-
1
-
-
0036486793
-
The Growing Complexity of the
-
United States Patent System, 82 B.U. L. REV. 77, 93 tbl.1 2002, noting that until quite recently the majority of all U.S. patents were for mechanical inventions
-
John R. Allison & Mark A. Lemley, The Growing Complexity of the United States Patent System, 82 B.U. L. REV. 77, 93 tbl.1 (2002) (noting that until quite recently the majority of all U.S. patents were for mechanical inventions).
-
-
-
Allison, J.R.1
Lemley, M.A.2
-
2
-
-
33846321139
-
As Many As Six Impossible
-
Patents Before Breakfast: Property Rights for Business Concepts and Patent System Reform, 14 BERKELEY TECH. L.J. 577, 585 1999
-
Robert P. Merges, As Many As Six Impossible Patents Before Breakfast: Property Rights for Business Concepts and Patent System Reform, 14 BERKELEY TECH. L.J. 577, 585 (1999).
-
-
-
Merges, R.P.1
-
3
-
-
34547824135
-
-
We have occasionally seen problems like this before. See Ted Sabety, Nanotechnology Innovation and the Patent Thicket: Which IP Policies Promote Growth, 15 ALB. L.J. SCI. & TECH. 477, 495-503 2005, discussing the example of radio patents in the 1920s, But they are much more common now than they were in the past
-
We have occasionally seen problems like this before. See Ted Sabety, Nanotechnology Innovation and the Patent Thicket: Which IP Policies Promote Growth?, 15 ALB. L.J. SCI. & TECH. 477, 495-503 (2005) (discussing the example of radio patents in the 1920s). But they are much more common now than they were in the past.
-
-
-
-
4
-
-
34547554610
-
-
David J. Goodman & Robert A. Myers, 3G Cellular Standards and Patents, in PROCEEDINGS OF IEEE INTERNATIONAL CONFERENCE ON WIRELESS NETWORKS, COMMUNICATIONS AND MOBILE COMPUTING 2 (2005), available at http://eeweb.poly.edu/dgoodman/wirelesscom2005.pdf.
-
David J. Goodman & Robert A. Myers, 3G Cellular Standards and Patents, in PROCEEDINGS OF IEEE INTERNATIONAL CONFERENCE ON WIRELESS NETWORKS, COMMUNICATIONS AND MOBILE COMPUTING 2 (2005), available at http://eeweb.poly.edu/dgoodman/wirelesscom2005.pdf.
-
-
-
-
5
-
-
0032076909
-
-
For further discussion of how numerous patents often read on a single product, see Michael A. Heller & Rebecca S. Eisenberg, Can Patents Deter Innovation? The Anti-Commons in Biomedical Research, 280 SCIENCE 698 (1998) (describing how biomedical researchers underuse scarce resources because the proliferation of IP rights allows owners to restrict use)
-
For further discussion of how numerous patents often read on a single product, see Michael A. Heller & Rebecca S. Eisenberg, Can Patents Deter Innovation? The Anti-Commons in Biomedical Research, 280 SCIENCE 698 (1998) (describing how biomedical researchers underuse scarce resources because the proliferation of IP rights allows owners to restrict use)
-
-
-
-
6
-
-
34547768018
-
Navigating the
-
Patent Thicket: Cross Licenses, Patent Pools, and Standard Setting, in 1 INNOVATION POLICY AND THE ECONOMY 119, 119-23 Adam B. Jaffe et al. eds, 2001, discussing the patent thicket's effect on cumulative technological development
-
and Carl Shapiro, Navigating the Patent Thicket: Cross Licenses, Patent Pools, and Standard Setting, in 1 INNOVATION POLICY AND THE ECONOMY 119, 119-23 (Adam B. Jaffe et al. eds., 2001) (discussing the "patent thicket's" effect on cumulative technological development).
-
-
-
Shapiro, C.1
-
7
-
-
33746645963
-
-
We expressly do not consider in our analysis portfolio patent licensing, which presents different issues than the ones we address here. For a discussion of such issues, see Richard J. Gilbert & Michael L. Katz, Should Good Patents Come in Small Packages? A Welfare Analysis of Intellectual Property Bundling, 24 INT'L J. INDUS. ORG. 931, 934-46 (2006)
-
We expressly do not consider in our analysis portfolio patent licensing, which presents different issues than the ones we address here. For a discussion of such issues, see Richard J. Gilbert & Michael L. Katz, Should Good Patents Come in Small Packages? A Welfare Analysis of Intellectual Property Bundling, 24 INT'L J. INDUS. ORG. 931, 934-46 (2006)
-
-
-
-
9
-
-
34547821381
-
-
The analysis in this Part draws heavily on Carl Shapiro's work. Carl Shapiro, Injunctions, Hold-Up, and Patent Royalties 1 (Competition Policy Ctr, Working Paper No. CPC06-062, 2006, available at http://faculty.haas.berkeley.edu/shapiro/royalties.pdf deriving the equations and relationships asserted here
-
The analysis in this Part draws heavily on Carl Shapiro's work. Carl Shapiro, Injunctions, Hold-Up, and Patent Royalties 1 (Competition Policy Ctr., Working Paper No. CPC06-062, 2006), available at http://faculty.haas.berkeley.edu/shapiro/royalties.pdf (deriving the equations and relationships asserted here).
-
-
-
-
10
-
-
33744512160
-
-
In that case, one of us has argued for granting the downstream firm prior-user rights, in which case it would not have to pay any royalties at all. See Carl Shapiro, Prior User Rights, 96 AM. ECON. REV. (PAPERS & PROC.) 92, 95 (2006) (stating that when nearly simultaneous, independent invention occurs, awarding prior-user rights can enhance competition and produce a better alignment of private and social incentives);
-
In that case, one of us has argued for granting the downstream firm prior-user rights, in which case it would not have to pay any royalties at all. See Carl Shapiro, Prior User Rights, 96 AM. ECON. REV. (PAPERS & PROC.) 92, 95 (2006) (stating that when nearly simultaneous, independent invention occurs, awarding prior-user rights can enhance competition and produce a better alignment of private and social incentives);
-
-
-
-
11
-
-
34547803647
-
-
see also Carl Shapiro, Patent Reform: Aligning Reward and Contribution, in 7 INNOVATION POLICY AND THE ECONOMY (Adam B. Jaffe et al. eds., forthcoming 2007) (explaining the economic benefits of an expanded independent invention defense in patent infringement cases);
-
see also Carl Shapiro, Patent Reform: Aligning Reward and Contribution, in 7 INNOVATION POLICY AND THE ECONOMY (Adam B. Jaffe et al. eds., forthcoming 2007) (explaining the economic benefits of an expanded independent invention defense in patent infringement cases);
-
-
-
-
12
-
-
33845900231
-
Independent Invention as a Defense to
-
Patent Infringement, 105 MICH. L. REV. 475, 494-500 2006, proposing a broader reinvention defense
-
Samson Vermont, Independent Invention as a Defense to Patent Infringement, 105 MICH. L. REV. 475, 494-500 (2006) (proposing a broader reinvention defense).
