp is greater than the costs of litigation.

    Moreover, it can be shown that there exists a settlement that prevents entry that
Pareto dominates any feasible settlement that allows entry. To see this, take a feasible
entry allowing settlement with payment ME that satisfies (15). The patentee’s net payoff
will equal =πpd + ME, and the entrant’s will equal πid – ME. Now consider a entry
blocking reverse settlement that makes the entrant indifferent, so that MB = -πid + ME.
The patentee’s net payoff will equal πm + MB = πm – πid + ME. The patentee’s payoff
will be greater than with the entry allowing settlement if πm – πid + ME > πpd + ME or
equivalently if πm > πid +πpd. Because the monopoly profits are greater that the joint
duopoly profits, this settlement will be strictly preferred by the patentee. We now only
need to show that an entry blocking reverse settlement exists. Using (15), the largest
feasible entry allowing settlement MEMAX = pGi +Ci, so the largest entry blocking
payment (i.e., the smallest reverse payment from the patentee to the infringer) MBMAX = -
(p - 1)Gi +Ci, which is the upper limit for MB from (13). Using (15), the smallest feasible


                                              18
entry allowing settlement payment MEMIN = pLp – Cp. Thus, the smallest feasible entry
deterring settlement payment (or the largest reverse payment) MBMIN = pLp – Cp – Gi.
Using (13), this minimum entry deterring payment is feasible as long as MEMIN = pLp – Cp
– Gi > pLp – Cp – Lp, or equivalently, if Gi < Lp. As noted above, the patentee’s loss
exceeds the infringer’s gain, so a feasible Pareto preferred entry-blocking settlement
exists. Intuitively, the former settlement allows the patentee to maintain monopoly
profits, while the latter type of settlement results in the lower joint profits associated with
duopoly. The higher profits associated with former type of settlement allows the parties
to find an entry blocking settlement that yields higher payoffs to both parties.60 Thus, the
settlement where a defendant/entrant recognizes the validity of patentee/plaintiff’s patent
and results in negative MB is Pareto preferred because it preserves the monopoly of the
patentee.


IV.     Multiple Serial Entrants and Relitigation in Patent Cases

     The analysis presented in Section III abstracts away from the effects of the current
litigation has on non-parties. However, in intellectual property litigation, the non-party
effects are often central to litigants’ incentives to litigate of settle, and also their
incentives to invest in litigation. In this section, we examine how the existence of
multiple serial entrants alters these incentives.

     Consider extending the two party example presented in Section III to the case where
there are two potential entrants, Firm i and Firm j, facing a common patentee, Firm p.
Assume infringement is not an issue, and that entry will not take place absent a judgment
holding the patent invalid or unenforceable. The existence of a second entrant (Firm j)
potentially alters the analysis presented above by altering the external payoffs in the
litigation between the first entrant (Firm i) and the patentee. The extent to which the
external effects are altered will depend upon how the outcome of the current case, either
through litigation or settlement, alters the probability of entry by the second entrant. This
in turn will be a function of q, the probability that the patentee will successfully defend
the patent if challenged by Firm j.

     The effects of precedent, preclusion, and persuasion will affect this probability.
These effects are taken into account by extending the model presented above to allow
judgment in the first case to alter q. Specifically, we capture this effect on subsequent
cases by including an additive term δ that adjusts the probability the patentee will obtain
a judgment in the second case. Thus, if the probability the patent will be held valid in the
first case is p, the probability that it will be held valid in the second case will equal q = p
+ δ. When the patentee litigates against the first entrant and the patent is held valid and
infringed, it makes it less likely that the second entrant will be able to successfully
challenge the patent, so δ = δ+ ≥ 0. Following a loss in the first case, the second entrant
will be more likely to successfully challenge the patent, so that δ = δ- ≤ 0.


60
  This point has been recognized by others. See, e.g., Roger D. Blair & Thomas F. Cotter, Are Settlements
of Patent Disputes Illegal Per Se? 47 ANTITRUST BULL. 491 (2002).


                                                   19
    The direct effect on the payoffs in the litigation between Firm i and the patentee will
depend upon how the spillover effects alter the probability of entry. This in turn will
depend upon the patentee’s prior on whether or not the second entrant will challenge the
patent in the absence of a judgment for or against the first entrant. Consider the
following cases, z and x:

   (Case z) No Second Challenge in the Absence of a Judgment Adverse to the
Patentee in the First Case

    Suppose that, given the parties’ prior and common estimate of the probability that the
patent will be held valid, the first entrant will choose to challenge the patent and enter if
held invalid. However, at the current q0 = p, the second entrant will not. 61 Under this
assumption, a judgment for the patentee in the first case will not result in a challenge to
the patent by Firm j. Thus, the monopolist will continue to make monopoly profits during
the life of the patent. The competitive outcome in this case is the status quo without a
judgment (no entry by either Firm i or j), so that D = 0, and Gp = Li = 0. Likewise, a
settlement in the first case will not induce a challenge by the second entrant. As a result,
the injunctive effects of a settlement are also identical to those set out in the single entrant
model in Section III B.1.

    However, if the patentee loses the first litigation, a challenge to the patent and the
possibility of entry by Firm j can be induced. Suppose there is some threshold δ* < 0
below which the second entrant will be induced to challenge the validity of the patent and
enter if the challenge is successful. Let q* = q0 + δ*. We need to consider two cases in
this setting, the first where δ- > δ* so that q- > q*, and the second where δ- ≤ δ* so that q-
≤ q*. If δ- > δ*, there will be no challenge and thus no entry by Firm j. In this case,
Firm i would enter but Firm j would not, so a duopoly structure would result. As a result,
the external payoffs, and thus the incentives in litigation, would be identical to those
derived in Section IIIb.62

    However, if instead δ- < δ*, an adverse judgment in the first case will increase the
external losses faced by the patentee. Instead of entry by only Firm i and duopoly profits,
the patentee now faces entry by Firm j with probability q- = p + δ-, resulting in expected
profits equal to

(16)    E(πp|j challenges) = q-πpd + (1 – q-)πpc,

where πpc < πpd. Thus, the expected profits that result in when the patentee receives an
adverse judgment in the first case are smaller than those in the single entrant case, which
equal πpd.


