PATENT SETTLEMENT AGREEMENTS

Chapter 85 ATNT STTLMNT AGRMNTS Sumanth Addanki and Alan J. akin * Variou commentator have argued that while agreement in ettlement of patent litigation are generally procompetitive, they can harm conumer if they include o-called revere payment from the incumbent patentee to the would-be entrant. Therefore, they ugget, ettlement that include revere payment hould be condemned. We how that thi propoed filter i not particularly ueful: in fact, ettlement agreement that include uch term are not necearily anticompetitive. Moreover, eemingly innocuou agreement i.e., one that exclude uch term may well turn out to be anticompetitive and to harm conumer. 1. Introduction The interface between antitrut and the law governing intellectual property preent intereting and challenging quetion to tudent, practitioner, and policy maker alike. The analyi of agreement that firm enter into in order to ettle patent dipute, in particular, ha a rich hitory in the antitrut literature, including the Antitrut Guideline for the Licening of Intellectual roperty, 1 numerou cholarly article, 2 and important recent court deciion. 3 Not urpriingly, a thinking on the ubject ha evolved, idea about what contitute anticompetitive patent ettlement have evolved a well. In thi chapter, we demontrate that the competitive effect of ettlement agreement may not be a obviou a they eem: apparently anticompetitive agreement may actually benefit conumer, while eemingly innocuou or beneficial ettlement may harm conumer. In Section 2 below, we conider one example of the former type of ettlement, one that include a o-called revere payment from the incumbent patentee to the would-be entrant. While ome commentator ugget that uch ettlement are preumptively anticompetitive, we how that uch a general preumption i invalid. In Section 3, we conider example of licening agreement that eem to have beneficial (or, at wort, neutral) effect on conumer; we demontrate that they may in fact harm conumer. * NRA conomic Conulting. 1. U.S. T OF JUSTIC & FRAL TRA COMM N, ANTITRUST GUILINS FOR TH LICNSING OF INTLLCTUAL RORTY (1995), reprinted in 4 Trade Reg. Rep. (CCH) 13,132. 2. See, e.g., Marc G. Schildkraut, atent-splitting Settlement and the Revere ayment Fallacy, 71 ANTITRUST L.J. 1033 (2004); Carl Shapiro, Antitrut Limit to atent Settlement, 34 RAN J. CON. 391 (2003); Robert. Willig & John. Bigelow, Antitrut olicy Toward Agreement that Settle atent Litigation, ANTITRUST BULL. 655 (2004); Robert Kneuper, Four conomic rinciple Underlying the FTC oition Againt Revere ayment in atent Settlement Agreement, ANTITRUST SOURC (Jan. 2006), www.antitrutource.com. 3. See, among other, the leventh Circuit deciion in Schering-lough Corp. v. FTC, 402 F.3d 1056 (11th Cir. 2005), and the Supreme Court denial of the FTC petition for certiorari, 126 S. Ct. 2929 (2006). 2127

2128 ISSUS IN COMTITION LAW AN OLICY 2. Revere payment need not be anticompetitive In recent year, the Federal Trade Commiion (FTC) and variou economic and legal commentator have argued that ettlement agreement that include revere payment are inherently anticompetitive and hould be condemned. In thi ection, we demontrate that uch blanket condemnation are unwarranted. 2.1. A propoed litmu tet for anticompetitive ettlement The FTC, in it enforcement action, publication, and public tatement, ha endored a bright line litmu tet under which any ettlement that incorporate a ocalled revere payment i.e., a payment by the patentee to the alleged infringer raie a red flag... and mandate a further inquiry. 4 While thi approach ha not been univerally accepted, other commentator have apparently endored it. 5 The FTC poition appear to be that the following three-tep tet i ufficient to determine whether an agreement that ettle a patent infringement cae i anticompetitive: (1) oe the patent holder (plaintiff) have monopoly power? (2) I there a threat to that monopoly power? and (3) I there a payment to the potential entrant (defendant) to delay entry by the defendant? 6 If the anwer to all thee quetion i 4. Schering-lough Corp., FTC ocket No. 9297, at 29 (ec. 18, 2003) (opinion of the Commiion) [hereinafter FTC Schering Opinion]. In an earlier filing in that cae, the FTC tated, [Repondent] never directly repond to our contention that paying a potential competitor to accept an entry date i a payment not to compete and preumptively anticompetitive. Reply Brief in Support of Complaint at 26, available at http://www.ftc.gov/o/adjpro/d9297/index.htm. According to the Commiion opinion in the cae, Complaint Counel made an alternative argument that the ettlement agreement in iue hould be characterized a either per e illegal or preumptively anticompetitive. Tranlated into the term of the tructure outlined above, their claim wa that the nature of the retraint i ufficiently troubleome to obviate pecific proof of market effect. FTC Schering Opinion at 12 (footnote omitted). In 2000, avid Balto, then Aitant irector of the Office of olicy and valuation in the FTC Bureau of Competition, wrote, Typically in patent infringement cae the payment flow from the alleged infringer to the patent holder. A payment flowing from the innovator to the challenging generic firm may ugget trongly the anticompetitive intent of the partie in entering the agreement and the rent-preerving effect of that agreement. avid Balto, harmaceutical atent Settlement: The Antitrut Rik, 55 FOO & RUG L.J. 321, 335 (2000) (footnote omitted). In a recent peech, Jon Leibowitz expreed concern about what he called excluion payment. Jon Leibowitz, FTC Commiioner, xcluion ayment to Settle harmaceutical atent Cae: They re B-a-a-a-ck!, Remark at the Second Annual In-Houe Counel Forum on harmaceutical Antitrut (Apr. 24, 2006). 5. For varying degree of endorement, ee, e.g., Keith B. Leffler & Critofer I. Leffler, Want to ay a Competitor to xit the Market? Settle a atent Infringement Cae; An Argument for er Se Condemnation of ayment by the atent Holder, CON. COMM. NWSL. (ABA Section of Antitrut Law), Spring 2002, at 26-35; Merril Hirh & an Zoloth orfman, I idn t Say Orphan Often: The Benefit of a Bright-Line Rule Barring Brand to Generic ayment in Hatch-Waxman atent Settlement, 19 ANTITRUST HALTH CAR CHRON. 2 (Summer 2005); and Thoma F. Cotter, Antitrut Implication of atent Settlement Involving Revere ayment: efending a Rebuttable reumption of Illegality in Light of Some Recent Scholarhip, 71 ANTITRUST L.J. 1069 (2004). 6. Thi three-part tet tem from the tetimony of rofeor Timothy Brenahan, the FTC economic expert in it proceeding againt Schering-lough and it correpondent. See FTC Schering Opinion, at 15. Addanki, who erved a the economic expert for Schering-lough, addreed thee and other iue in hi expert report, which wa filed in September 2001.