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-
-
Vermont, S.1
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13
-
-
34547782685
-
-
The law has some mechanisms to limit such intentional delay, such as the twenty-year patent term and the doctrine of prosecution laches, but they are not particularly robust
-
The law has some mechanisms to limit such intentional delay, such as the twenty-year patent term and the doctrine of prosecution laches, but they are not particularly robust.
-
-
-
-
14
-
-
34547774542
-
-
Until 2006, the Federal Circuit treated injunctions as effectively mandatory after a finding of patent infringement. See MercExchange, L.L.C v. eBay, Inc., 401 F.3d 1323, 1339 (Fed. Cir. 2005), (following the general rule that courts will issue permanent injunctions against patent infringement absent exceptional circumstances), vacated, 126 S. Ct. 1837 (2006). The Supreme Court's decision in eBay replaced that rule with a case-specific, four-factor test for deciding whether injunctive relief is appropriate. eBay Inc. v. MercExchange, L.L.C., 126 S. Ct. 1837, 1838-39 (2006). At this writing, the Federal Circuit had not applied that test in a challenge to a permanent injunction. We discuss the proper application of the new eBay test in Part VI.
-
Until 2006, the Federal Circuit treated injunctions as effectively mandatory after a finding of patent infringement. See MercExchange, L.L.C v. eBay, Inc., 401 F.3d 1323, 1339 (Fed. Cir. 2005), (following "the general rule that courts will issue permanent injunctions against patent infringement absent exceptional circumstances"), vacated, 126 S. Ct. 1837 (2006). The Supreme Court's decision in eBay replaced that rule with a case-specific, four-factor test for deciding whether injunctive relief is appropriate. eBay Inc. v. MercExchange, L.L.C., 126 S. Ct. 1837, 1838-39 (2006). At this writing, the Federal Circuit had not applied that test in a challenge to a permanent injunction. We discuss the proper application of the new eBay test in Part VI.
-
-
-
-
15
-
-
34547728595
-
-
A more complex model of the litigation process would recognize that the patent holder and downstream firm update their views on patent strength as information is elicited during the litigation process, and that they can negotiate a license throughout this process. Information learned during the litigation process can be modeled as inducing a mean-preserving spread on patent strength. Joseph Farrell & Carl Shapiro, How Strong Are Weak Patents? 16-17 (Jan. 2007) (unpublished manuscript), available at http://faculty.haas. berkeley.edu/shapiro/weak.pdf.
-
A more complex model of the litigation process would recognize that the patent holder and downstream firm update their views on patent strength as information is elicited during the litigation process, and that they can negotiate a license throughout this process. Information learned during the litigation process can be modeled as inducing a mean-preserving spread on patent strength. Joseph Farrell & Carl Shapiro, How Strong Are Weak Patents? 16-17 (Jan. 2007) (unpublished manuscript), available at http://faculty.haas. berkeley.edu/shapiro/weak.pdf.
-
-
-
-
16
-
-
34547739507
-
-
In his classic article The Bargaining Problem, John Nash provided a simple formula characterizing the bargaining outcome in a wide class of bargaining situations, so long as certain bargaining axioms (including efficiency) are assumed to hold. John F. Nash, Jr., The Bargaining Problem, 18 ECONOMETRICA 155 (1950). In our setting, the Nash bargaining solution implies that the parties split the gains from trade equally, i.e., B = 0.5. More recently, Ariel Rubinstein showed how the bargaining skill parameter is determined in the noncooperative equilibrium in a game in which the two parties alternate in making offers that can then be accepted or rejected.
-
In his classic article The Bargaining Problem, John Nash provided a simple formula characterizing the bargaining outcome in a wide class of bargaining situations, so long as certain bargaining axioms (including efficiency) are assumed to hold. John F. Nash, Jr., The Bargaining Problem, 18 ECONOMETRICA 155 (1950). In our setting, the Nash bargaining solution implies that the parties split the gains from trade equally, i.e., B = 0.5. More recently, Ariel Rubinstein showed how the bargaining skill parameter is determined in the noncooperative equilibrium in a game in which the two parties alternate in making offers that can then be accepted or rejected.
-
-
-
-
17
-
-
34547822397
-
-
Ariel Rubinstein, Perfect Equilibrium in a Bargaining Model, 50 ECONOMETRICA 97, 104-06 (1982). If the time between offers is short and the players discount the future equally, B again equals 0.5. Id. at 107-08.
-
Ariel Rubinstein, Perfect Equilibrium in a Bargaining Model, 50 ECONOMETRICA 97, 104-06 (1982). If the time between offers is short and the players discount the future equally, B again equals 0.5. Id. at 107-08.
-
-
-
-
18
-
-
34547751296
-
-
We are agnostic about the patent holder's bargaining skill as measured by the variable B. Our analysis and conclusions apply regardless of the value of B. Indeed, the percentage royalty overcharges we compute below are independent of B. However, readers may find it useful to simplify our results by assuming that B = 0.5.
-
We are agnostic about the patent holder's bargaining skill as measured by the variable B. Our analysis and conclusions apply regardless of the value of B. Indeed, the percentage royalty "overcharges" we compute below are independent of B. However, readers may find it useful to simplify our results by assuming that B = 0.5.
-
-
-
-
19
-
-
84929868257
-
-
See, e.g
-
See, e.g., ROGER D. BLAIR & THOMAS F. COTTER, INTELLECTUAL PROPERTY: ECONOMIC AND LEGAL DIMENSIONS OF RIGHTS AND REMEDIES 229-30 (2005).