61
   Such a scenario might occur under the Hatch-Waxman Act. Under the Act, the first to file a Paragraph
IV ANDA is given a 180 day exclusive marketing period as an incentive to challenge patents. Subsequent
Paragraph IV ANDA filers do no receive this benefit and thus have a smaller incentive to enter the market,
whether or not the first Paragraph IV ANDA filer enters the market or not.
62
   That is Gi = πid and Lp = πm - πpd


                                                    20
    Let φ denote the probability that an adverse decision against the patentee does not
result in Firm j challenging the patent, i.e., φ = Prob(δ- > δ*). The expected profits for
the patentee after a loss equals:

(17)   E(πp|judgment for Firm i) = φπpd + (1 - φ)E(πp|j challenges)

Since E(πp|j challenges) < πpd, E(πp|judgment for Firm i ) <πpd

If we denote the external losses in the single entrant case as Lps and those in the multiple
entrant case z as Lpz, then Lps = πm - πpd < Lpz = πm - E(πp|judgment for Firm i).

    In addition, the external gains to the first entrant are decreased. Intuitively, the
positive spillover effect a favorable judgment for Firm i has on Firm j has a negative
effect of Firm i. Because Firm i’s profits after Firm j enters, πic, are less than its duopoly
profits πid, Firm i will now make lower profits with probability q-:

(18)   E(πi|j challenges) = q-πid + (1 – q-)πic < πid

   Firm i’s expected profits after he successfully invalidates the patent equal:

(19)   E(πi|judgment for Firm i) = φπid + (1 - φ)E(πi|j challenges) < πid.

    Equation (19) equals Firm i’s gain from a judgment invalidating the patent. If we
denote the external gains to Firm i in the case where he is the sole entrant as Gis and those
in the multiple entrant case z as Giz, then (19) defines Giz, and Giz < Gis = πid. The
condition for litigation becomes:

(20)   (1 - p)(Giz - Lpz) + Ii – Ip > Ci +Cp

    Since Giz < Gis, Lpz > Lps, and given that Ii = Ip = 0, the presence of a second entrant
will increase the pressure to settle relative to the single entrant case. When there is
agreement, all cases settle if entry-blocking settlements are allowed. The range of
feasible entry blocking settlements is given by:

(21)   (p – 1)Lpz – Cp ≤ MB ≤ (p – 1)Gi z + Ci < 0.

     The patentee’s maximum acceptable reverse payment increases (i.e., the lower bound
for MB falls), reflecting the effect of the larger losses caused by the potential for multiple
entry. Because these losses can exceed the first entrant’s now diminished gains from
litigation, the patentee may be willing to give the first challenger more than his expected
gross benefit from the litigation (1 – p)Gi z. Moreover, given that Gi z is smaller, the net
benefits of a patent challenge by Firm i are now smaller, and there is a higher probability
that the patent will not be challenged at all. The patentee’s relative benefits of the entry
blocking over the entry allowing settlement is also made greater by the greater benefits of
avoiding an adverse judgment. Moreover the first entrant also benefits from settlement,



                                               21
as the patent is not weakened, and the second entrant is not induced to challenge the
patent.

     If a settlement allows entry, and given that Ii = -Gis, Ip = -Lps, the condition for
litigation (20) becomes:

(22)     (p - 1)(Lpz - Giz) + Lps – Gis > Ci +Cp.

The first term is negative, and the second is positive, given that the loss to the patentee is
greater than gain to the entrant. Since (Lpz - Giz) > (Lps – Gis), equation (22) will be
positive for large values of p and negative for small values of p. Again, stronger patents
that are challenged will be litigated, while relatively weaker ones will settle and allow
entry. The range of feasible settlement payments that allow entry is given by:

(23)     (p – 1)Lpz + Lps– Cp ≤ ME ≤ (p – 1)Giz + Gis + Ci

The range of feasible settlement payments is smaller than in (21), and can cease to exist
for p close to 1.

    (Case x) Second Entrant Will Challenge the Patent in the Absence of a Judgment
for the Patentee in the First Case

     The example above still does not generate litigation if entry-blocking settlements are
available to the parties. However, if the second potential entrant will challenge the patent
if there is no judgment favoring the patentee, then litigation can be generated even in the
absence of optimistic disagreement between the parties. Intuitively, obtaining a judgment
that holds the patent valid creates a the spillover effect that can diminish the probability
of future challenges, an effect not present when future challenges were contingent on a
loss in the first litigation. As a result, a patentee might prefer litigation and a judgment
against Firm i over an entry blocking settlement with Firm i because of the effect it has
on the probability of blocking Firm j’s entry.63

    To see this, note that if the patentee settles with Firm i, Firm j will still challenge the
patent, and the patentee’s expected profits will equal:

(24)      E(πp0) = q0πm + (1 – q0)πpd.

    When the patentee loses against Firm i, Firm i will enter and Firm j will challenge the
patent and enter with probability q-. The payoff for Firm i is given by equation (18), so:


63
   It is possible that the filing of a suit can deter entry, an thus raise potential antitrust concerns. However,
such activity is protected from antitrust liability under the Court’s Noerr-Pennington doctrine which
protects the right to petition the government, including the right to file suits. One exception is if the suit is
a sham. However, the Court has limited this exception through the application of a strict standard for sham
litigation generally, and in patent suits in particular. See Professional Real Estate v. Columbia Pictures,
508 U.S. 49 (1993); Walker Process Equipment, Inc., v. Food Machinery Corp., 382 U.S. 172 (1965).