ATNT STTLMNT AGRMNTS 2129 affirmative, the FTC aert that the agreement mut be anticompetitive, that it would necearily make conumer wore off than they could have expected to be had the matter been reolved through litigation. The propoed tet i defended a follow. To begin with, the FTC argue that the appropriate meaure of any anticompetitive effect of a given ettlement agreement i the amount of time by which it delay entry relative to alternative ettlement or litigation, becaue conumer are better off the ooner the entrant enter the market. 7 The FTC then argue that ettlement that involve payment from the patentee to the alleged infringer are necearily anticompetitive, becaue, if the partie could reach a ettlement without a ide payment, the ettlement reached with ide payment are more anticompetitive, i.e., reult in later entry, than the ettlement that thoe ame partie would have reached otherwie. 8 On the other hand, the argument goe, when payment are neceary for ettlement even to be feaible, uch payment in the wrong direction, from incumbent to entrant, lead to outcome more anticompetitive i.e., later entry date than either party expect under litigation. Thi concluion ret on the following argument: Suppoe for implicity that the litigation ha reached a tage where dicovery i complete, o that the partie have learned all that they could expect to learn prior to trial about their odd of winning at trial; uppoe further that both partie agree that each one probability of prevailing in the litigation i roughly 50 percent. Then each party expect that, if they continued to litigate, the probability that the defendant will prevail and entry will occur virtually immediately i 50 percent, while the probability that the patentee will prevail and entry will be delayed until expiration of the patent i alo 50 percent. 9 Therefore, the argument goe, the expected time to entry under litigation (i.e., the probabilityweighted average of the two entry date under the two alternative outcome) i approximately one-half of the term remaining on the patent. 10 Any ettlement that reult in an entry date later than thi benchmark would then be deemed anticompetitive. 7. Thi formulation i not trictly correct; rik averion and dicounting (the economic reality that a dollar today i worth more than a dollar payable in the future, even etting aide inflation), among other thing, mean that a date certain entry four year in the future, for intance, i not equivalent, from the conumer tandpoint, to a lawuit under which the expected outcome i an entry date four year into the future. It i certainly entirely poible to incorporate thee feature into an economic model, but we have not done o here, becaue their incluion greatly complicate the expoition without materially changing our qualitative reult. In any event, much of the public debate ha been framed (implitically) in term of entry date. 8. The iue of excluion payment ha been the ubject of ignificant debate, but the Commiion poition i clear. Where a patentholder make a payment to a challenger to induce it to agree to a later entry than it would otherwie agree to, conumer are harmed either becaue a ettlement with an earlier date might have been reached, or becaue continuation of the litigation without ettlement would yield a greater propect of competition. Barrier to Generic ntry: Hearing Before the Sen. Special Comm. on Aging, 109th Cong. 18 (2006) (tatement of FTC) (footnote omitted). 9. For implicity of expoition only, we aume that the outcome of the trial will be made known relatively quickly, o that, hould the alleged infringer prevail, it entry would not be ubject to any additional delay. 10. For intance, if the patent ha eight year to run, the probability of intantaneou entry i 50%, but the probability that entry would be deferred for eight year i alo 50%, o the expected time to entry under litigation i four year (50% probability of zero and 50% probability of eight year).

2130 ISSUS IN COMTITION LAW AN OLICY The argument further hold that if the partie agreed that their repective odd of prevailing were 50 percent each, neither ide would agree, abent ide payment, to any ettlement that pecified an entry date different from thi benchmark date; the patentee, according to thi view, would accept no date earlier than the benchmark, wherea the entrant would accept no date later than the benchmark, each party reaoning that it could expect to do at leat a well hould it purue the litigation to it concluion. Therefore, the argument for the propoed tet conclude, any payment from patentee to entrant mut necearily be a bribe to peruade the entrant to delay it entry. 11 2.2. The propoed tet cannot be ued to identify anticompetitive ettlement One crucial flaw in thi chain of reaoning lie in the aertion that the patentee would not ettle for an entry date earlier than the benchmark (i.e., the expected, or probability-weighted average, date of entry under litigation). The logical flaw tem from the implicit aumption that the patentee would view a date certain entry of, ay, four year in the future a exactly equivalent to engaging in litigation whoe expected entry date i alo four year in the future (becaue, for example, it offer equal odd of entry today or entry eight year hence). The problem with thi aumption i that it i frequently violated in practice. There are many ound economic reaon why a patentee may be willing to ettle for an entry date earlier than that expected under litigation. Among thee are rik and people attitude toward rik. conomit have long undertood that mot individual are rik avere, in that they value outcome that are inherently uncertain le than outcome that can be known with certainty. veryday experience i replete with example. Companie whoe fortune are more riky have to offer higher expected return to their invetor than do companie that are le riky. The interet rate on corporate bond reflect the ame reality: companie whoe propect are regarded a more riky (and whoe rating by bond rating ervice like Moody reflect that aement) have to offer higher interet rate in order to attract invetor interet than do companie that are regarded a le riky. 11. According to Carl Shapiro, for example: Conumer benefit from a negotiated entry date t if and only [if] t [i earlier than the entrant expected date of entry under litigation]. Auming that duopoly profit are le than monopoly profit, however, there i little reaon to expect the firm to find uch entry date mutually attractive. If the firm are rik neutral, a reaonable aumption for large, publicly traded firm if not individual manager at thoe firm, and ignoring litigation cot, there are imply no gain from ettlement under thee condition when the only available intrument i the entry date.... To the extent that the patentholder believe the patent i tronger than doe the challenger, ettlement i made even more difficult, a the patentholder will init on a later entry date and the challenger will not agree to wait o long to enter. In thi imple model, a naked cah payment flowing from the patentholder to the challenger (in exce of avoided litigation cot) i a clear ignal that the ettlement i likely to be anticompetitive. reumably, the patentholder would not pay more than avoided litigation cot unle it believed that it wa buying later entry than it expect to face through the litigation alternative. Shapiro, upra note 2, at 407-08.

ATNT STTLMNT AGRMNTS 2131 The immediate implication, of coure, i that an individual who i rik avere might well be willing to acrifice ome portion of hi expected return from a venture, if, in exchange, he could reduce the uncertainty aociated with that venture. A patentee who ha built a ubtantial buine around a patent i very likely to be rik avere in exactly that fahion: when chooing between a ettlement and puruing litigation to it final outcome, the patentee would recognize that the nonzero probability aociated with loing it all create very real rik, regardle of the expected value aociated with litigation. If, a in our example above, the expected date of entry aociated with litigation were four year (equal likelihood of immediate entry or entry after eight year, upon patent expiration), the rik avere patentee would be willing to acrifice ome of that expected value in exchange for reducing the uncertainty attendant upon litigation. In other word, the rik avere patentee would be willing to ettle for entry by the would-be entrant at a date certain earlier than the expected date under litigation. In effect, the patentee rik averion could make the ettlement more favorable to conumer than the expected outcome under litigation. Of coure, uch a ettlement could alo be attractive to the entrant, becaue it would permit entry ooner than might have been expected under litigation. The problem i that the would-be infringer may well alo find that it liquidity poition doe not permit it to wait out the period until that entry date. In other word, while attractive, the ettlement may not be feaible for the entrant without ome ort of cah infuion that would help it to urvive until the entry date at iue (even though that date i earlier than the expected date of entry under litigation). In thi ituation, the only path to a ettlement could well be one in which the patentee provide uch a cah infuion. Without the infuion, even though the patentee would be willing to entertain a definite entry date earlier than the expected outcome of litigation, that earlier date would remain infeaible for the entrant. Any date that the entrant would regard a feaible (abent the cah infuion) would be too early for the patentee to accept, given it odd of prevailing in the lawuit (even allowing for rik averion). Thu, the only alternative to the ettlement with a cah payment might, in fact, have been litigation. Note that thi doe not mean that the reulting date of entry would be later than the expected outcome of the litigation. In fact, the date agreed upon by partie even with the cah payment may well be earlier than the date that might be expected under litigation. That, of coure, i the crucial quetion: i the entry date pecified in the ettlement earlier or later than the benchmark entry date that might be expected under litigation? In thi example, whether it i earlier than the benchmark date depend upon the degree of rik averion of the patentee, the amount of the payment required and the return that each party expect to earn under the alternative. 12 The propoed tet, therefore, i inappropriate a a litmu or bright line tet. It critical aumption that the patentee would never agree to a ettlement that embodied an entry date earlier than the date that might be expected under litigation i fundamentally 12. A Shapiro note, Thi i not to ay that uch payment [from the patentholder to the challenger] are necearily anticompetitive if other factor are brought into the analyi, uch a rik averion and aymmetric information about market condition, a revere cah payment may be important in more complex etting for ucceful ettlement. Shapiro, upra note 2, at 408 (footnote omitted).