-
(2005)
, vol.229 -30
-
-
BLAIR, R.D.1
COTTER, T.F.2
PROPERTY, I.3
AND LEGAL, E.4
OF, D.5
AND REMEDIES, R.6
-
20
-
-
34547817595
-
-
The patent holder's contribution is $0 with probability 0.6 and $1 with probability 0.4, for an expected value of $0.40. With equal bargaining skill, the patent holder captures half of this value, or $0.20 per unit.
-
The patent holder's contribution is $0 with probability 0.6 and $1 with probability 0.4, for an expected value of $0.40. With equal bargaining skill, the patent holder captures half of this value, or $0.20 per unit.
-
-
-
-
21
-
-
34547809862
-
-
In general, the benchmark royalty also will reflect the parties' litigation costs, and the model in Shapiro, supra note 7, does in fact include those costs. However, if the parties have equal litigation costs and equal bargaining skill, including litigation costs does not alter the benchmark royalty rate. More generally, because litigation costs are relevant in both the benchmark and the holdup royalty calculations, they drop out of the comparison of the two and are of no significance for our purposes.
-
In general, the benchmark royalty also will reflect the parties' litigation costs, and the model in Shapiro, supra note 7, does in fact include those costs. However, if the parties have equal litigation costs and equal bargaining skill, including litigation costs does not alter the benchmark royalty rate. More generally, because litigation costs are relevant in both the benchmark and the holdup royalty calculations, they drop out of the comparison of the two and are of no significance for our purposes.
-
-
-
-
23
-
-
34547754970
-
-
There are of course other possible strategies, and they are discussed in more detail in Shapiro, supra note 7, at 12-14
-
There are of course other possible strategies, and they are discussed in more detail in Shapiro, supra note 7, at 12-14.
-
-
-
-
24
-
-
34547776758
-
-
The negotiated royalty rate is, of course, a function of the probability θ that the patent would be found valid. However, the patent strength, θ, does not appear in the expression for the percentage royalty overcharge because we are measuring the negotiated royalty rate as a percentage of the benchmark rate, and θ appears in both the numerator and the denominator of this ratio
-
The negotiated royalty rate is, of course, a function of the probability θ that the patent would be found valid. However, the patent strength, θ, does not appear in the expression for the percentage royalty overcharge because we are measuring the negotiated royalty rate as a percentage of the benchmark rate, and θ appears in both the numerator and the denominator of this ratio.
-
-
-
-
25
-
-
34547780612
-
-
The Litigate strategy is indeed optimal for the downstream firm with these numbers so long as θ × B ≤ 2/9. With equal bargaining skill, B = 1/2, the Litigate strategy is optimal if the patent strength is less than 4/9.
-
The Litigate strategy is indeed optimal for the downstream firm with these numbers so long as θ × B ≤ 2/9. With equal bargaining skill, B = 1/2, the Litigate strategy is optimal if the patent strength is less than 4/9.
-
-
-
-
26
-
-
34547752916
-
Inc., 401 F.3d 1323, 1325-26 (Fed. Cir. 2005) (noting that eBay replaced the disputed method of selling with another method), vacated, 126
-
See
-
See MercExchange, L.L.C. v. eBay, Inc., 401 F.3d 1323, 1325-26 (Fed. Cir. 2005) (noting that eBay replaced the disputed method of selling with another method), vacated, 126 S. Ct. 1837 (2006).
-
(2006)
S. Ct. 1837
-
-
MercExchange, L.L.C.1
eBay2
-
27
-
-
34547727696
-
-
We can no longer talk about the design cost C as a fraction of the underlying value of the patented feature since the latter is 0. When V > 0, C and K are related by C, K/V
-
We can no longer talk about the design cost C as a fraction of the underlying value of the patented feature since the latter is 0. When V > 0, C and K are related by C = K/V.
-
-
-
-
28
-
-
34547797339
-
-
The stronger patent makes Redesign and Litigate rather than Litigate optimal for the downstream firm
-
The stronger patent makes Redesign and Litigate rather than Litigate optimal for the downstream firm.
-
-
-
-
29
-
-
33846467857
-
-
Part III
-
See infra Part III.
-
See infra
-
-
-
30
-
-
22144437353
-
-
See Mark A. Lemley & Carl Shapiro, Probabilistic Patents, 19 J. ECON. PERSP., Spring 2005, at 75, 95 (concluding that patents are not the well-defined property rights that some economic models assume, and demonstrating that patents contain a greater level of uncertainty than other property rights).
-
See Mark A. Lemley & Carl Shapiro, Probabilistic Patents, 19 J. ECON. PERSP., Spring 2005, at 75, 95 (concluding that patents are not the well-defined property rights that some economic models assume, and demonstrating that patents contain a greater level of uncertainty than other property rights).
-
-
-
-
31
-
-
34547728594
-
-
In a more general model, where the downstream firm had additional design options, such as the ability to design the product to facilitate subsequent redesign, the downstream firm would value early awareness of the patent
-
In a more general model, where the downstream firm had additional design options, such as the ability to design the product to facilitate subsequent redesign, the downstream firm would value early awareness of the patent.
-
-
-
-
32
-
-
34547816041
-
-
For an explanation of these rules, see, for example, Mark A. Lemley & Ragesh K. Tangri, Ending Patent Law's Willfulness Game, 18 BERKELEY TECH. L.J. 1085, 1087-88, 1100-02 (2003) (discussing the perverse situation where a company discourages its engineers from reading patents to avoid liability for willfulness).
-
For an explanation of these rules, see, for example, Mark A. Lemley & Ragesh K. Tangri, Ending Patent Law's Willfulness Game, 18 BERKELEY TECH. L.J. 1085, 1087-88, 1100-02 (2003) (discussing the perverse situation where a company discourages its engineers from reading patents to avoid liability for willfulness).