                                                       22
(25)     Gi = E(πi|j challenges) = q-πid + (1 – q-)πic < πid.

     The patentee’s external loss from a judgment for Firm i equals:

(26)     Lp = E(πp0) - E(πp|j challenges) = q0πm + (1 – q0– q-)πpd - (1 – q-)πpc.

    Now consider what happens when the patentee obtains a favorable judgment against
Firm i. Given a judgment for the patentee, Firm i is out of the market, so Li = 0. Let ω =
Prob(δp > δ**), where δ** > 0 is the threshold value of δ above which a challenge to the
patent by Firm j is deterred. Define q** = q0 +δ**. If a challenge by Firm j is deterred,
the patentee will make monopoly profits πm. If it is not, the patentee will make monopoly
profits with probability q+ = p + δ+, and duopoly profits with probability 1 – q+. The
expected profit of the patentee will equal

(27)     E(πp|judgment for p) = ωπm + (1 - ω)[q+πm + (1 – q+)πpd].

The patentee’s external gain from a favorable judgment

(28)     Gp = E(πp|judgment for p) - E(πp0)

         Gp = ωπm + (1 - ω)[q+πm + (1 – q+)πpd] – [q0πm + (1 – q0)πpd] > 0.

    Let Lix, Gix, Lpx and Gpx denote the external effects derived in case x. The
comparisons Firm i to the single entrant case are: Lix = Lis = 0, Gix < Gis. As was the case
in case z above, the potential of multiple entry reduces the incentives for Firm i to
challenge the patent. The comparisons for the gain to the patentee to the single entrant
case are that Gpx > Gps = 0. As noted above, the external benefits from a judgment
holding the patent valid and infringed are the reduction in probability that Firm j will
challenge the patent and a reduction in the probability that Firm j will be successful in
those cases where a challenge in made. The relationship between Lpx and Lps is
ambiguous.64

    The positive external gains from obtaining a favorable judgment can induce the
patentee to litigate, even when entry-blocking settlements are available to the parties.
The condition for litigation when entry blocking settlements are available becomes:

(29)     pGpx + (1 – p)(Gix – Lpx) > Ci + Cp,

which can be satisfied if pGpx is large.

     The bounds for an entry blocking settlement are:
64
   Recall, Lps = πm - πd, while Lpx = [qoπm + (1-qo)πpd] – [q-πpd + (1-q-)πpc]. The first bracketed term of Lpx
is less than πm (due to the fact that the patentee faces probable entry by Firm j if he does not litigate the
status of the patent) while the second bracketed term is less than πd (due to the possibility of a more
competitive market with more than one entrant) As a result, the effect of an additional entrant on the
patentee’s external losses at trial is ambiguous.


                                                      23
(30)     pGpx – (1 – p)Lpx – Cp < MB < (p – 1)Gix + Ci. < 0.

Equation (30) shows that the patentee’s maximum acceptable reverse payment will be
reduced by the entry deterring benefit a judgment against Firm i has on Firm j. If this
effect is large enough, it may cause the lower bound to exceed the upper bound, resulting
in the absence of a bargaining range. As was true under case z, the existence of an
additional potential entrant causes the upper bound to increase, resulting in Firm i being
willing to accept a smaller reverse payment to delay entry until the patent expires.

    For an entry accommodating settlement, Ii = -(q0πid + (1 – q0)πic) < 0 and Ip = q0(πpd
- πm) + (1 – q0)(πpc - πpd) < 0.65 The condition for litigation for and entry accommodating
settlement will be:

(31)     pGpx + (1 – p)(Gix – Lpx) + Ii - Ip > Ci + Cp,

Compared to the condition for litigation with an entry blocking settlement, the condition
for litigation will be more likely to be satisfied with an entry accommodating settlement
as Ii - Ip = q0(πm – (πpd+πid)) + (1 – q0)(πpd – (πpc +πcc) > 0.

The lower bound for feasible entry accommodating settlements increases by -Ip and the
upper bound also increases, but by a smaller amount -Ii.

(32)     pGpx – (1 – p)Lpx – Ip - Cp < ME < (p – 1)Gix – Ii + Ci.

     (The Combined Case)

    Case x and Case z can be combined by specifying a prior ρ that Firm j will not
challenge the patent (i.e., Case z holds). In this case, the patentee’s baseline outcome and
the his expected profit if he agrees to an entry blocking settlement with Firm i equals:

(33)     E(πp0,ρ) = ρπm + (1 - ρ)E(πp0).

    Firm i’s baseline profits will be πi = 0, and Ii = Ip = 0 for an entry blocking
settlement. Firm i’s external loss Li = 0, and its external gain from a judgment will equal
the expected profits from a judgment in his favor:

(34)     Gi(ρ) = ρGiz + (1 - ρ)Gix, or

         Gi(ρ) = ρ(φπid + (1 - φ)(q-πid + (1 – q-)πic) + (1 - ρ)(q-πid + (1 – q-)πic).

Firm i’s external gain from litigation in the combined case is less than the gain when he is
the sole entrant.

65
  The analysis here assumes that the settlement-induced entry of firm i and the lower associated profits doe
not deter Firm j from challenging the patent.


                                                    24
   The patentee’s expected profit after a judgment in favor of Firm i equals (1 - ρ)[q-πpd
+ (1 – q-)πpc] +ρ[φπpd + (1 - φ)(q-πpd + (1 – q-)πpc)]. The external loss from litigation
equals:

(35) Lp(ρ) = ρπm + (1-ρ)(q0πm + (1-q0)πpd) – {ρ[φπpd + (1-φ)(q-πpd + (1-q-)πpc)] + (1-
ρ)[q-πpd + (1-q-)πpc]}.