2132 ISSUS IN COMTITION LAW AN OLICY invalid. The invalidity of thi underlying aumption, of coure, necearily nullifie the propoed tet. Moreover, the rik averion dicued above repreent only one of everal poible reaon why the tet key underlying aumption could eaily be invalid. For intance, the patentee might imply be unduly peimitic about it cae; the judge or magitrate may have placed particular preure on the patentee to ettle; or litigation cot, including out-of-pocket cot a well a the ignificant opportunity cot that litigation impoe on enior management time and attention, could be a factor. There are certainly other reaon a well why the aumption may be violated. 13 Therefore, contrary to the argument made by proponent of the litmu tet, agreement that provide for payment from the patentee to the entrant could, in fact, be procompetitive. 14 3. Agreement without revere payment may be anticompetitive Jut a revere payment may have procompetitive effect, licene agreement with payment flowing from the licenee to the licenor may have anticompetitive effect. Thu, the direction of the flow of payment will not, in and of itelf, indicate the effect of the agreement on cutomer. 3.1. A eemingly innocuou licene agreement In the lat ection, we demontrated that licene agreement that embody revere payment from patentee to alleged infringer may, in fact, be procompetitive, o that the bright line tet for anticompetitive agreement doe not work. Unfortunately, the obvere doe no better: licene agreement that appear perfectly normal with royaltie flowing in the right direction may, neverthele, be anticompetitive in their effect: they may lead to market outcome that are inferior, from the tandpoint of cutomer, to the expected outcome of litigation. 15 Firt, however, conider the following agreement, reached in ettlement of patent litigation between atco (the patent holder) and Mitou (an alleged infringer): Mitou will pay atco 14 percent of it net revenue in royaltie each year. If Mitou net ale exceed $100 million in any year, in recognition of the marketing and market development effort undertaken by Mitou, it will earn a credit of $10 million againt it royalty obligation that year, reducing it net payment by that amount. I there anything about thi agreement that could raie antitrut concern? Certainly, on it face, thi eem like an eminently procompetitive ettlement: Mitou will enter the market right away; the royalty rate i not obviouly overly onerou; and, moreover, by rewarding Mitou for beating certain ale goal, the agreement eem to 13. Among other thing, there might be antitrut counterclaim that would be dipoed of concurrently with the patent litigation, which could bear on the partie incentive to ettle. 14. Appendix A provide an analytical development of thi point. 15. For a dicuion uggeting that it i not obviou what the correct direction i for payment to flow in patent ettlement, ee aniel A. Crane, xit ayment in Settlement of atent Infringement Lawuit: Antitrut Rule and conomic Implication, 54 FLA. L. RV. 747, 769-76 (2002). See alo Kevin. Mconald, atent Settlement and ayment that Flow the Wrong Way: The arly Hitory of a Bad Idea, 15 ANTITRUST HALTH CAR CHRON. 2 (Winter 2002).

ATNT STTLMNT AGRMNTS 2133 provide explicit incentive for increaing output. Could an antitrut enforcer ak for more? Unfortunately, thing are not quite o imple. In fact, thi eemingly benign, apparently procompetitive agreement may actually be quite the oppoite! It may actually be wore from the tandpoint of cutomer than the expected outcome of litigation. 16 3.2. Undertanding the partie incentive To ee why, it i helpful firt to undertand the economic incentive facing the three intereted partie patentee, potential entrant, and cutomer under the alternative cenario of continued litigation and ettlement via a licene. To keep thing imple, aume for now, a before, that litigation would be intantaneou and cotle and that the probability that the patentee will prevail i known in advance by both partie. In other word, there i no diagreement about the odd of the outcome and we do not need to concern ourelve with delay due to dicovery, appeal and the like. In thi tylized world, litigation could yield two poible outcome: firt, the patentee could prevail, which we will further aume mean that for the remaining life of the patent, the patentee will preerve it monopoly, in that no further entry will occur; econd, the alleged infringer could prevail, in which cae entry would occur intantaneouly to provide competition to the patentee. Should the patentee prevail, the would-be entrant get nothing for it trouble, and the patentee retain it pretrial profitability. Should the patentee loe, entry occur immediately, and the entrant and patentee hare the market opportunity. Litigation, therefore, repreent a lottery with two poible outcome; the value of the lottery to each firm i imply the mathematical expected value the probability-weighted average of the value of the two outcome. Finally, what about the effect on the cutomer? The cutomer like the would-be entrant benefit from entry, although the benefit garnered by the cutomer are not the ame a the profit that will be earned by the entrant. However, the expected value of the litigation outcome from the cutomer tandpoint i calculated uing the ame principle: it i imply the probability-weighted average of the two poible market price/quantity outcome that could reult from litigation. Let u turn now to the alternative cenario, in which the patentee licene the wouldbe entrant for immediate entry in exchange for running royalty payment. Thi cenario differ from the litigation alternative for each of the three partie in two key repect. Firt, there i no longer any uncertainty, o there i no need to weight outcome by the probability of their occurrence. Rather, the definite outcome i that entry will occur, the market opportunity will be hared by patentee and entrant, and the cutomer will enjoy the benefit of the competition between them. The econd important difference i that, unlike the litigation outcome in which the patentee loe, competition between patentee and entrant and, hence, the market outcome of that competition will be fettered omewhat by the royalty payable by the entrant to the patentee. That i becaue the royalty will, in effect, repreent additional variable cot to the entrant: each additional unit old by the entrant will reult in added cot to the entrant, who now incur 16. See Appendix B for analytical detail.