-
-
-
-
33
-
-
34547756846
-
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, 958 2004, describing the public goods problem leading to undersupply of patent challenges
-
See 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, 958 (2004) (describing the public goods problem leading to undersupply of patent challenges);
-
-
-
Joseph Farrell, S.1
Merges, R.P.2
-
34
-
-
34547820206
-
-
Joseph Scott Miller, Building a Better Bounty: Litigation-Stage Rewards for Defeating Patents, 19 BERKELEY TECH. L.J. 667, 687 (2004) (arguing that patent litigation jurisprudence eliminates a patent attacker's ability to exclude others from appropriating the benefit of its successful patent attack);
-
Joseph Scott Miller, Building a Better Bounty: Litigation-Stage Rewards for Defeating Patents, 19 BERKELEY TECH. L.J. 667, 687 (2004) (arguing that patent litigation jurisprudence "eliminates a patent attacker's ability to exclude others from appropriating the benefit of its successful patent attack");
-
-
-
-
35
-
-
84965871502
-
-
note 11, at, I]ncentives [for downstream firms that compete] to challenge patents are sub-optimal
-
Farrell & Shapiro, supra note 11, at 2 ("[I]ncentives [for downstream firms that compete] to challenge patents are sub-optimal . . . .").
-
supra
, pp. 2
-
-
Farrell1
Shapiro2
-
36
-
-
34547740516
-
-
Farrell & Shapiro, supra note 11, at 2
-
Farrell & Shapiro, supra note 11, at 2.
-
-
-
-
37
-
-
34547787598
-
-
See Blonder-Tongue Labs., Inc. v. Univ. of Ill. Found., 402 U.S. 313, 334 (1971) ([I]t is insufficient in and of itself to justify patentees relitigating validity issues as long as new defendants are available.); Brulotte v. Thys Co., 379 U.S. 29, 32 (1964) ([A] patentee's use of a royalty agreement that projects beyond the expiration date of the patent is unlawful per se.).
-
See Blonder-Tongue Labs., Inc. v. Univ. of Ill. Found., 402 U.S. 313, 334 (1971) ("[I]t is insufficient in and of itself to justify patentees relitigating validity issues as long as new defendants are available."); Brulotte v. Thys Co., 379 U.S. 29, 32 (1964) ("[A] patentee's use of a royalty agreement that projects beyond the expiration date of the patent is unlawful per se.").
-
-
-
-
38
-
-
34547819699
-
-
See, e.g., Aronson v. Quick Point Pencil Co., 440 U.S. 257, 265-66 (1979) (upholding a continuing royalty obligation for trade secrets even after a patent application was rejected and the secret became public).
-
See, e.g., Aronson v. Quick Point Pencil Co., 440 U.S. 257, 265-66 (1979) (upholding a continuing royalty obligation for trade secrets even after a patent application was rejected and the secret became public).
-
-
-
-
39
-
-
34547764746
-
-
See, e.g., Jay P. Kesan & Gwendolyn G. Ball, How Are Patent Cases Resolved? An Empirical Examination of the Adjudication and Settlement of Patent Disputes, 84 WASH. U. L. REV. 237, 259 (2006) (finding that 80% of patent disputes settle);
-
See, e.g., Jay P. Kesan & Gwendolyn G. Ball, How Are Patent Cases Resolved? An Empirical Examination of the Adjudication and Settlement of Patent Disputes, 84 WASH. U. L. REV. 237, 259 (2006) (finding that 80% of patent disputes settle);
-
-
-
-
40
-
-
33847180786
-
Rational Ignorance at the
-
Patent Office, 95 NW. U. L. REV. 1495, 1501 2001, noting that the vast majority of patent disputes settle or are abandoned prior to trial
-
Mark A. Lemley, Rational Ignorance at the Patent Office, 95 NW. U. L. REV. 1495, 1501 (2001) (noting that the vast majority of patent disputes settle or are abandoned prior to trial).
-
-
-
Lemley, M.A.1
-
41
-
-
34547805213
-
-
When the downstream firms are rivals and the patent holder is charging running royalties as distinct from fixed fees, the analysis is more complex. On the one hand, by protecting its running royalties in the event of an invalidity finding, the patent holder limits its downside, thereby making it more credible that the patent holder will in fact litigate rather than ignore an infringing firm and strengthening its bargaining position with any given downstream firm. On the other hand, if the patent holder will be able to continue to charge running royalties to other firms, even if one downstream firm successfully challenges the patent, the upside to a single downstream firm from litigating will be greater because winning the patent litigation will give that firm a competitive advantage over its rivals who will be paying higher running royalties
-
When the downstream firms are rivals and the patent holder is charging running royalties (as distinct from fixed fees), the analysis is more complex. On the one hand, by protecting its running royalties in the event of an invalidity finding, the patent holder limits its downside, thereby making it more credible that the patent holder will in fact litigate rather than ignore an infringing firm and strengthening its bargaining position with any given downstream firm. On the other hand, if the patent holder will be able to continue to charge running royalties to other firms, even if one downstream firm successfully challenges the patent, the upside to a single downstream firm from litigating will be greater because winning the patent litigation will give that firm a competitive advantage over its rivals who will be paying higher running royalties.
-
-
-
-
42
-
-
34547766442
-
-
An adverse decision on infringement or claim construction by one downstream firm may or may not have effects on royalties earned from other downstream firms, depending upon the similarity between the different downstream firms' products, and thus on the correlation between one downstream firm infringing and another doing so
-
An adverse decision on infringement or claim construction by one downstream firm may or may not have effects on royalties earned from other downstream firms, depending upon the similarity between the different downstream firms' products, and thus on the correlation between one downstream firm infringing and another doing so.
-
-
-
-
43
-
-
0037821598
-
-
Mark R. Patterson, Commentary, Antitrust and the Costs of Standard-Setting: A Commentary on Teece & Sherry, 87 MINN. L. REV. 1995, 2001 n.33 (2003) (referring to the different royalties Rambus charged).
-
Mark R. Patterson, Commentary, Antitrust and the Costs of Standard-Setting: A Commentary on Teece & Sherry, 87 MINN. L. REV. 1995, 2001 n.33 (2003) (referring to the different royalties Rambus charged).
-
-
-
-
44
-
-
34547745362
-
-
See NTP, Inc. v. Research in Motion, Ltd, No. Civ. A. 3:01CV767, 2003 WL 23100881, at *1 E.D. Va. Aug. 5, 2003, awarding reasonable royalty damages in the amount of about $33.5 million, The settlement was eighteen times the jury award
-
See NTP, Inc. v. Research in Motion, Ltd., No. Civ. A. 3:01CV767, 2003 WL 23100881, at *1 (E.D. Va. Aug. 5, 2003) (awarding reasonable royalty damages in the amount of about $33.5 million). The settlement was eighteen times the jury award.