    Compared to the single entrant case, the size of the patentee’s loss from a judgment
for Firm i is ambiguous. The expected status quo profits in (35) are smaller than in the
single entrant case because of the patentee’s belief that he will face entry in the absence
of a judgment with probability (1 - ρ). However, the patentee’s expected profits after
judgment for Firm i also fall because of the potential entry by Firm j.

    The patentee’s external gain from a favorable judgment is positive in the combined
case, and equals:

(36)   Gp(ρ) = (1 - ρ){ωπm + (1 - ω)[q+πm + (1 – q+)πpd] – [q0πm + (1 – q0)πpd]}.

   The condition for litigation is given by:

(37)   pGp(ρ) + (1 – p)(Gi(ρ) – Lp(ρ)) > Ci + Cp,

which can be satisfied if pGp(ρ) is large. Thus, the patentee will be more likely to litigate
when ρ is small (the patentee’s prior estimate of the probability that the second entrant
will challenge the patent is large, and when the litigation deterring effect of a persuasive
judgment upholding the validity of the patent is large).

   The bounds for an entry blocking settlement are:

(38)   pGp(ρ) – (1 – p)Lp(ρ) – Cp < MB < (p – 1)Gi(ρ) + Ci. < 0.

The condition for litigation with an entry accommodating settlement is:

(39)   pGp(ρ) + (1 – p)(Gi(ρ) – Lp(ρ)) + Ii - Ip > Ci + Cp,

where Ii = ρ(-πid) + (1 - ρ)[-(q0πid + (1 – q0)πic)] < 0 and Ip = ρ(πpd - πm) + (1 - ρ)[q0(πpd
- πm) + (1 – q0)(πpc - πpd)] < 0. Since Ii - Ip > 0, the condition for litigation (39) is more
likely to be satisfied for an entry accommodating settlement than an entry blocking one.

Again, since Ii and Ip < 0, both the upper and lower bounds for an entry accommodating
settlement increase to:

(40)   pGp(ρ) – (1 – p)Lp(ρ) – Cp – Ip < ME < (p – 1)Gi(ρ) – Ii + Ci.




                                               25
V.     Relitigation Rules: Triplett, Blonder-Tongue, U.S. Bancorp v. Bonner Mall
and the Effects of Non-Mutual Non-Party Collateral Estoppel and Vacatur

         A.       Relitigation and the Triplett Rule

    The model in Section IV assumes that patentees and challengers are free to relitigate
the issue of patent validity or enforceability. That is, it models serial litigation under the
Court’s Triplett rule. If relitigation is allowed, the effects of the first litigation on the
future litigation involving an alleged infringer that was not a party to the first litigation
and not bound by the first judgment will be the extent to which the first court’s resolution
of an issue is found persuasive by a second court. In the model presented in the prior
Section, such effects are transmitted through the effects δ has on the outcome of litigation
involving Firm j. Note that the right to relitigate an issue does not mean that the issue
will be relitigated.66 Non-persuasive decisions in the model do not affect Firm j’s
decision to relitigate the validity of the patent. Even with a right to relitigate the issue of
validity, a persuasive decision upholding the validity of a patent in the first litigation can
deter a challenge to the validity of the patent by Firm j. Suppose case x holds so that
Firm j will challenge the patent if q = q0 = p. If the judgment upholding the validity of
the patent is persuasive, so that the probability the patentee will prevail against Firm j, q+
= p0 + δ+ rises above q**, Firm j will choose not to file a challenge to the patent. Thus,
the example shows that it is possible that persuasive decisions can reduce relitigation.

     Persuasive decisions can also serve to increase litigation. Suppose case z holds so that
Firm j would not choose to challenge the patent if q = q0 = p. A persuasive decision
finding the patent invalid can induce Firm j to challenge the patent if δ- is small enough
(i.e., large in magnitude and negative) so that q- = p + δ- falls below q*. However, if
Firm j is the only potential challenger left, such filed cases are unlikely to be litigated, as
such cases are likely to settle for the reasons derived in Section IV. On the other hand, if
the original holding is not persuasive, the holding in the first case will not have a
marginal effect on the decision of Firm j not to relitigate the issue of patent validity.

         B.       Blonder-Tongue and the Effects of Non-Mutual Non-Party Collateral
                  Estoppel

   In the context of patent litigation set out in the model above, under the Court’s
Blonder-Tongue rule and under the assumption that the patentee sued for infringement,67

66
   See Bruce L. Hay, Some Settlement Effects of Preclusion, 1993 U. ILL. L. REV. 48 (1993) (noting
importance of promoting finality is overstated given the effects that settlements would have on preventing
the costs of relitigation). See also Taylor v. Sturgell 533 U.S. at _ (2009), (noting that relitigation can be
suppressed by the effect of precedent and the facts that “the human tendency not to waste money will deter
the bringing of suits based on claims or issues that have already been adversely determined against
others.”).
67
   In theory, in a declaratory judgment action, the plaintiff would use a prior holding of invalidity
offensively under Parklane Hosiery v. Shore, 439 U.S. 322 (1979) to prevent the patentee from relitigating
this issue. However, filing of such actions are not necessary given that the patentee would be estopped from
asserting the patent.


                                                     26
if the patent is held invalid or unenforceable in the litigation between the patentee and
Firm i, the patentee would not be able to relitigate the issue of validity against Firm j as
long as the issue of validity or unenforceability was actually litigated and necessary to the
judgment.68 In terms of the model presented in Section IV, to the extent that the estopped
issue is dispositive, the effect of Blonder-Tongue is to make decisions holding the patent
invalid in effect completely persuasive, i.e., δ- = q0, so that q- = 0 and φ = 0. Because
non-mutual non-party estoppel cannot be invoked by the patentee against Firm j, δ+, p+
and ω are not affected. In terms of the incentives for litigation and settlement in equation
(37), the Blonder-Tongue rule leaves patentee’s external gain from a adverse judgment,
Gp(ρ), unaffected.