2134 ISSUS IN COMTITION LAW AN OLICY production and ditribution cot a well a the additional royalty obligation engendered becaue of that unit. Thee added cot impair the competitivene of the entrant, to the patentee benefit. The direct effect of thi diminihed competitivene i that market price will be higher and market quantitie lower than if the entrant were unhindered by any ongoing royalty obligation. All ele equal, the higher the royalty rate, the greater will be the additional cot impoed on the entrant, and the higher the reulting market price. Again, the effect on the cutomer, while quantitatively ditinguihable from the effect on the entrant, move in the ame direction. Note that the royalty rate of interet i the one that would apply to an additional unit that the licenee might contemplate producing; it i the incremental royalty rate that count in influencing the licenee behavior and, hence, market price and quantity. To um up, litigation can reult in two outcome the patentee prevailing and retaining it monopoly or the patentee loing and facing unfettered competition from the alleged infringer and the value of thi litigation lottery, to patentee, would-be entrant, and cutomer alike, i imply the probability-weighted average of the value that each party realize under the alternative outcome. Settlement via a licene, in contrat, reult in immediate entry and competition by the entrant, although that competition (and it reulting impact on patentee and cutomer) i omewhat attenuated by the added cot that the licene impoe on the entrant. 3.3. Impact of the partie incentive on the feaibility, private value, and public value of ettlement Armed with thi undertanding of the partie incentive, we are ready to explore the circumtance under which ettlement are feaible, and then to ae whether feaible ettlement will necearily inure to the benefit of the cutomer. In what follow, for implicity, we will focu on potential agreement under which the licenee (alleged infringer) pay a running royalty to the licenor (patentee) and exclude complication uch a lump um payment (in either direction), cro-licene, and other trapping that may well come into play in real life. The condition under which a given licene agreement i feaible i imple enough to tate: an agreement i feaible if it offer the litigant patentee and alleged infringer alike an alternative that each prefer to continued litigation. We aume, moreover, that a party will prefer the ettlement agreement if that party total profit under the agreement are no lower than the mathematical expectation (the probability-weighted average) of the value of litigation. 17 Let repreent the probability that the patentee prevail in the lawuit, let ROFIT repreent the entrant profit under a pure duopoly (i.e., the ituation in which the partie do not ettle and the patentee loe the lawuit), let ROFIT repreent incumbent patentee profit under the ame cenario, and let ROFIT M repreent the patentee profit in the event that it win the lawuit and retain it patent monopoly. Finally, let R 17. In other word, we will not deal with the poibility that one or both partie may be rik avere. Adding that feature doe not change the baic outcome or concluion of the model conidered here, but it doe needlely complicate it expoition.

ATNT STTLMNT AGRMNTS 2135 denote the royalty payment under the ettlement, and let ROFIT L and ROFIT L repreent profit that the entrant and patentee, repectively, earn under the licene agreement, prior to any royalty payment. Feaibility then require the following: and ROFIT L R > (1 )* ROFIT ROFIT L + R > * ROFIT M + (1 )* ROFIT The firt of thee imply tate that the profit earned by the entrant/licenee, after paying it royalty obligation, ha to exceed the expected value to the entrant of the litigation alternative the profit that it would earn a an unfettered duopolit weighted by the probability that it would attain that tate. The econd i the correponding condition for the patentee/licenor: it profit plu it royalty receipt mut exceed it expected value of litigation the value of a victory weighted by the probability of that outcome plu the correpondingly weighted value of a litigation lo. 18 xamination of thee feaibility condition yield ome ueful inight. In particular, the tet for feaibility i a total profit tet for each party. In other word, if a licene agreement yielded each party total profit that exceeded what that party could expect to get under the litigation alternative, that agreement would be feaible and plauible, regardle of the incremental royalty rate it contained. But recall from the lat ection that the licenee incentive to expand (or contract) it output are determined by the incremental royalty rate that it face, not the total royalty obligation engendered by the licene. There i no reaon, therefore, to uppoe that a licene agreement that atifie the partie (becaue it meet the total profit criterion that each party total profit are at leat a great a it could expect under litigation) would create the appropriate incentive for the licenee to expand it output enough to make the licening outcome uperior from the cutomer tandpoint to continued litigation. And that, indeed, i why the agreement between atco and Mitou may, in fact, be le competitive and therefore le beneficial to cutomer than continued litigation. Becaue the agreement allow a lump-um reduction in Mitou royalty obligation to atco, it embodie a higher incremental rate than would licene term that offered the ame total royalty obligation but with no credit or lump-um reduction. There are, of coure, other way to effect the ame divergence between the incremental royalty rate and the total royalty obligation: liding cale, where the royalty rate increae with licened output, and royalty holiday for the firt portion of licened output are but two. A one example of the latter, a ettlement between atco and Mitou might allow the entrant to ell 200 unit annually royalty-free and require royalty payment of $70 per unit for any additional unit old. Under ome condition, uch an agreement would reduce conumer welfare relative to the litigation alternative. 19 oe thi mean, then, that we hould procribe, a a matter of policy, licene agreement that embody uch term, on the ground that uch arrangement probably 18. There i only one term on the right-hand ide of the firt inequality, becaue the would-be entrant earn no profit if it loe the litigation. 19. See Appendix B for analytical detail.

2136 ISSUS IN COMTITION LAW AN OLICY pring from initer motive and are likely to be anticompetitive? Unfortunately for the policy maker (but fortunately for potential litigant, becaue licening term of thi type are quite commonplace), there i no uch eay olution. The mere fact that the credit (or liding cale or royalty holiday) mean that the licene incremental rate can be made higher (and remain attractive to Mitou becaue the total royalty obligation i till uperior to litigation) doe not, in and of itelf, make the licene agreement anticompetitive relative to the litigation alternative; it imply create the wedge between total and incremental royalty rate that make uch an outcome more plauible. In a variety of ituation, however, depending on market demand condition and the partie relative cot tructure, uch term may be neceary in order for there to be an agreement at all, and the reulting agreement may well be uperior to litigation from the cutomer tandpoint! In other word, it would be unwie to adopt a blanket procription on agreement that embodied uch term. Such a policy could preclude many procompetitive and beneficial agreement, reulting in more (and, from the cutomer tandpoint, le favorable) litigation. 4. rincipled analyi require evaluating monopoly power and litigation odd What, then, i the correct analytical approach to deal with agreement that appear facially anticompetitive, perhap becaue they include a revere payment, or agreement that appear entirely innocuou but may depre output and elevate price relative to the expected outcome of litigation? A it turn out, the correct analytical framework for dealing with both of thee problem i the ame. In many ituation, the monopoly power portion of the FTC propoed tet if properly applied could obviate the need for further inquiry. If there i no monopoly power preent, there i no need for any further inquiry; the agreement could not be anticompetitive in it effect. Aume, however, that further analyi etablihe that the patentee doe have monopoly power. In that cae, the appropriate tet i whether cutomer are better off under the ettlement than they would have been (in expectational term) under litigation. 20 In evaluating a ettlement agreement with a o-called revere payment and an agreed date of entry, for example, the appropriate tet i whether the ettlement reulted in an agreed-upon entry date later than what might have been expected under litigation. To etablih whether or not thi occurred, one mut evaluate the likely outcome of the patent cae, a well a each party odd of prevailing in litigation. Thee fact would help etablih what the expected outcome would have been under litigation. 21 20. Shapiro ugget a imilar approach: I propoe and explore... the following imple antitrut rule: a patent ettlement cannot lead to lower expected conumer urplu than would have arien from ongoing litigation. Shapiro, upra note 2, at 396. 21. The FTC ha tated, however, that we believe that it would not be neceary, practical, or particularly ueful for the Commiion to embark on an inquiry into the merit of the underlying patent dipute when reolving antitrut iue in patent ettlement. Schering-lough Corp., FTC ocket No. 9297, at 35 (ec. 18, 2003).

