Bundling of RAND-committed patents

(1)

ContentslistsavailableatScienceDirect

Research

Policy

j ou rn a l h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / r e s p o l

Bundling

of

RAND-committed

patents

Anne

Layne-Farrar

a

_,

_Michael

_A.

_Salinger

b,∗

a_Charles_River_Associates,_One_South_Wacker_Drive,_Chicago,_IL_60606,_USA

b_Boston_University,_Questrom_School_of_Business,₅₉₅_Commonwealth_Ave.,_Boston,_MA_02215,_USA

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received31July2015

Receivedinrevisedform25February2016 Accepted2March2016

Availableonline21March2016 JELclassiﬁcation: O3 K21 Keywords: Patents Licensing Bundling Tying RAND FRAND Hold-up Intellectualproperty

a

b

s

t

r

a

c

t

GilbertandKatz(2006)(GK)showthatallowing(pure)patentbundlingincreasestheincentivesforpatent ownerstoenterinto“long-term”patentlicensingthatcommitsthemnottoexpropriatelicensees’sunk costsincomplementaryassetswithopportunisticlicensingterms.WeinterpretRANDcommitments asaformoflong-termcontracting,andextendtheirframeworktoanalyzethetyingof non-RAND-committedpatentstoRAND-committedpatents.Purepatentbundling/tyingiscommonandoftenhas soundefﬁciencyjustiﬁcations,sowecautionagainstprohibitingthepurebundlingofRAND-committed andnon-RAND-committedpatents.WhethersuchalicensehonorsaRANDcommitmentturns,however, onthelicensingterms.Wearguethatincludinganon-RAND-committedpatent(patent2)inabundlewith aRAND-committedpatent(patent1)doesnotincreasethelicensefeethathonorstheRANDcommitment. If,however,thepatentownerofferspatent1separatelyataRANDrate,itsRANDcommitmentdoesnot restrictwhatitchargesforabundleofpatent1andpatent2.

1. Introduction

Inthispaper,weaddresstherelationshipbetweentwo com-monpracticesinpatentlicensing:RANDcommitmentsandpatent bundling.ARANDcommitmentisacommitmenttolicense tech-nologyon“Reasonable and Non-Discriminatory”terms1_._Patent

bundling(or,more precisely,purepatentbundling) islicensing patentsonlyinbundles(orportfolios)ratherthanofferinglicenses toindividualpatentsonanàlacartebasis.Weaskwhether,once apatentownermakesageneralcommitmenttolicenseitspatents onRANDterms,itispermissibletoofferthosepatentssolelyina bundlewithotherpatents.Ifso,whatdoestheRANDcommitment implyfortheroyaltieschargedforthebundle?Alternatively,does aRANDcommitmentnecessarilyobligeapatentholdertolicense itspatentonastand-alonebasis?

To address the general issue of bundling RAND-committed patents, we must understand why patent bundling is such a

∗_{Corresponding}_author._Tel.:₊₁₆₁₇₃₅₃_4408;_fax:₊₁₆₁₇₃₅₃_6667.

E-mailaddresses:alayne-farrar@crai.com(A.Layne-Farrar),salinger@bu.edu (M.A.Salinger).

1_As_we_understand_the_{nomenclature,}_RAND_is_synonymous_with_“FRAND,”_which isanacronymfor“Fair,Reasonable,AndNon-Discriminatory.”Licensingtermsthat areboth“reasonable”and“non-discriminatory”arenecessarily“fair.”

commonphenomenon,whateffectpatentbundlinghason licens-ing terms, and why patent holders make RAND commitments. Asubstantialandgrowingeconomicsliteraturehasemergedon bundlingingeneral,andsomeofitspeciﬁcallyfocusesonbundling intellectualproperty (likecomputersoftware,music, and video entertainment), but theformal literatureonpatent bundling is remarkablythin2_._A_notable_exception_is_the_Gilbert_and_Katz₍₂₀₀₆₎

(henceforth“GK”)modelofpatentbundling.

TheGKmodelisanaturalstartingpointforouranalysis.Akey ideaintheGKmodelisthedistinctionbetween“long-term”and “short-term”patentlicensing,whichturnsonwhethertheparties enterintocontractsbeforeorafterthepatentuserincurssunkcosts. Thepatentownercanimposetermsthatexpropriatethepatent user’ssunkcostswithshort-termcontracts,butnotwithlong-term licensing.