    However, Firm i’s external gain from a judgment in his favor, Gi(ρ), falls. Using
equation (34) with q- = 0 and φ = 0, Gi(ρ) = πic as Firm j will enter the market with
probability 1. As a result, Firm i’s gain is limited to the lower profits that result when
entry by Firm j occurs. Similarly, the patentee’s external loss from such a judgment,
Lp(ρ), increases. The patentee now faces competition from both Firm i and Firm j,
resulting in lower profits when the patent is held invalid. Using equation (35) with q- = 0
and φ = 0, Lp(ρ) = ρπm + (1-ρ)(q0πm + (1-q0)πpd) – [πpc]. As a result of Gi(ρ) falling
and Lp(ρ) increasing, the condition for litigation given by equation (37) is less likely to be
satisfied.

    Thus, the analysis shows that the Blonder-Tongue rule increases the pressure for
patentees to settle patent litigation by increasing the external loss imposed by an adverse
judgment on the patentee. An additional effect of this increased loss is an increase in the
effective stakes faced by the patentee. That is, incremental increases in litigation
expenditures to increase the probability that the patentee wins will operate on both the
external gains from a favorable judgment, and the external losses from an adverse
judgment. That is, if litigation expenditures Cp operate to increase the probability of
prevailing p = p(Cp), with p’(Cp) > 0 and p”(Cp) < 0,

(37)     dTp/dCp = p’(Cp) (Gp +Lp ) – 1.

    In contrast, expenditures by Firm i lower the probability the patent will be held valid,
so p’(Ci) < 0. Since Li = 0 and Gi < Lp, Firm i’s marginal incentives are smaller and will
be given by:

(38)     dTi/dCi = p’(Ci)Gi + 1,

   These asymmetric incentives exist under the Triplett rule. However, as result of the
Blonder-Tongue rule, these asymmetric effects are further increased by the increase in Lp
and the decrease in Gi. One result of this increase in the asymmetry of stakes is an

68
  This requirement would not be satisfied for example, in a case where the court held the patent not-
infringed, making it unnecessary to determine the validity of the patent to render a judgment for the alleged
infringer. See Morton International, Inc. v. Cardinal Chemical Company, 959 F.2d 948 (Fed. Cir. 1992).
However, this holding was reversed by the Court in Cardinal Chem. Co. v. Morton Int’l, Inc.
508 U.S. 83 (1993).


                                                     27
increase in the relative expenditures in litigation by the patentee, and an increase in the
probability the patent will be held valid.69 As a result, the Blonder-Tongue rule further
reduces the incentive of potential infringers to initiate patent litigation by decreasing the
gain when a patent is successfully challenged, and also by reducing the probability such a
challenge will be successful.

     Much of the Court’s decision in Blonder-Tongue focused on the narrow issue of the
costs that would be incurred in relitigating redundant issues, and how barring relitigation
of these issue would save both the court’s and the parties resources. The model shows
that the Blonder-Tongue rule can increase follow-in challenges to patents by changing
non-persuasive holdings into de facto persuasive ones. However, initial challenges will
decrease. Thus, the net effect on the total number of challenges is unclear. While follow
on challenges to the patent and entry increase, the cost of these challenges will fall given
the patentee is barred from re-litigating the issue. The net direct cost savings may be
small. Many of the cases filed after a persuasive invalidation of a patent under a re-
litigation rule would likely be settled quickly.70 The overall effect on welfare will depend
upon whether the cost of an increased number of type I errors (allowing more
uncompensated use of valid patents) are outweighed by the cost savings associated with a
decrease in the rate of type II errors (allowing more use of invalid patents).

        C.       Vacatur as an Antidote to Blonder-Tongue and Non-Mutual, Non-
                 Party Estoppel.

    The Blonder-Tongue rule for patents and other forms of intellectual property led to
the use of vacatur as a way to undo the effects of non-mutual collateral estoppel. In a
standard case, a repeat patentee litigates against an infringer who challenges the validity
or enforceability of the patent. Because the patentee is estopped from relitigating the
validity of an invalidated patent, a post-judgment settlement where Firm i agrees to delay
entry until the patent expires does not prevent Firm j from entering based on the
judgment invalidating the patent. Thus, the spillover effects of Firm i’s successful
invalidation of the patent reduces the relative benefits to the patentee and Firm i of post-
judgment entry blocking settlements.

    In order to control this spillover effect, losing patentees have offered post-judgment
settlements that include an agreement that both parties will seek to have to court vacate
the judgment holding the patent invalid or unenforceable. The effects of vacatur can be
examined using the model presented above. A post-judgment settlement conditioned on

69
   S. J. Spurr, An Economic Analysis of Collateral Estoppel, 11 INT. REV. L. & ECON. 47 (1991); William
M. Landes & Richard A. Posner, The Economics of Anticipatory Adjudication, 23 J. LEG. STUD. 683
(1994). See generally, Marc S. Galanter, Why the Haves Come Out Ahead: Speculation on the Limits of
Legal Change, 9 L. & SOCIETY REV. (1983). In terms of the model, the effect of these asymmetric
expenditures would be to increase p under a rule of non-mutual non-party estoppel over the p that would
apply to litigation under the Triplett rule.
70
   See Blonder-Tongue, supra note _ at 339, citing a 1961 staff study of infringement and declaratory
judgment actions by the Senate Judiciary Subcommittee on Patents, Trademarks, and Copyrights, showing
the ‘vast majority’ of actions commenced after an earlier determination that the patent was not valid
terminated without a second adjudication of validity.