ATNT STTLMNT AGRMNTS 2137 The bet ource of information about the likely competitive effect of the ettlement relative to the litigation alternative i likely to be found in the fact urrounding the underlying patent cae itelf. The objective fact elicited in the patent infringement cae preumably including finding regarding patent claim contruction and the like may contitute the bet available information regarding the relative odd that each party would have prevailed in the underlying patent uit. Thu, an agreement that, ay, plit the remaining patent term in half, could be viewed a relatively procompetitive if the objective fact uncovered in the litigation ugget that the expected time to entry under litigation wa longer i.e., that the patentee had a tronger cae. Analogouly, if the patentee had monopoly power, uch a ettlement might be viewed a anticompetitive if the objective fact uggeted that the patentee had relatively low odd of prevailing. Several practical point are worth noting. Firt, the court need to determine the likely outcome of the patent cae and the objective odd that each party will prevail in the litigation, not the partie ubjective etimate of thoe odd. Conequently, there would generally be no need to examine privileged document to etimate thoe odd. Second, it i not generally neceary to etimate thoe odd with tremendou preciion. If the propoed ettlement plit the remaining patent term in half, for example, the court need only determine if the expected time to entry under litigation would have been longer, not whether the patentee probability of prevailing in the litigation i 0.6, 0.7, or 0.75. In thi connection, it i important to recall that the aumption underlying thee dicuion i that entry would be virtually intantaneou hould the entrant prevail in the litigation. In actual fact, even a victory by the entrant could reult in deferred entry, either becaue of appeal or becaue the entrant entry would be delayed by the need to undertake variou invetment or eek regulatory approval, among other ource of delay. In that cae, the expected time to entry would exceed one-half the time remaining on the patent even if the probability of the entrant prevailing were 50 percent. Therefore, any empirical evaluation of whether or not a given agreement involving delayed entry and revere payment i anticompetitive require that we inquire not only about the odd of each party prevailing, but alo about the likely entry date under alternative litigation outcome. Analogouly, the aement of whether a eemingly innocuou licene agreement one in which entry i immediate and the payment flow in the right direction i in fact procompetitive (i.e., reult in lower price or higher conumer urplu than the expected outcome of litigation), depend on the ame fact-pecific invetigation outlined above. If the patentee ha no monopoly power, the inquiry can end. But if the patentee i found to poe monopoly power, evaluation of the competitive effect of the licene vi-à-vi the litigation alternative mut conider the likely outcome under litigation a well a the likelihood that the patentee would have prevailed in the lawuit. Thu, in thoe ituation in which a properly applied tet indicate that the patentee poee monopoly power, analyi of the competitive effect of a ettlement agreement would necearily involve an aement of all of the pertinent fact urrounding the underlying patent cae, in order to acertain the outcome that the cae could have generated a well a the relative likelihood of each of thoe outcome in litigation. Only

2138 ISSUS IN COMTITION LAW AN OLICY then could one etablih whether or not the agreement reulted in an outcome that wa uperior whether in term of entry date or in term of price and quantitie prevailing in the marketplace than the outcome that might have been expected under litigation. Although analyi of the underlying patent cae i by no mean trivial, other commentator both economit and attorney have reached imilar concluion about the need to conduct uch analyi. Carl Shapiro, for example, note: I would like to highlight one key practical problem with the approach advocated and analyzed here: typically, to compare conumer urplu under a ettlement with conumer urplu from ongoing litigation require an informed judgment a to the trength of the patent() at iue.... xcept in pecial cae..., there doe not appear to be any way around the need to ae patent trength directly if one i trying to determine whether a ettlement benefit conumer. 22 Similarly, in an amicu brief regarding the FTC petition for certiorari in the Schering-lough cae, the Solicitor General and the epartment of Jutice tated that the mere preence of a revere payment in the Hatch-Waxman context i not ufficient to etablih that the ettlement i unlawful. Rather, an appropriate legal tandard hould take into account the relative likelihood of ucce of the partie claim, viewed ex ante. 23 In a footnote, the brief added, in part, A court would not need to conduct a full trial on the merit of the patent claim in order to make a determination regarding the likelihood of a patent owner litigation ucce. Rather, a court could conduct a limited examination into the relative merit of the patent claim and other relevant factor urrounding the partie negotiation. 24 5. Concluion Variou commentator have uggeted the ue of relatively imple red flag (and correponding afe harbor ) to vet propoed agreement deigned to ettle patent litigation. For intance, ome have argued that the preence of a revere payment from patentee to licenee hould be a litmu tet: agreement that embody thee payment hould be deemed likely to be anticompetitive, while agreement that do not can be preumed, all ele equal, to be innocuou. We have examined the economic incentive facing the partie involved patentee, licenee/entrant, and cutomer and concluded that uch tet are unhelpful. Agreement that involve revere payment may, in fact, be procompetitive relative to litigation, while apparently innocuou agreement that involve no uch payment may, in fact, be anticompetitive relative to the litigation alternative. There i, therefore, no ubtitute for cloer, fact-pecific analyi of the agreement and it context. Thi, in turn, undercore two important realitie: firt, the agreement cannot be anticompetitive if the patentee lack monopoly power; econd, it i difficult to ae the competitive effect of a licene agreement in a vacuum. The agreement can only be evaluated relative to the expected outcome of litigation; therefore, a principled 22. Shapiro, upra note 2, at 397. 23. Amicu Brief for United State at 11, FTC v. Schering-lough Corp., 548 U.S. 919 (2006) (No. 05-273). 24. Id. n.1.

ATNT STTLMNT AGRMNTS 2139 antitrut analyi mut necearily examine the likely outcome of the litigation alternative in ome detail. 1. Introduction Appendix A Thi appendix develop a model in which an incumbent patentee () and a would-be entrant () individually decide whether to purue patent infringement litigation brought by the patentee or ettle the cae without litigation by agreeing that the entrant will defer entry to ome date certain in the future. In the model below, we how that there are certain value for the parameter of interet for which there i no feaible ettlement that involve only an agreed-upon date of entry for. For uch parameter value, the latet date for entry by entrant that would induce to ettle i earlier than the earliet date that would induce patentee to ettle. We how, however, that the partie can reach a ettlement in which (1) pay a lump um, (2) each party prefer to ettle rather than litigate, and (3) the agreed-upon date for entry by i earlier than the expected date of entry under litigation. 2. Baic aumption and outline of the model 1. The current date i t = 0; the patent will expire at t = 2T. In all cae, after expiration of the patent (for t > 2T), free entry enure that all upplier, including both and, earn zero economic profit. 2. At time t = 0, each party decide unilaterally whether it prefer to ettle or litigate. 3. Unle both partie prefer to ettle, they litigate at t = 0; each party probability of winning i 0.5. The deciion in the litigation unknown to the partie before they chooe between ettlement and litigation i intantaneou. 4. If the partie do litigate, If win the litigation, enter immediately (at t = 0) and earn profit at a rate of ( for duopolit and for entrant) 25 from t = 0 to t = 2T; and earn profit at a rate of from t = 0 to t = 2T. ( for duopolit and for patentee) 25. For the numerical example/imulation below, we have aumed that the entrant and the patentee rate of duopoly profit (i.e., their rate of profit before expiration of the patent if both are elling the product) are equal. In the algebraic development of the model, however, we allow for more generality, allowing for different value of (and uing different notation for) the two firm rate of profit. The model, therefore, allow for more elaborate example/imulation in which the duopolit rate of profit are not equal.