GKdonotaddresshowlong-termlicensingoccursinpractice. Onepossibility,ofcourse,isthatthepatentuserseeksalicense beforestarting tocommercializethetechnology. Analternative

2_Patent_bundling_is_related_to_but_different_from_patent_pooling,_which_Shapiro (2001)andLernerandTirole(2004)haveanalyzed.Patentpoolingentailslicensing patentsofdifferentpatentownersinasinglepackage.Patentbundlingrefersto licensingmultiplepatentsofasinglepatent-ownerasapackage.

http://dx.doi.org/10.1016/j.respol.2016.03.003

(2)

mechanism,however,istomakeaRANDcommitment.Asastarting point3_,_we_interpret_a_RAND_commitment_to_mean_a_commitment

onthepartofthepatentownernottochargehigherlicensingfees orimposeothertermsthataremoreonerousthanitwouldhave soughttoimposebeforethepatentusermadeirreversible deci-sions(suchasincurringsunkcostsincomplementaryassets)to usethepatent4_._Under_this_{interpretation,}_the_GK_model_provides

ageneralframeworkforanalyzingRANDcommitments,andthe patentlicensebundlingintheirmodelisoftwoRAND-committed patentsfortechnologiesthatarebothneededtoimplementasingle standard.

GK’sresultsarethatthepatentownerwouldofferitstwo com-plementarypatentsasabundleratherthanàlacarte.Thus,thepure bundlingofthetwopatentsdoesnotviolatethepatent-owner’s commitmenttolimitthelicensefeetowhatitwouldhavesought beforethepatent userincurredanysunk costs.Moreover,they showthatbanningbundledpatentlicensing(andtherebyforcing thepatent owner tolicense its patents separately) might pre-ventthepatentholderfrombeingwillingtoenterintolong-term licensesor,underourinterpretation,tomakeRANDcommitments. Ascommitmentstoavoidexpropriationcanbenecessarytoinduce otherstoinvestincomplementaryassets,GKurgecautionabout restrictionsonpatentbundling.

Inthisarticle,weadaptandextendtheGKframeworktoaddress adifferentquestionaboutpatentlicensebundling.Ourfocusisnot thepurebundling ofmultipleRAND-committedpatent licenses but,rather,thepurebundlingoftwopatentlicenses,oneofwhich isRAND-encumberedandoneofwhichisnot.Doingsorequires analyzing the meaning of a RAND commitment on one patent when a patent owner hasnot made a similar commitmenton anotherpatentthatapatentusermightneedtousewiththe RAND-committedpatent.Notethat,whilemostcommonlymadeinthe contextofstandardsettingwithincooperativestandard develop-mentorganizations(SDOs),RANDpledgesarenotlimitedtoSDOs, inlargepartbecauseSDOsarenottheonlywaythatstandards emerge5_.

Weanalyzeexpropriationthroughtyingastheoutcometowhat wecallthe“SomeOpportunismGame”inwhichtheowneroftwo patentscanbehaveopportunisticallyinthelicensingofoneofits patentsbutnottheother.Asafoundationforthatgame,we ana-lyzea“NoOpportunismGame”thathasthebasicstructureofthe GKmodelbutwithonlyasinglepatenttolicense.Theresultof thismodelbringsouta keydistinctionbetweenourmodel and theGKmodelrelatedtothemeaningofaRANDcommitment.In particular,weshowthatthereisnouniversalformulaforRAND. Instead,forsomeparameters,theRANDroyaltyis“value-based,” meaningthatitreﬂectstheexanteupperboundvaluecreatedby thepatentedtechnology.Forotherparameters,theRANDroyaltyis “cost-based,”meaningonethatislowenoughtoeliminateapatent user’sincentivetotrytoinventaroundthepatent.

3 _This_{interpretation}_is_consistent_with_Swanson_and_Baumol_(2005)._As_we_show inSection4,ithasmorecomplicatedimplicationsthanonemightexpect,andthese complicationsmightcausesometoargueforareﬁnementonthisinterpretationof RAND.

4 _In_addition_to_sunk_investments_in_{complementary}_assets,_irreversible_decisions includethedecisionnottotrytoinventaroundthepatentand,aswediscussin Section5,thedecisiontoadoptonetechnologyinsteadofanavailablealternative. Inwhatfollows,whenwerefertoatimebeforethepatentuserincurssunkcostsin complementaryassets,wearereferringmoregenerallytoatimebeforethepatent usermakesanyirreversibledecisionwithrespecttoitsuseofthepatent.