                                                  28
vacatur has two intended effects. The first is to eliminate the effect of non-mutual non-
party collateral estoppel that allows other entrants to benefit from the invalidation of the
patent. The second is to make the earlier decision unpersuasive, specifically to make δ =
0, so that q- = q0 and φ = 1, by placing “the parties in the position of no trial having taken
place at all.”71 The agreement to vacate is Pareto optimal for both of the settling parties,
as it eliminates or reduces the probability of subsequent entry by Firm j.72

     Because estoppel only applies after a judgment adverse to the patentee, Firm i’s
external loss Li and the patentee’s external gain Gp(ρ) are unchanged. However, Firm i’s
external gain with estoppel and vacatur Gi(ρ) = ρ(φπid) + (1 - ρ)(q0πid + (1 – q0)πic) is
increased relative to the external gain under both the Triplett rule and the Blonder-
Tongue rule without vacatur. Similarly, the patentee’s external loss with estoppel and
vacatur Lp(ρ) = ρπm + (1-ρ)(q0πm + (1-q0)πpd) – {ρ[πpd] + (1-ρ)[q0πpd + (1-q0)πpc]} is
smaller then under the Triplett rule, and thus a fortori is smaller than under the Blonder-
Tongue rule without vacatur. Examining the condition for litigation (37), since Gp(ρ) is
unchanged under the three rules, and given that Gi(ρ) – Lp(ρ) is increased, the incentive
to litigate when vacatur is allowed is greater that under the Triplett rule.

    The analysis shows that the effect of vacatur is not just a return to the Triplett rule.
While it does allow the possibility for relitigation, it provides greater incentives, ceteris
paribus for patentees to litigate the validity of their patents. Moreover, because it reduces
the patentee’s expected external losses associated with an adverse judgment, it mutes the
incentives for the patentee to invest in litigation based on asymmetric stakes, and thus
reduces the litigation distortion. And while it increases the probability that the validity of
the patent will be litigated by the patentee and Firm i, it reduces both the probability that
the patent will be challenged by Firm j and the probability that Firm j enters.

     In the appendix, we present a model of relitigation under the various rules. If we
abstract away from settlement and litigation costs, the choice between allowing
relitigation by allowing vacatur versus restricting vacatur is one of trading off type I and
type II errors. Collateral estoppel makes earlier decisions invalidating patents persuasive
by rule, and can lock-in type I errors. Vacatur in effect makes earlier decisions
unpersuasive, and can eliminate future challenges to patents induced by persuasive
judgments invalidating patents. For good patents, this reduces type I errors, but it
increases the cost of type II error that results from bad patents going unchallenged.
Moreover, if one makes the assumption that erroneous decisions are generally
unpersuasive when the patent’s validity is relitigated while correct decisions are generally
persuasive, the Triplett rule serves as a sorting mechanism that promotes the relitigation
of errors while discouraging relitigation of earlier correct decisions. Because the use of
collateral estoppel with or without vacatur does not sort between good and bad decisions,
the model shows that the Triplett rule will have lower rates of error than either of the
alternative rules under Blonder-Tongue. Thus, if one wants to allow parties to relitigate

71
  United States v. Williams, 904 F.2d 7 (7th Cir. 1990).
72
  Because both parties benefit, vacatur of the decision is anticipated in the payoffs. The analysis assumes
that the price for the vacatur is zero.


                                                     29
patent invalidations, it may be better to reinstate the Triplett rule than to allow parties to
use vacatur to avoid non-mutual non-party collateral estoppel.

                                        [INSERT FIGURE 2 HERE]

    Similar effects are illustrated by simulations of the litigation and settlement model.
Figure 2 shows the range of acceptable settlements for both the entry blocking (MB) and
entry accommodating (ME) settlements as a function of the probability the patentee will
prevail p. The Figures illustrate the bid-ask spreads for case z, where the second entrant
(Firm j) will not challenge the patent unless the first entrant (Firm i) obtains a judgment
holding the patent invalid or unenforceable. The simulations also assume that correct
decisions are persuasive, but incorrect ones are completely unpersuasive.73 The top panel
illustrates the bid ask spreads for both valid (left top panel) and invalid (right top panel)
patents under the Triplett relitigation rule. The middle panel illustrates the effect of
collateral estoppel without the possibility of vacatur, while the bottom panel illustrates
the effect of collateral estoppel with vacatur.

     The top-left panel shows the bid ask spreads for a valid patent under the Triplett
relitigation rule. Challenges to the patent will have a positive value as long as the
maximum entry blocking settlement is negative, which is true for p ≤ .90. Because all
cases are settled if entry blocking settlements are allowed, no patents are invalidated
through litigation and no patent challenges by the second entrant occur. Under these
circumstances, all filed cases will settle with “reverse payments” (MB < 0) and the bid ask
spreads are identical to those in the single entrant case. Under the assumption that the
patents are valid and enforceable, the absence of successfully challenged patents is the
correct outcome.

    Making entry-blocking settlements with “reverse payments” (MB < 0) illegal will
prevent such settlements from occurring. Under these circumstances, any settlements
will include a positive payment from the entrant to the patentee and entry, and result in
entry by the initial challenger, but no challenge by the second challenger. In addition,
strong patents (p ≥ .65) are litigated rather than settled.

    The top-right panel of Figure 2 shows the bid ask spreads for an invalid patent under
the Triplett Rule. Again, when entry-blocking settlements are allowed, all cases settle,
though fewer of them are initially brought. Because judgments invalidating the patent
will have a persuasive effect, the lower bound for the “reverse” payment falls. The
maximum bound also moves closer to zero given that subsequent challenges would be
more successful. When entry-blocking settlements are made unlawful, the range for
entry accommodating settlements becomes larger, and settlement, which results in entry
by the first challenger, is feasible over a much larger range.

    The differences between the top-left and top-right panels in Figure 2 illustrate the
sorting function of the Triplett rule, especially in the case where entry-blocking
settlements are unlawful. Valid patents are much more likely to be litigated, while
73
     The simulations assume a symmetric Cournot equilibrium with N firms in the output market.