2140 ISSUS IN COMTITION LAW AN OLICY If win the litigation, cannot enter until t = 2T. Since it economic profit will be 0 after t = 2T and, by aumption, it will have to incur ongoing expenditure from t = 0 until t = 2T to maintain it viability (ee below) never enter. It earn profit at a rate 0, therefore, tarting at t = 0 (jut after reolution of the litigation in favor of the patentee). earn profit at a rate (and 0 thereafter). m 5. If the partie each prefer to ettle, enter at t = t *. earn profit at a rate of earn profit at a rate of m (m for monopolit) from t = 0 to t = 2T from t = 0 to t = t *, and from t = t * to t = 2T (and 0 thereafter). In addition, pay a lump um payment of B at t = 0. (In the model below, B can, of coure, be zero.) receive the lump um payment of B at t = 0; earn profit at a rate of R from t = 0 to t = t * (i.e., mut make ongoing expenditure at a rate of R to remain viable until it enter at t = t * ); and earn profit at a rate of from t = t * to t = 2T (and 0 thereafter). 6. The patentee i rik-avere: The utility of the preent value of the patentee U V ( profit) ln V profit. profit i given by 3. The patentee deciion In thi ection, we develop expreion for the preent value of the patentee tream of profit under ettlement and under litigation. We then develop an expreion for the break-even date t at which the patentee i indifferent between ettling and litigating. 3.1. The patentee profit from ettlement If the partie ettle, the preent value of the patentee tream of profit i t 2T m rt rt 0 t e dt e dt B rt rt 2rT 1 m e e e B 26 (A1) r r 26. The patentee and entrant dicount rate need not be equal and, in general, they will not be equal. To minimize notational clutter, however, we omit ubcript on r in the general development of the model below. In the numerical example/imulation that follow, moreover, we aume equal dicount

ATNT STTLMNT AGRMNTS 2141 The interpretation of the firt two term in quation (A1) i traightforward: 1 m rt m m rt e m e give the value (at t = 0) of a perpetuity at rate tarting at r r r m t = 0 minu the value (at t = 0) of a perpetuity at rate tarting at t = t * ; rt 2rT r e e give the value of a perpetuity at rate tarting at t = t * minu the value of a perpetuity at rate tarting at t = 2T. 3.2. The patentee profit from litigation If the partie litigate, the preent value of the patentee tream of profit take one of two value, each with probability ½. The preent value of tream of profit i m 2T m rt 2rT 0 e dt 1 e if win the lawuit or r 2T rt 2rT e dt 1 e if win the lawuit 0 r 3.3. Condition under which the patentee i indifferent between ettlement and litigation (A2) (A3) The patentee will be indifferent between ettlement and litigation when hi utilitie from thoe two option are equal. Uing quation (A1), (A2), and (A3), the patentee will be indifferent when m rt rt 2rT 1 2rT e e e B e m ln 1 ln 1 r r 2 r 1 ln 2 1 rt e 2 r xponentiating both ide of the equation and implifying the right ide, 1 m e e e B r r r 2rT rt rt 2rT 1 e m (A4) If B i contrained to be 0 i.e., we retrict our attention to ettlement that do not include lump um payment between the partie then the third term on the left ide of quation (A4) drop out. We can then implify quation (A4) and olve for t, the patentee break-even value of t * at which he i indifferent between litigation and ettlement when B = 0: 2 2 e e e e m rt rt rt rt m 1 1 0 1 e 2rT m 2rT m 1 e t ln m r (A5) rate for the two partie. Generalization of the model to allow for different dicount rate for the two partie i traightforward and obviou.

2142 ISSUS IN COMTITION LAW AN OLICY For given value of the parameter in the expreion on the right ide of quation (A5), the patentee will prefer ettlement to litigation if t t, will prefer litigation to ettlement if t t, and will be indifferent between litigation and ettlement if t t. 4. The entrant deciion In thi ection, we develop expreion for the preent value of the entrant tream of profit under ettlement and under litigation. We then develop an expreion for the break-even date t at which the entrant i indifferent between ettling and litigation. 4.1. The entrant profit from ettlement If the partie ettle, the preent value of the entrant tream of profit i R t 2T rt rt 0 t e dt e dt B rt rt 2rT 1 e e e B r r R (A6) Note that an increae in t * affect both of the firt two term of quation (A6). By delaying the entry of, an increae in t * reduce the preent value of duopoly profit (the econd term), and increae the duration of net outflow required before it entry, thereby increaing the magnitude of the firt term in quation (A6), which i negative. 4.2. The entrant profit from litigation If the partie litigate, the preent value of the entrant tream of profit take one of two value, each with probability ½. The preent value of tream of profit i 0 if win the lawuit or (A7) 2T rt 2rT e dt 1 e if win the lawuit 0 r (A8) 4.3. Condition under which the entrant i indifferent between ettlement and litigation The entrant will be indifferent between ettlement and litigation when the preent value of hi profit from thoe two option are equal. quating the expreion in quation (A6) and the expected value of the two expreion in quation (A7) and (A8), the entrant will be indifferent when 1 rt rt 2rT 2 1 rt e e e B e R r r 2r (A9)

ATNT STTLMNT AGRMNTS 2143 If B i contrained to be 0 i.e., we retrict our attention to ettlement that do not include lump um payment between the partie the third term on the left ide of quation (A9) drop out. We can then implify quation (A9) and olve for t, the entrant break-even value of t * at which he i indifferent between litigation and ettlement when B = 0: 2 rt rt 2rT 2rT R e 1 e e 1 e 2 2 1 e rt 1 R t ln r R (A10) For given value of the parameter in the expreion on the right ide of quation (A10), the entrant will prefer ettlement to litigation if t t, will prefer litigation to ettlement if t t, and will be indifferent between litigation and ettlement if t t. 5. For ome et of parameter value, there i no feaible ettlement without a payment B A noted in the introduction to thi appendix, it i poible to find et of parameter value for which there i no feaible ettlement without a payment B but for which the partie can reach a ettlement in which (1) pay a lump um, (2) each party prefer to ettle rather than litigate, and (3) the agreed-upon date for entry by i earlier than T, the expected date of entry if the partie litigate. To ee one uch example, conider the following et of parameter value: 27 m 4 R T 2 r 1.5 0.5 r 0.2 20% (A11) Note, of coure, that the two partie dicount rate, r and r, could differ. To make the point below, however, we need not pecify different value for r and r. lugging thoe value into the expreion in quation (A5) and (A10) give t 1.173 and t 1.157. In word, if B = 0, the patentee will ettle (rather than litigate) only if the ettlement date i later than t 1.173, while 27. The value lited for m and are the monopoly and Cournot duopoly profit, repectively, if demand i given by Q = 16p 2 and both partie have contant marginal cot of 1. (To verify thoe reult, ee the dicuion in Appendix B, which dicue uch a Cournot model.)