5 _The_Program_for_Information_Justice_and_Intellectual_Property_at_Washington CollegeofLawmaintainsadatabaseofmorethan150suchpublicnon-SDOpatent pledges:http://www.pijip.org/non-sdo-patent-commitments/. Contreras (2015) andElhauge(2015)discussthelegalbasisforenforcingRANDcommitmentsmade outsideanSDOsetting.Forotherdiscussionsofnon-SDOpatentpledges,see Layne-Farrar(2014)andHarkrider(2013).

Theremainderof this paperis organizedasfollows.Section 2 discusses the economics of bundling in general,highlighting theaspectsthatweconsideressentialforunderstandingpatent bundling.Section3thenexplainstheGKmodel andtheroleof bundlinginit.Section4presentstheNoOpportunismGame, bring-ingoutthedistinctionbetweenvalue-basedandcost-basedRAND royalties.Section5presentsamodiﬁedversionoftheNo Oppor-tunism Game toshow that ourresults applyin a wider setof circumstancesthanmightinitiallyappeartobethecase6_._In

Sec-tion6,whichcontainsourmainresults,weusetheGKframework toanalyzelicensingtwopatentswherethepatentholderhasmade aRANDcommitmentonjustone.

Section7containsourconclusions.Briefly,thepurebundling ofpatentlicensesraisesabasicpolicydilemma.Ontheonehand, thepracticecouldbeawaytorenegeontheRANDcommitment. Ontheotherhand,asweexplaininSection2,thepurebundlingof patentsisprevalentbecauseitcanbeanefficientformof contract-ingthatminimizestransactionandlitigationcosts.Wearguethat becauseoftheseefficiencies,theownerofmultiplepatentsshould beallowedtoengageinpurebundlingofpatentswithandwithout RANDcommitments,butthatRANDcommitmentslimitthelicense feesthatitcancharge.Indeed,weshowthatthelicensefeesthat honoraRANDcommitmentonabundleofRAND-committedand nonRAND-committedlicensesmaybelessthantheRANDlicense feeifthepatentownerhad madeRANDcommitmentsonboth patents.

2. Bundlingandtyingingeneral

Whileacompletereviewoftheextensiveeconomicsliterature onbundlingandtyingisunnecessaryforwhatfollows,afewkey pointsareessential.

A key concept in the literature on bundling is the “single monopolyproﬁt”7_(or,_more_generally,_“single_rent”8₎_theorem,_and

thistheoremplaysanimportantroleintheGKresults.Asiswell understood,ifa companyhasa monopoly over twogoods–call them“A”and“B”—thatconsumersusetogetherinfixed propor-tions,thereisacombinedpriceforthetwogoodsthatmaximizes thecompany’sprofits.Anycombinationofpricesthatsumstothis optimalbundledpricewillgeneratethesamelevelofprofits(and consumersurplus).Indeed,thecompanycanearnthislevelof pro-fitsonjustoneofthetwogoodsaslongasthepriceoftheother goodequalsmarginalcost.

Thesinglerentprinciplewasoneofthekeyunderpinningsof theso-calledChicagocritiqueofawiderangeofantitrustpolicies, including tying. Arguably the dominant interpretation of the

6_In_the_GK_model_and_in_the_model_in_Section_4,_the_opportunity_for opportunis-ticlicensingarisesbecausethepatentuserhastoinvestinsunkcoststoearnany commercialvaluefromthetechnology.Anotherformofopportunismthatis some-timesalleged(particularlyinformalstandardsettingproceedings)ariseswhenthere aremultiplepatentsthatcompeteforinclusioninastandard(withtheonechosen beingessential).Priortoadoptionofthestandard,thelicensingtermsapatentowner couldnegotiateareconstrainedbytheavailablealternatives.Onceapatentbecomes essential,however,thealternativesceasetobeaconstraintandthepatentowner hasanincentivetoextracttheentirevalueofthestandardratherthanits contribu-tiontothevalueoverthevaluethatcouldhavebeenrealizedwithanalternative patent.ThemodelinSection5showsthatwecaninterprettheopportunitycostof notadoptinganalternativepatentasasunkcostthathasthesameeconomiceffect asthesunkcostsintheGKandSection4models.

7_As_evidenced_by_the_title_to_Elhauge₍₂₀₀₉₎_the_term_is_widely_recognized. How-ever,wehavenotbeenabletodocumentthesourceoftheterm.Whinston(1990) attributestheargumentstoaChicagooraltradition.Bowman(1957)recognizesthe strongassumptionsunderlyingtheprincipleandasetofexceptionstoitwhenthose assumptionsdonotapply.

8_While_economists_(as _well_as_lawyers_and _courts)_use_the _phrase_“single monopolyproﬁt,”weprefertheterm“singlerent”becausetheargumentapplies torentsofanykind,includingpatentroyalties.