                                                     30
invalid patents will result in entry accommodating settlements that reflect the nature of
the case (lower settlement payments and accommodation of entry).74 The middle and
bottom panels illustrate how collateral estoppel, and collateral estoppel with vacatur
interfere with this sorting function. Under a rule of non-mutual, non-party collateral
estoppel and no vacatur, both patentees with valid and invalid patents face outcomes
similar to those faced by patentees with invalid patents under the Triplett relitigation rule.
Thus, the middle panel illustrates the increase in the cost of type I errors associated with
collateral estoppel. The bottom panel illustrates the effects of allowing vacatur to avoid
non-mutual, non-party collateral estoppel. Here, both parties face outcomes similar to
those faced by patentees with valid patents under the Triplett rule.


VI.      Conclusion

     This paper examines a model of patent litigation with multiple potential
entrant/infringers. The paper demonstrates how the patentee’s and entrants incentives to
litigate and settle a case is affected by the existence of other potential entrants and by the
rules that regulate relitigation of litigated issues. Table 2 summarizes the relative effects
of the relitigation rules. The Table shows that the tradeoffs are more complex than courts
and academics have treated them. Moreover, the court system’s struggle with issues
such as vacatur can be directly traced to the Court’s earlier decision in Blonder-Tongue to
eliminate the mutuality rule allowing application of collateral estoppel to non-parties.
The analysis suggests that the court system may be well served by minimizing use of the
uncertain and hard to administer “exceptional circumstances” test in deciding whether to
allow patentees with invalidated patents to relitigate. Rather patentees with invalidated
patents should be given the ability to relitigate the validity of the patent by reinstating the
mutuality rule.




74
   This results in an adverse selection of cases for trial – that is, firms with valid patents are forced to
defend their patents, while those with invalid patents avoid trial. For a similar result in the plea bargaining
literature, see Gene M. Grossman and Michael L. Katz, Plea Bargaining and Social Welfare, 73 AM. ECON.
REV. 749 (1983).


                                                      31
Figure 1 – The Tamoxifen Patent Litigation




                            Estoppel bars
                            relitigation




                                        Vacatur
                                        allows
                                        relitigation




                                            32
                      Table 1 – The Error Structure in Patent Cases

                               Patent Held Valid (-)     Patent Held Invalid (+)
                               or not challenged
Patent Valid (Null)            Specificity (correctly    Type I error (False
                               holding valid patent      positive where valid
                               valid)                    patent is held invalid)
Patent Invalid (Alternative)   Type II error (False      Sensitivity (correctly
                               negative, where invalid   holding invalid patent
                               patent is held valid).    invalid)




                                        33
     Figure 2 – Bid-Ask Spreads for Entry Blocking and Entry Accommodating
                                    Settlements

                       Valid Patent                 Invalid Patent

A.     Triplett Rule




B.     Blonder-Tongue + U.S. Bancorp




C.     Blonder-Tongue + vacatur




                                       34
Table 2 – A Summary of the Effects Association with Alternative Relitigation Rules

                      Potential   Distorted      Factual    Litigation/        Incentives
                      for         Litigation     Error      Settlement         for Patent
                      Relitiga-   Incentives     Correction Incentives         Challenges
                      tion Cost                                                & Entry
1. Triplett Rule      Yes         Based on       Yes.           Baseline       Baseline
(Mutuality/Privity)               Stakes in      Efficient
                                  individual     sorting in
                                  case and       correct
                                  anticipated    decisions
                                  non-party      are
                                  effects of     persuasive
                                  judgment       while
                                                 incorrect
                                                 ones are
                                                 not.

2. Blonder-Tongue No              Greater than   Only on        Reduces        Increases
Rule (Defensive                   Triplett       appeal         incentive to   follow-on
Non-Party, Non-                   Rule, based    under          settle while   challenges
Mutual Collateral                 on stakes in   clearly        appeal is      and entry
Estoppel) +                       individual     erroneous      pending,       relative to
Application of U.S.               case and       standard,      increases      Triplett
Bancorp v. Bonner                 based on       increases      incentive to   Rule,
Mall (no vacatur)                 enhanced       type I error   settle prior   decreases
                                  non-party      rates.         to             initial
                                  effects.                      litigation.    challenges.

3. Blonder-Tongue Yes             Lower than     Yes, with      Increases      Decreases
Rule with Vacatur                 Triplett       vacatur.       incentive to   follow on
Allowed.                          Rule, based    Allows         settle while   challenges
                                  on stakes in   relitgation    appeal is      and entry
                                  individual     of             pending,       relative to
                                  case and       invalidated    reduced        Triplett
                                  based on       patents,       incentives     rule,
                                  muted non-     increases      to settle      increases
                                  party          type II        prior to       initial
                                  effects.       error rates.   litigation.    challenges.




                                           35
                   Appendix – A Model of Relitigation Rules and Error Rates

    In this appendix, we look at the litigation error rates under the various rules
considered in the paper. This analysis is incomplete in the sense that it does not, as the
analysis in the body of the paper does, take into account the effects of settlement. This
assumption is consistent with the assumption used in Bone’s analysis of error rates under
different preclusion rules, which serves as the point of departure.75 The analysis may also
be of interest given both the Court’s and policymakers’ recent interest in curtailing the
ability of patentees to settle patent litigation.