2144 ISSUS IN COMTITION LAW AN OLICY the entrant will ettle (rather than litigate) only if the ettlement date i earlier than t 1.157. Clearly, without ome ort of payment B, there i no ettlement date that will induce both partie to ettle; without a payment B, therefore, they will litigate. But there are an infinite number of feaible ettlement ettlement that both partie prefer to litigation once we allow a nonzero payment B from the patentee to the entrant. It i eay to how, for example, that both partie will prefer ettlement to litigation if the entrant enter at t * = 1.5 and the patentee pay the entrant B = 0.6. In fact, for entry by at t * = 1.5 (and the parameter value indicated in quation (A11) above), it i poible to how that both partie will prefer ettlement to litigation a long a 0.526801 < B < 0.62549. 28 Similarly, for entry by at t * = 1.75 (and the parameter value indicated in quation (A11) above), it i poible to how that both partie will prefer ettlement to litigation a long a 0.888103 < B < 1.077116. In that cae, for example, a payment of B = 1 would induce both partie to ettle. Note that in both et of example in the previou paragraph, the partie can reach a ettlement with certain entry by the entrant at a date t * that i earlier than the expected date of entry under litigation. 1 0 2 1 T 0 22 2, 2 2 Appendix B Thi appendix develop everal model that lie behind variou example in the text of thi chapter. In particular, we develop model that how how the ettlement agreement between atco and Mitou may harm conumer, even though the partie may prefer ettlement to litigation in both cae. 1. Notation Thi ection et out briefly the notation ued below. Q = total market outupt q = the patentee output q = the entrant output = the elaticity of market demand; demand i ioelatic: Q = Kp equivalently, p = (Q/K) 1/ K = a multiplicative contant (a cale factor) c = the patentee contant marginal cot of production (normalized to 1) 28. For a given value of t *, we can find the break-even value of B at which the patentee i indifferent between ettlement and litigation by olving quation (A4) for B in term of the other parameter, including t *. Similarly, for a given value of t *, we can find the break-even value of B at which the entrant i indifferent between ettlement and litigation by olving quation (A9) for B in term of the other parameter, including t *.

ATNT STTLMNT AGRMNTS 2145 c = the entrant marginal cot of production (aumed to be contant) = the probability that the patentee win the litigation if the partie litigate In general, the ubcript and refer to the patentee and entrant, repectively. To ditinguih variable in the litigation cenario from thoe in the ettlement cenario, we ue upercript L and, repectively. 2. Baic overview of the model 2.1. Litigation If the partie decide to litigate i.e., they do not reach a ettlement there are two poible outcome: The patentee win the lawuit. In that cae, the would-be entrant i not allowed to enter, and the patentee price the product a a monopolit. The patentee loe the lawuit. In that cae, the entrant enter, and the partie compete a Cournot duopolit. 2.2. Settlement If the partie decide to ettle, they compete a Cournot duopolit. We conider two alternative type of ettlement if the partie decide to ettle: a royalty that i a linear function of the entrant revenue (i.e., an ad valorem royalty) and a royalty pecified a a certain dollar amount per unit old by the entrant (i.e., a pecific royalty). We provide further detail about thee ettlement in the dicuion below. 3. Solution of the model 3.1. Litigation SCNARIO 1: TH ATNT WINS TH LAWSUIT In thi cae, the patentee behave a a monopolit in chooing the profit-maximizing quantity. Specifically, the patentee chooe the monopoly price p m to maximize 1 p p c q p 1 Q p 1 Kp K p p (B1) m m m m m m m The firt-order condition are then p m 1 K 1 pm p m 0 pm 1 At that price, the monopoly patentee profit are given by m p p 1Q p 1 K p m m m m 1 K 1 1 (B2) (B3)

2146 ISSUS IN COMTITION LAW AN OLICY SCNARIO 2: TH ATNT LOSS TH LITIGATION In thi cae, the patentee and entrant compete a Cournot duopolit. To compute the Cournot duopoly price and the partie profit, we ue the general expreion for the Cournot oligopoly price for a market with N firm in which firm i marginal cot i contant at c i : N i 1c i p N 1, (B4) where N i the number of firm. 29 (Note incidentally that with N = 1 and c = 1, which apply if the monopolit win the lawuit, the expreion in quation (B4) implifie to the expreion for p m in quation (B2).) In the duopoly cae at hand, the Cournot duopoly price i jut a pecial cae of quation (B4): p 1 2 1 L c, (B5) where the upercript L refer to the outcome under litigation. We can then compute total quantity demanded by ubtituting that price into the demand function: Q L K p L (B6) To compute the quantitie produced by each party, note that in thi model (ee note 29), q i i i 1 c qi 1 c Q, Q p p (B7) o the quantitie produced by the patentee and entrant, repectively, can be computed uing the following expreion: c 1 q 1 Q 1 K p L L p p L L L (B8) 29. Let Q and q i denote total market quantity and the quantity upplied by firm i, repectively. Firm i maximize profit i pqi cq i i. efining d j / i q dq ji i, the firt-order condition for firm i i a follow: i p qi pq1 i ci 0 qi If firm behave in Cournot fahion ( i = 0 for all i), the latter equation implie qi ci 1 Q p Following Roger Clarke & Stephen W. avie, Market Structure & rice-cot Margin, 49 CONOMICA 277 (1982), we can um both ide of the latter equation over the N firm and olve for p: N i 1c i p N 1

ATNT STTLMNT AGRMNTS 2147 c c q 1 Q 1 K p L L p p L L L (B9) Finally, we can ue the expreion in quation (B5), (B8), and (B9) above to generate expreion for the partie profit in the Cournot duopoly equilibrium: 1 p c q p q (B10) L L L L L p L L L p c q (B11) The partie expected profit from litigation are then jut weighted average of their profit in Scenario 1 and 2, with weight and (1 ), repectively. 3.2. Settlement 1: An ad valorem royalty If the partie decide to ettle, they compete a Cournot duopolit, taking account of the effect of the royalty on their profit. In the dicuion below, we conider two alternative type of ettlement. We firt conider a ettlement in which the entrant pay the patentee a linear royalty given by where and are parameter. TH ATNT S ROBLM The patentee chooe q entrant revenue, to maximize p c q p q p 1 q p q, where the upercript on price and quantitie indicate ettlement price and quantitie, and denote the patentee profit in the ettlement equilibrium. The patentee firt-order condition, therefore, i q p 1 q p q p 0 p q q p 1 q Q q Q p p p p p 1 Q p Q p q Q 1 1 p 1 (B12)

2148 ISSUS IN COMTITION LAW AN OLICY TH NTRANT S ROBLM The entrant chooe q to max p c q p q q The entrant firt-order condition, therefore, i q 0 p c q p p q p 1 p q p c (B13) q Q c p p p Q p 1 q Q 1 p c 1 (B14) TH QUILIBRIUM RIC WITH A LINAR ROYALTY We can then add the expreion for the two firm hare in quation (B12) and (B14) to olve for the equilibrium price in the ettlement cenario a a function of demand elaticity, the firm marginal cot, and : 1 1 p c 1 1 1 p 1 1 c p 2 1 (B15) TH ARTIS ROFITS Having derived the expreion for the equilibrium price p in quation (B15) a a function of c,, and and, therefore, the equilibrium quantity through the demand function Q = Kp a well a expreion for the firm equilibrium hare in quation (B12) and (B14), we are now in a poition to compute the partie profit under ettlement. 3.3. Settlement 2: A pecific (per unit) royalty In thi cae, we conider a ettlement in which the entrant pay the patentee a per unit royalty. We firt outline the model in which the per unit royalty i fixed at a certain level, regardle of the quantity old by the entrant (i.e., the royalty = aq, where a i a parameter); we refer to uch a royalty a a one-tier per unit royalty. We then outline