-
-
-
-
45
-
-
34547821380
-
-
See Mark Heinzl & Amol Sharma, Getting the Message: RIM to Pay NTP $612.5 Million to Settle BlackBerry Patent Suit, WALL ST. J., Mar. 4, 2006, at A1. To be sure, the damages the jury awarded were only for six of fifteen remaining years on the patent, so adding a going forward royalty would presumably have raised the total award. And there is reason to believe RIM will sell more BlackBerries in the future than it has in the past. But even that continuing royalty would likely have been significantly less than the $612.5 million settlement that was reached in March 2006.
-
See Mark Heinzl & Amol Sharma, Getting the Message: RIM to Pay NTP $612.5 Million to Settle BlackBerry Patent Suit, WALL ST. J., Mar. 4, 2006, at A1. To be sure, the damages the jury awarded were only for six of fifteen remaining years on the patent, so adding a going forward royalty would presumably have raised the total award. And there is reason to believe RIM will sell more BlackBerries in the future than it has in the past. But even that continuing royalty would likely have been significantly less than the $612.5 million settlement that was reached in March 2006.
-
-
-
-
46
-
-
34547765315
-
-
Mark A. Lemley et al., Tracking Patent Trolls (2007) (unpublished manuscript, on file with author).
-
Mark A. Lemley et al., Tracking Patent Trolls (2007) (unpublished manuscript, on file with author).
-
-
-
-
47
-
-
34547729103
-
-
MercExchange, L.L.C. v. eBay, Inc., 401 F.3d 1323, 1339 (Fed. Cir. 2005), vacated, 126 S. Ct. 1837 (2006).
-
MercExchange, L.L.C. v. eBay, Inc., 401 F.3d 1323, 1339 (Fed. Cir. 2005), vacated, 126 S. Ct. 1837 (2006).
-
-
-
-
48
-
-
34547807575
-
-
See Heller & Eisenberg, supra note 5, at 699 (warning against a potential tragedy of the anticommons in the biomedical industry that could deter innovation in the future);
-
See Heller & Eisenberg, supra note 5, at 699 (warning against a potential "tragedy of the anticommons" in the biomedical industry that could deter innovation in the future);
-
-
-
-
49
-
-
34547807576
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Shapiro, supra note 5, at 120 (expressing concern over the emergence of a patent thicket, where stronger patent rights can have the perverse effect of stifling, not encouraging, innovation).
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Shapiro, supra note 5, at 120 (expressing concern over the emergence of a "patent thicket," where "stronger patent rights can have the perverse effect of stifling, not encouraging, innovation").
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For evidence of royalty stacking in the semiconductor industry, see Rosemarie Ham Ziedonis, Don't Fence Me In: Fragmented Markets for Technology and the Patent Acquisition Strategies of Firms, 50 MGMT. SCI. 804, 817-18 2004, finding that firms acquire patents more aggressively when the patents for numerous component technologies of an industry, like the semiconductor industry, are widely distributed
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For evidence of royalty stacking in the semiconductor industry, see Rosemarie Ham Ziedonis, Don't Fence Me In: Fragmented Markets for Technology and the Patent Acquisition Strategies of Firms, 50 MGMT. SCI. 804, 817-18 (2004) (finding that firms acquire patents more aggressively when the patents for numerous component technologies of an industry - like the semiconductor industry - are widely distributed).
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For evidence of royalty stacking in the software industry, see Michael Noel & Mark Schankerman, Strategic Patenting and Software Innovation 27 (Ctr. for Econ. Policy Research, Discussion Paper No. 5701, 2006) (finding clear evidence that strategic patenting and technology spillover are present in the software industry). Rebecca Eisenberg and Richard Nelson argue that patents on biomedical research tools can retard innovation.
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For evidence of royalty stacking in the software industry, see Michael Noel & Mark Schankerman, Strategic Patenting and Software Innovation 27 (Ctr. for Econ. Policy Research, Discussion Paper No. 5701, 2006) (finding "clear evidence that strategic patenting and technology spillover are present" in the software industry). Rebecca Eisenberg and Richard Nelson argue that patents on biomedical research tools can retard innovation.
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Rebecca S. Eisenberg & Richard R. Nelson, Public vs. Proprietary Science: A Fruitful Tension?, DAEDALUS, Spring 2002 at 89, 101 (stating that in the biomedical industry, proprietary control of information can impose significant costs on subsequent research and thereby obstruct, rather than promote, product development). However, John Walsh, Ashish Arora, and Wesley Cohen found that researchers found various ways to work around patents on research tools, including licensing, inventing around, and infringement; they did not find clear evidence that basic biomedical research has been stifled by patents on biomedical research tools, but these results are significantly attributable to scientists simply ignoring patents.
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Rebecca S. Eisenberg & Richard R. Nelson, Public vs. Proprietary Science: A Fruitful Tension?, DAEDALUS, Spring 2002 at 89, 101 (stating that in the biomedical industry, "proprietary control of information can impose significant costs on subsequent research and thereby obstruct, rather than promote, product development"). However, John Walsh, Ashish Arora, and Wesley Cohen found that researchers found various ways to work around patents on research tools, including licensing, inventing around, and infringement; they did not find clear evidence that basic biomedical research has been stifled by patents on biomedical research tools, but these results are significantly attributable to scientists simply ignoring patents.
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John P. Walsh, Ashish Arora & Wesley M. Cohen, Working Through the Patent Problem, 299 SCIENCE 1021, 1021 (2003) (concluding nevertheless that because aggressive assertions of IP can still threaten scientific research, there is a continuing need for active defense of open science). Fiona Murray and Scott Stern find evidence of a modest anticommons effect using pairs of scientific articles and associated patents.
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John P. Walsh, Ashish Arora & Wesley M. Cohen, Working Through the Patent Problem, 299 SCIENCE 1021, 1021 (2003) (concluding nevertheless that because "aggressive assertions of IP can still threaten scientific research," there is a "continuing need for active defense of open science"). Fiona Murray and Scott Stern find evidence of a modest anticommons effect using pairs of scientific articles and associated patents.