     Bone’s analysis addressed the effect of a regime of mutual non-party collateral
estoppel under a theory of virtual representation relative to a regime of permissive
relitigation. In his analysis, he assumed that prior cases were not persuasive, so that in
the case of two infringers facing a common patentee, p = q, were p is the probability the
patentee prevails in litigation against Firm i, and q equals the probability that the patentee
prevails in litigation against Firm j. Assume that the patent is valid, so p and q represent
the probability of a correct outcome in the first and second litigation respectively. Under
a regime of mutual non-party estoppel, 2 correct outcomes are produced with probability
p, and zero correct outcomes are produced with probability (1-p). In general, with N
infringers, the expected number of correct decisions will equal Np, and the variance of
the outcomes will be N2p(1-p). In contrast, under a rule of permissive relitigation, and
under the assumption that the outcomes of individual cases are independent (no
persuasion) and all cases are relitigated and not settled, the expected number of correct
decisions is has a binomial distribution. Using the well known properties of the binomial
distribution, the mean equals Np, and the variance equals Np(1-p). Thus Bone’s analysis
shows that case-by-case litigation will have the same expected number of correct
decisions, but the variance of the outcomes will be larger. Any benefits of a reduction in
variance would have to offset the higher costs of independently relitigating cases.

     Bone’s relitigation model describes case x in the model presented in the body of the
paper with no persuasion and with complete persuasion under mutual non-party estoppel.
Suppose Bone’s analysis is modified so that there is a correlation between whether a case
is correctly decided and the persuasive nature of the case. For simplicity, suppose that
incorrectly decided cases are completely unpersuasive, so that δ = 0, and correctly
decided cases are completely persuasive, so that δ = 1 – p in the case of a valid patent so
that q+ = 1. Under a permissive relitigation rule, a rational entrant will not relitigate
valid patents that are held valid. Patents that are erroneously held invalid in the first
litigation will be relitigated with probability q0 = p. With N = 2, the number of correct
decisions under the relitigation rule with positive sorting equals 2p + (p – p2) > 2p.
Thus, compared to the case of no persuasion and relitigation, and the case of complete
persuasion (mutual non party estoppel), this regime will increase the number of correct
validity decisions and thus reduce the type I error rate (see Table 1). Relitigation only
occurs to correct erroneous decisions. Whether such a system is preferred to a system of
mutual non-party estoppel will depend upon whether or not the benefits of error
correction outweigh the additional costs associated with relitigation.
75
     See Bone, supra note _ at _.


                                              36
    Now consider the effect of non-mutual collateral estoppel. When the patentee wins,
non-party estoppel does not apply, so the outcomes are unchanged. Given the
assumption that the holding will be persuasive, the second litigation is deterred without
estoppel. In the case where there is an error and the patent is held invalid, the patentee
will be estopped from relitigating the patent. Thus, the effect of estoppel is to make the
erroneous decision that the patent is invalid in effect completely persuasive. Thus, in
effect, the rule of non-mutual non-party estoppel yields the same outcomes are the case of
complete persuasion. Because the patentee is prevented from correcting the initial error
through litigation, the expected number of correct decisions falls to 2p.

     Now consider the effect of vacatur in this model. If the patentee wins, the decision
will not be vacated by agreement of the parties. Because the decision is correct, the
decision will be persuasive and the second litigation will be deterred. So there will be 2
correct decisions and no relitigation. If the patent is initially held invalid, vacatur allows
the patentee an opportunity to correct the error by making the first decision unpersuasive.
In this case, vacatur allows the patentee to re-impose the outcomes associated with the
relitigation regime with positive sorting. Thus, the expected number of correct decisions
is higher, and the resulting type I error rate is lower. In terms of error rates, the
relitigation rule under Triplett and the rule of non-mutual non-party collateral estoppel
with vacatur are equivalent. To the extent that the costs of the latter system are higher,
the Triplett rule will be preferred.

    The same analysis of the regimes of relitigation and completely persuasive litigation
under non-mutual non-party estoppel applies to the case of an invalid patent and the rate
of type II error. Again, the expected number of correct decisions, assuming the
specificity and sensitivity of patent trials both equal p, is 2p under mutual non-party
estoppel and under unpersuasive relitigation. With positive sorting, the number of correct
invalidations equals 2p + (p – p2) > 2p.

     There is some difference in the error cost analysis of the regimes of non-mutual non-
party estoppel without and with vacatur when applied to an invalid or bad patent.
Consider first non-mutual non-party estoppel without vacatur. Because non-party
estoppel would not apply when the patent was erroneously held valid, and given the
assumption that such a holding was unpersuasive, the second entrant will relitigate the
validity of the patent. If the patent is correctly held invalid, non-mutual collateral
estoppel would bar relitigation of the validity of the patent. But under the permissive
relitigation rule with persuasive correct judgments, these cases would not be relitigated
either. Thus, non-mutual collateral estoppel is redundant as it simply mimics the
outcomes that would occur in a regime of permissive relitigation with positive sorting.
However, given its inferior error cost performance in the case where the patent is valid,
out analysis suggests that the permissive relitigation regime in Triplett will dominate a
regime of non-mutual non-party collateral estoppel as long as the cost of relitigation was
less than the benefits of error correction.




                                              37
    Now consider a regime of non-mutual non-party collateral estoppel with permissive
vacatur. In this case, patents incorrectly held valid would be relitigated. However,
patents correctly held invalid would be vacated post-judgment, making the earlier correct
judgment unpersuasive, and resulting in the patent being relitigated. Thus, the outcomes
with non-mutual non-party collateral estoppel with vacatur will mimic the case of
permissive relitigation without persuasion. In effect, allowing vacatur in this setting
destroys the positive sorting that would occur in a permissive relitigation regime. Thus,
compared to the regime of relitigation with positive sorting, allowing vacatur increases
both the cost of relitigation and the total cost of type II error. Thus, for invalid patents, a
regime that allows vacatur of invalidated patents will be inferior to either a system of
permissive relitigation or one of non-mutual non-party collateral estoppel. Overall, given
that the permissive relitigation system dominates or weakly dominates either of the
systems that allow non-mutual non-party collateral estoppel, the analysis demonstrates
the potential benefits of returning to the Triplett rule.




                                              38