ATNT STTLMNT AGRMNTS 2149 another verion of the model, the verion mentioned in the text, in which the per unit royalty increae once the entrant quantity exceed a certain threhold; we call that tructure a two-tier per unit royalty. TH ON-TIR R UNIT ROYALTY If the partie decide to ettle, they compete a Cournot duopolit, taking account of the effect of the royalty on their profit. The formal olution of the model i, of coure, very imilar to the olution of the Cournot model in Scenario 2 of the Litigation outcome (ee note 29 and the previou ection of the text). TH ATNT S ROBLM The patentee chooe q to maximize p c q aq p 1 q aq, where the upercript in denote the patentee profit in the ettlement equilibrium. The patentee firt-order condition i q p q p 1 0 Since the patentee firt-order condition doe not depend on q, we can ue the general expreion for firm i hare in uch a model (ee note 29) to rewrite the patentee firt-order condition a follow: qi c q i p 1 1 1 Q p Q p (B16) TH NTRANT S ROBLM The entrant chooe q to maximize p c q aq q p c a The entrant firt-order condition, therefore, i q p c a q p 0 Formally, the entrant problem i equivalent to the problem faced by a firm with marginal cot c + a. Therefore, we can rewrite that firt-order condition, uing the general expreion for firm i hare in uch a model (ee note 29), a follow: q c q c a i 1 i 1 Q p Q p (B17)

2150 ISSUS IN COMTITION LAW AN OLICY TH QUILIBRIUM RIC WITH A ON-TIR R UNIT ROYALTY We can then add the expreion for the two firm hare in quation (B16) and (B17) to olve for the equilibrium price in the ettlement cenario a a function of demand elaticity, the firm marginal cot, and a: 30 q q 1 c a 1 1 1 Q Q p p 1 2 c a 1 p 1 c a p 2 1 (B18) OVRVIW OF TH TWO-TIR R UNIT ROYALTY The tructure and the olution of the model with a two-tier per unit royalty are very imilar to their counterpart for the model with a one-tier per unit royalty, o we provide a briefer outline for the two-tier model. If the partie decide to ettle, the entrant pay the patentee a royalty of a per unit for each unit up to a threhold quantity q ; for each unit beyond that threhold, the entrant pay a royalty of a + b per unit. Formally, Royalty aq if q q aq bq q a bq bq if q q With that ettlement tructure, the patentee firt-order condition i the ame a in the model of the one-tier per unit royalty: although the patentee profit function depend on q, it firt-order condition doe not. In the ettlement equilibrium, therefore, the patentee hare i given by quation (B16). 31 The relevant verion of the entrant firt-order condition depend on whether the entrant' equilibrium quantity exceed the threhold q. Since we have already conidered the one-tier model, we focu here on parameter value for which q doe exceed q. In that cae, the entrant firt-order condition i imilar to it firt-order condition in the one-tier model ee quation (B17) except that a + b replace a: q c a b 1 Q p (B19) Similarly, the equilibrium price i given by quation (B18), except that a + b replace a: 30. A expected, the expreion for p i a pecial cae of the general expreion for equilibrium price in the Cournot model dicued in note 29. 31. Becaue the entrant firt-order condition with a two-tier royalty i different from it firt-order condition with a one-tier royalty (ee the dicuion below), the equilibrium ettlement price will alo differ for the two type of royaltie.

ATNT STTLMNT AGRMNTS 2151 1 c a b p 2 1 (B20) Having derived the expreion for the equilibrium price p in quation (B20) a a function of c,, a, and b and, therefore, the equilibrium quantity through the demand function Q = Kp a well a expreion for the firm equilibrium hare in quation (B16) and (B19), we are now in a poition to compute the partie profit under ettlement. 4. The partie preference for ettlement or litigation If each firm i rik neutral, it will prefer ettlement to litigation if it equilibrium profit under ettlement exceed it expected profit under litigation. The partie expected profit under litigation depend on the probability that the patentee will win the litigation, which we denote by ; we aume that both partie have the ame etimate of The patentee will prefer ettlement to litigation if L, i.e., if m L 1 m L L, (B21) where m L,, and are function of the underlying parameter (, c, etc.). For given value of thoe underlying parameter, quation (B21) indicate the value of for which the patentee would prefer ettlement. 32 The entrant will prefer ettlement to litigation if L, i.e., if 0 1 L L, (B22) L L where and are function of the underlying parameter. For given value of thoe underlying parameter, quation (B22) indicate the value of for which the entrant would prefer ettlement. 5. Conumer urplu If demand i ioelatic (Q = Kp, a aumed, and > 1, conumer urplu at any price p i given by 32. More generally, given value of all but one of the underlying parameter, quation (B21) generate the range of value for the other parameter for which the patentee would prefer ettlement.

2152 ISSUS IN COMTITION LAW AN OLICY x 1 1 Kx Kp Kx dx 1 1 p x p (B23) Uing quation (B23) and the appropriate expreion for price in the variou cenario conidered above, we can compute expected conumer urplu under litigation and conumer urplu under ettlement for any particular parameter value. To compute expected conumer urplu under litigation, we ue the ame etimate of a the partie. 6. Choice of parameter value It i now poible to how that ettlement that both partie prefer to litigation and that look quite innocuou may well harm conumer. 6.1. Settlement 1: The ad valorem royalty Suppoe, for example, the ettlement include an ad valorem royalty of the type conidered in Settlement 1, with the following parameter value: 3 K 1,000 c c 1 1.1 10 0.14 0.5 If Q i meaured in million of unit, thee parameter correpond to the example cited in the text: a royalty rate of 14 percent per dollar of the entrant gro revenue, with a rebate of $10 million if the entrant revenue exceed $100 million. (In equilibrium, given thee parameter value, that condition will be atified.) The reader can verify that both quation (B22) and (B21) are atified i.e., both partie prefer thi ettlement to litigation but expected conumer urplu i higher under litigation than conumer urplu under thi ettlement. 6.2. Settlement 2: The two-tier per unit royalty Alternatively, uppoe the ettlement include a two-tier per unit royalty of the ort conidered in Settlement 2, with the following parameter value: 2 K 1,000 c c 1 1 a 0 b 0.07

ATNT STTLMNT AGRMNTS 2153 q 200 0.1 If price are denominated in thouand of dollar, thoe parameter value correpond to the lat example cited in the text: royalty-free ale of the firt 200 unit, with royaltie of $70 per unit for any additional unit old. For thoe parameter value, in equilibrium, q doe exceed q, o the entrant doe pay a two-tier royalty, and both partie prefer ettlement to litigation. xpected conumer urplu under litigation, however, i actually higher than conumer urplu in the ettlement equilibrium. Thu, a indicated in the text, although the partie would prefer to ettle, ettlement will actually harm conumer. Note alo that for ome parameter value there i no one-tier per unit royalty that both partie would prefer to litigation. 33 To effect a ettlement that both partie and conumer prefer to litigation, therefore, a two-tier royalty or ome other royalty tructure may be neceary. 33. For example, if h = 2, c = 1, c = 0.95, a = 0.01, b = 0.1, q 200, and = 0.15, it i poible to how that there i no one-tier per unit royalty that both partie would prefer to litigation.