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Fiona Murry & Scott Stern, Do Formal Intellectual Property Rights Hinder the Free Flow of Scientific Knowledge? An Empirical Test of the Anti-Commons Hypothesis 31 (Nat'l Bureau of Econ. Research, Working Paper No. 11465, 2005) (Overall, we are able to reject the null hypothesis that IP rights have no impact on the diffusion of scientific knowledge.). For a discussion of the role of patents and the danger of royalty stacking in biomedical research and in the software industry,
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Fiona Murry & Scott Stern, Do Formal Intellectual Property Rights Hinder the Free Flow of Scientific Knowledge? An Empirical Test of the Anti-Commons Hypothesis 31 (Nat'l Bureau of Econ. Research, Working Paper No. 11465, 2005) ("Overall, we are able to reject the null hypothesis that IP rights have no impact on the diffusion of scientific knowledge."). For a discussion of the role of patents and the danger of royalty stacking in biomedical research and in the software industry,
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see generally WENDY H. SCHACHT, CONGRESSIONAL RESEARCH SERVICE REPORT FOR CONGRESS, PATENT REFORM: ISSUES IN THE BIOMEDICAL AND SOFTWARE INDUSTRIES 12 (2006), available at http://www.fas.org/sgp/crs/misc/RL33367.pdf (discussing the sometimes divergent views of the biomedical and software industries toward patents and proposed patent reform), and INTELLECTUAL PROPERTY RIGHTS IN FRONTIER INDUSTRIES: SOFTWARE AND BIOTECHNOLOGY (Robert W. Hahn ed., 2005) (collecting essays addressing the pertinent policy debates surrounding patent issues in these fields).
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see generally WENDY H. SCHACHT, CONGRESSIONAL RESEARCH SERVICE REPORT FOR CONGRESS, PATENT REFORM: ISSUES IN THE BIOMEDICAL AND SOFTWARE INDUSTRIES 12 (2006), available at http://www.fas.org/sgp/crs/misc/RL33367.pdf (discussing the sometimes divergent views of the biomedical and software industries toward patents and proposed patent reform), and INTELLECTUAL PROPERTY RIGHTS IN FRONTIER INDUSTRIES: SOFTWARE AND BIOTECHNOLOGY (Robert W. Hahn ed., 2005) (collecting essays addressing the pertinent policy debates surrounding patent issues in these fields).
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Simple benchmarking could provide a fourth reason if the rate negotiated between the downstream firm and one patent holder is used as a benchmark in negotiations with other patent holders. However, for benchmarking to be important, the second patentee must have information about the negotiated rate, and the patents involved must be considered at least somewhat comparable by the negotiating parties
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Simple benchmarking could provide a fourth reason if the rate negotiated between the downstream firm and one patent holder is used as a benchmark in negotiations with other patent holders. However, for benchmarking to be important, the second patentee must have information about the negotiated rate, and the patents involved must be considered at least somewhat "comparable" by the negotiating parties.
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See Douglas Gary Lichtman, Patent Holdouts and the Standard-Setting Process 6-7 (Univ. of Chi. Law Sch., John M. Olin Law & Economics Working Paper No. 292, 2006), available at http://www.law.uchicago.edu/ Lawecon/WkngPprs_251-300/292.pdf (noting that a larger number of overlapping patent holders can be a self-limiting problem because a larger number of patents means less money for each patent holder).
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See Douglas Gary Lichtman, Patent Holdouts and the Standard-Setting Process 6-7 (Univ. of Chi. Law Sch., John M. Olin Law & Economics Working Paper No. 292, 2006), available at http://www.law.uchicago.edu/ Lawecon/WkngPprs_251-300/292.pdf (noting that a larger number of overlapping patent holders can be a self-limiting problem because a larger number of patents means less money for each patent holder).
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Of course, in practice, higher royalty burdens will lead to higher prices and reduced output, with associated deadweight loss. Accounting for these effects, while complicating the math, strengthens our argument
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Of course, in practice, higher royalty burdens will lead to higher prices and reduced output, with associated deadweight loss. Accounting for these effects, while complicating the math, strengthens our argument.
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U.S. PATENT & TRADEMARK OFFICE, U.S. PATENT ACTIVITY CALENDAR YEARS 1790 TO THE PRESENT (2006), http://www.uspto.gov/web/offices/ac/ido/oeip/ taf/h_counts.pdf (providing a table that shows the number of patents more than tripled between the years 1980 and 2005); Mark A. Lemley & Bhaven Sampat, Is the Patent Office a Rubber Stamp? (2007) (unpublished manuscript, on file with author) (finding that modern patent applications are filed disproportionately in the information technology industries).
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U.S. PATENT & TRADEMARK OFFICE, U.S. PATENT ACTIVITY CALENDAR YEARS 1790 TO THE PRESENT (2006), http://www.uspto.gov/web/offices/ac/ido/oeip/ taf/h_counts.pdf (providing a table that shows the number of patents more than tripled between the years 1980 and 2005); Mark A. Lemley & Bhaven Sampat, Is the Patent Office a Rubber Stamp? (2007) (unpublished manuscript, on file with author) (finding that modern patent applications are filed disproportionately in the information technology industries).
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Ten Things To Do About
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See, e.g, Patent Holdup of Standards (And One Not To, 48 B.C. L. REV. 149, 151 2007, stating that IT products are often covered by numerous patents because they are technologically complex and integrate many components
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See, e.g., Mark A. Lemley, Ten Things To Do About Patent Holdup of Standards (And One Not To), 48 B.C. L. REV. 149, 151 (2007) (stating that IT products are often covered by numerous patents because they are technologically complex and integrate many components).
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Lemley, M.A.1
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Cournot used the example of copper and zinc suppliers selling to manufacturers of brass. AUGUSTIN COURNOT, RESEARCHES INTO THE MATHEMATICAL PRINCIPLES OF THE THEORY OF WEALTH 99-116 (Nathaniel T. Bacon trans., Augustus M. Kelley Publishers 1971) (1838).
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Cournot used the example of copper and zinc suppliers selling to manufacturers of brass. AUGUSTIN COURNOT, RESEARCHES INTO THE MATHEMATICAL PRINCIPLES OF THE THEORY OF WEALTH 99-116 (Nathaniel T. Bacon trans., Augustus M. Kelley Publishers 1971) (1838).
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For a derivation of this well-known result, see Shapiro, supra note 5, app. In the special case of constant elasticity demand for the final product, if there are N essential inputs, each controlled by a single firm, and if the downstream firm(s) simply price at their marginal cost, the resulting markup on the final good, i.e., the percentage gap between price and the true marginal cost of producing that good, is N times the monopoly level.
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For a derivation of this well-known result, see Shapiro, supra note 5, app. In the special case of constant elasticity demand for the final product, if there are N essential inputs, each controlled by a single firm, and if the downstream firm(s) simply price at their marginal cost, the resulting markup on the final good, i.e., the percentage gap between price and the true marginal cost of producing that good, is N times the monopoly level.
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Formally, these two problems are very similar; both involve multiple markups in the value chain, set in an uncoordinated fashion. While double marginalization refers to situations in which there are two such markups, with royalty stacking the number of markups can be much larger
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Formally, these two problems are very similar; both involve multiple markups in the value chain, set in an uncoordinated fashion. While double marginalization refers to situations in which there are two such markups, with royalty stacking the number of markups can be much larger.
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This is a fundamentally different approach than the one taken in the text above, where the downstream firm's threat was either to litigate the patent or redesign its product to avoid infringing, and the output by the downstream firm was fixed. The analysis in Appendix A thus complements that provided in the text above
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This is a fundamentally different approach than the one taken in the text above, where the downstream firm's threat was either to litigate the patent or redesign its product to avoid infringing, and the output by the downstream firm was fixed. The analysis in Appendix A thus complements that provided in the text above.
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Baker and Lichtman have suggested contractual mechanisms by which this might be accomplished. Scott Baker & Doug Lichtman, Discouraging Patent Holdouts Through Reciprocal Commitment 15-25 Nov. 27, 2006, unpublished manuscript, available at http://www.law.northwestern.edu/colloquium/ law_economics/lichtman.pdf
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Baker and Lichtman have suggested contractual mechanisms by which this might be accomplished. Scott Baker & Doug Lichtman, Discouraging Patent Holdouts Through Reciprocal Commitment 15-25 (Nov. 27, 2006) (unpublished manuscript), available at http://www.law.northwestern.edu/colloquium/ law_economics/lichtman.pdf.
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Anne Layne-Farrar and Josh Lerner examine the decisions by patent holders whether or not to participate in nine specific patent pools, eight of which grew out of standard-setting efforts. Anne Layne-Farrar & Josh Lerner, To Join or Not to Join: Examining Patent Pool Participation and Rent Sharing Rules 7 Nov. 15, 2006, unpublished manuscript, available at http://ssrn.com/abstract=945189. They find that as many as one-half to two-thirds of the eligible members chose not to participate in some patent pools. Id. at 23. Often, nonparticipants held relatively few patents and thus appear to have elected to assert their patents independently, perhaps engaging in holdup, rather than accepting a relatively small share of the royalties collected by the pool. Id. at 32 tbl.1. This finding is consistent with the analysis of Reiko Aoki and Sadao Nagaoka. Reiko Aoki & Sadao Nagaoka, Coalition Formation for a Consortium Standard Through a Standard Body and a Patent
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Anne Layne-Farrar and Josh Lerner examine the decisions by patent holders whether or not to participate in nine specific patent pools, eight of which grew out of standard-setting efforts. Anne Layne-Farrar & Josh Lerner, To Join or Not to Join: Examining Patent Pool Participation and Rent Sharing Rules 7 (Nov. 15, 2006) (unpublished manuscript), available at http://ssrn.com/abstract=945189. They find that as many as one-half to two-thirds of the eligible members chose not to participate in some patent pools. Id. at 23. Often, nonparticipants held relatively few patents and thus appear to have elected to assert their patents independently, perhaps engaging in holdup, rather than accepting a relatively small share of the royalties collected by the pool. Id. at 32 tbl.1. This finding is consistent with the analysis of Reiko Aoki and Sadao Nagaoka. Reiko Aoki & Sadao Nagaoka, Coalition Formation for a Consortium Standard Through a Standard Body and a Patent Pool: Theory and Evidence from MPEG2, DVD and 3G 4-11 (Hitotsubashi Univ. Inst. of Innovation Research, Working Paper No. 05-01, 2005), available at http://www.iir.hit-u.ac.jp/event/WP05-01aoki, %20nagaoka.pdf.
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Ziedonis, supra note 40, at 813-15
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Ziedonis, supra note 40, at 813-15.
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Id. at 805, 817.
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Id. at 817.
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Lemley et al, supra note 37
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Lemley et al., supra note 37.
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See Ben Depoorter & Sven Vanneste, Putting Humpty Dumpty Back Together: Pricing in Anticommons Property Arrangements 6 (George Mason Univ. Sch. of Law, Working Paper No. 11, 2004), available at http://law.bepress.com/gmulwps/gmule/art11/ (measuring the pricing effect of uncertainty and fragmentation).
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See Ben Depoorter & Sven Vanneste, Putting Humpty Dumpty Back Together: Pricing in Anticommons Property Arrangements 6 (George Mason Univ. Sch. of Law, Working Paper No. 11, 2004), available at http://law.bepress.com/gmulwps/gmule/art11/ (measuring the pricing effect of uncertainty and fragmentation).
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See, e.g, Rambus, Inc. v. Infineon Techs. AG, 318 F.3d 1081 (Fed. Cir. 2003, overturning a district court judgment of fraud against Rambus, In re Rambus, Inc, No. 9302, Opinion of the Commission (F.T.C Aug. 2, 2006, finding Rambus liable for monopolization for concealing the existence of patents in order to influence the standard selected by the Joint Electron Device Engineering Council, In re Union Oil Co. of Calif, No. 9305, 2004 WL 1632816, Order of the Commission (F.T.C. July 6, 2004, reversing an administrative law judge's decision to dismiss an antitrust claim against Unocal, and remanding for trial before the administrative law judge, In re Dell Computer Corp, 121 F.T.C. 616 May 20, 1996, granting a consent decree prohibiting Dell from enforcing patent rights against computer manufacturers related to a technology Dell had failed to disclose to a standard-setting organization
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See, e.g., Rambus, Inc. v. Infineon Techs. AG, 318 F.3d 1081 (Fed. Cir. 2003) (overturning a district court judgment of fraud against Rambus); In re Rambus, Inc., No. 9302, Opinion of the Commission (F.T.C Aug. 2, 2006) (finding Rambus liable for monopolization for concealing the existence of patents in order to influence the standard selected by the Joint Electron Device Engineering Council); In re Union Oil Co. of Calif., No. 9305, 2004 WL 1632816, Order of the Commission (F.T.C. July 6, 2004) (reversing an administrative law judge's decision to dismiss an antitrust claim against Unocal, and remanding for trial before the administrative law judge); In re Dell Computer Corp., 121 F.T.C. 616 (May 20, 1996) (granting a consent decree prohibiting Dell from enforcing patent rights against computer manufacturers related to a technology Dell had failed to disclose to a standard-setting organization).
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Timothy S. Simcoe, Explaining the Increase in Intellectual Property Disclosure (Dec. 8, 2005) (unpublished manuscript), available at http://www.rotman.utoronto.ca/timothy.simcoe/papers/SSO_IPR_Disclosures.pdf.
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Timothy S. Simcoe, Explaining the Increase in Intellectual Property Disclosure (Dec. 8, 2005) (unpublished manuscript), available at http://www.rotman.utoronto.ca/timothy.simcoe/papers/SSO_IPR_Disclosures.pdf.
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§ 284 (2000, For a detailed discussion of the history of patent damages, see Amy L. Landers, Let the Games Begin: Incentives to Innovation in the New Economy of Intellectual Property Law, 46 SANTA CLARA L. REV. 307, 311-22 2006
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35 U.S.C. § 284 (2000). For a detailed discussion of the history of patent damages, see Amy L. Landers, Let the Games Begin: Incentives to Innovation in the New Economy of Intellectual Property Law, 46 SANTA CLARA L. REV. 307, 311-22 (2006).
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35 U.S.C
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The basic test is set out in Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152 (6th Cir. 1978). Under Panduit, the patentee must show demand for the patented product, the absence of noninfringing substitutes, the patentee's ability to meet the demand for the infringing goods, and the amount of profit the patentee would have made from those sales. Id. at 1156. The Federal Circuit has adopted this test. See Hebert v. Lisle Corp., 99 F.3d 1109, 1119-20 (Fed. Cir. 1996); State Indus., Inc. v. Mor-Flo Indus., Inc., 883 F.2d 1573, 1577 (Fed. Cir. 1989).
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The basic test is set out in Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152 (6th Cir. 1978). Under Panduit, the patentee must show demand for the patented product, the absence of noninfringing substitutes, the patentee's ability to meet the demand for the infringing goods, and the amount of profit the patentee would have made from those sales. Id. at 1156. The Federal Circuit has adopted this test. See Hebert v. Lisle Corp., 99 F.3d 1109, 1119-20 (Fed. Cir. 1996); State Indus., Inc. v. Mor-Flo Indus., Inc., 883 F.2d 1573, 1577 (Fed. Cir. 1989).
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318 F. Supp. 1116 (S.D.N.Y. 1970).
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318 F. Supp. 1116 (S.D.N.Y. 1970).
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Those factors are: 1. The royalties received by the patentee for the licensing of the patent in suit, proving or tending to prove an established royalty. 2. The rates paid by the licensee for the use of other patents comparable to the patent in suit. 3. The nature and scope of the license, as exclusive or nonexclusive; or as restricted or nonrestricted in terms of territory or with respect to whom the manufactured product may be sold. 4. The licensor's established policy and marketing program to maintain his patent monopoly by not licensing others to use the invention or by granting licenses under special conditions designed to preserve that monopoly. 5. The commercial relationship between the licensor and licensee, such as, whether they are competitors in the same territory in the same line of business; or whether they are inventor and promoter. 6. The effect of selling the patented specialty in promoting sales of other products of the licensee; the existing value of the invention to
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Those factors are: 1. The royalties received by the patentee for the licensing of the patent in suit, proving or tending to prove an established royalty. 2. The rates paid by the licensee for the use of other patents comparable to the patent in suit. 3. The nature and scope of the license, as exclusive or nonexclusive; or as restricted or nonrestricted in terms of territory or with respect to whom the manufactured product may be sold. 4. The licensor's established policy and marketing program to maintain his patent monopoly by not licensing others to use the invention or by granting licenses under special conditions designed to preserve that monopoly. 5. The commercial relationship between the licensor and licensee, such as, whether they are competitors in the same territory in the same line of business; or whether they are inventor and promoter. 6. The effect of selling the patented specialty in promoting sales of other products of the licensee; the existing value of the invention to the licensor as a generator of sales of his nonpatented items; and the extent of such derivative or convoyed sales. 7. The duration of the patent and the term of the license. 8. The established profitability of the product made under the patent; its commercial success; and its current popularity. 9. The utility and advantages of the patent property over the old modes or devices, if any, that had been used for working out similar results. 10. The nature of the patented invention; the character of the commercial embodiment of it as owned and produced by the licensor; and the benefits to those who have used the invention. 11. The extent to which the infringer has made use of the invention; and any evidence probative of the value of that use. 12. The portion of the profit or of the selling price that may be customary in the particular business or in comparable businesses to allow for the use of the invention or analogous inventions. 13. The portion of the realizable profit that should be credited to the invention as distinguished from nonpatented elements, the manufacturing process, business risks, or significant features or improvements added by the infringer. 14. The opinion testimony of qualified experts. 15. The amount that a licensor (such as the patentee) and a licensee (such as the infringer) would have agreed upon (at the time the infringement began) if both had been reasonably and voluntarily trying to reach an agreement; that is, the amount which a prudent licensee-who desired, as a business proposition, to obtain a license to manufacture and sell a particular article embodying the patented invention - would have been willing to pay as a royalty and yet be able to make a reasonable profit and which amount would have been acceptable by a prudent patentee who was willing to grant a license. Id. at 1120.
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See Nickson Indus., Inc. v. Rol Mfg. Co., 847 F.2d 795, 798 (Fed. Cir. 1988) (relying on established market royalties as the strongest evidence of what royalty is reasonable);
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See Nickson Indus., Inc. v. Rol Mfg. Co., 847 F.2d 795, 798 (Fed. Cir. 1988) (relying on established market royalties as the strongest evidence of what royalty is reasonable);
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See AM. INTELLECTUAL PROP. LAW ASS'N, REPORT OF THE ECONOMIC SURVEY 2005, at 22 (2005) (reporting in 2005 that patent litigants spent $4.5 million per side in legal fees in cases where more than $25 million was at stake).
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See AM. INTELLECTUAL PROP. LAW ASS'N, REPORT OF THE ECONOMIC SURVEY 2005, at 22 (2005) (reporting in 2005 that patent litigants spent $4.5 million per side in legal fees in cases where more than $25 million was at stake).
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