(3)

principleisthatitcastsdoubtonclaimsthattheincentivetotie goods together is “leveraging” or “foreclosure.” An alternative interpretation,however, isthattheassumptions underlyingthe singlerentprinciplearesostrongthatrelaxingthemcouldundo theprinciple.

Understanding the assumptions provides a framework for understandingwhyasinglesourceofrentsmaynotbesufficient tocapturealltherentsavailable.FarrellandWeiser(2003)and Elhauge(2009)havearticulatedthisperspectiveatlength,asdid KrattenmakerandSalop(1986).Oneofthestrongerassumptions underlyingthesinglerentprinciplepresumesthatthemonopoly orproperty rightonatleast oneof thegoodsis iron-clad.The threatofentryintobothgoodscanviolatethisassumption,though athreatofentryintojustoneofthegoodsdoesnot.Supposeentry intoAisnotpossiblebutentryintoBis.Accordingtothesingle rentprinciple,thesellershouldwelcomeentryintoBbya com-panyofferingalower-cost,higherquality,ordifferentiatedversion sincetheimprovementinBwouldincreasetheprofitstheseller couldearnfromA.But,thethreatofentryinAaswellcanmakeit impossibleforthefirmtoraisethepriceofAtotakeadvantageof costreductionsorimprovementsinB.Withthepotentialforentry intobothAandB,tyingcanraiseentrybarriersbyforcing two-stageentry.Thisexceptiontothesinglerentprincipleunderlies theanalysesofChoiandStefanadis(2001)andNalebuff(2004).

Failureofthesinglerentprincipledoesnot,however, necessar-ilyimplythatmodularizedcompetitionresultsinbetteroutcomes. Because of double marginalization, the proﬁts a company can earnbycontrollingtherightstoboth Aand Bexceedthetotal proﬁtsthatseparateownersofAandBwouldearn.Eliminating doublemarginalizationisthereasonthatpatentpoolscanbein thepublicinterest. AsLerner and Tirole (2004)show, whether patentsarecomplementsorsubstitutesismoresubtlethaninthe caseofconsumergoods9_._However,_to_the_extent_that_bundles_of

separately-ownedcomplementarypatentscanbecombinedinthe publicinterest,onemustbecautiousaboutcondemningthetying ofcommonly-ownedpatents10_.

While the formaleconomics literature hasfocused onprice discriminationandforeclosureaspossiblemotivesfortying,the practiceisfartoocommonforthespecializedmodelsintheprice discriminationorforeclosureliteraturetoexplainthemall.Instead, transactionalandorganizationalefﬁciencyislikelytoexplainmuch moreofthetyingthatoccursinpractice.Virtuallynoonewants everysectionofanewspaper.EvansandSalinger(2005,2008)argue thatonecannotunderstandthediverseinstancesoftyingwithout

9_Observe_that_Lerner_and_Tirole₍₂₀₀₄₎_make_a_different,_though_related,_point_to theonewefocuson.Speciﬁcally,Proposition5inLernerandTirole(2004) estab-lishesthatawelfareenhancingpatentpoolcontainscomplementarypatentsandis stronglystable,suchthatthepresenceofindividualpatentlicensingwillnotunravel thepool,whereasawelfaredecreasingpoolcontainspatentsthataresubstitutes foroneanother,inwhichcasethepresenceofindividualpatentlicensingwill unravelthepool,aslicenseescanobtainloweraggregateratesthrough individ-uallicensingofthesubsetofpatentsneeded.Inourmodel,thebundle(or“pooled” patentlicense)canbeusedtoachieveahigherratewhenthepatentsare comple-ments,notsubstitutes,suchthatthepresenceofindividuallicensing(hereacross patents,ratherthanacrosspatentholders)wouldunravelthebundle.The differ-encebetweenLernerandTirole(2004)andouranalysisstemsfromthepresence ofRANDcommitments,somethingnotincludedinLernerandTirole.Asweargue below,combiningRAND-encumberedpatentswithnon-RAND-encumberedpatents cancreateamechanismtoavoidtheRANDcommitment.

10_To_be_sure,_participants_in_patent_pools_often_offer_to_license_their_patents sepa-ratelyaswellaspartofthepool,andwhethertheydocanbeafactorindetermining whetherapoolisinthepublicinterest.SeethediscussioninLernerandTirole (2004).Whileatleastonepaper,Quint(2014),developstheorydemonstratingthat theinclusionofpatentsthatarenotperfectlycomplementaryneednotbe anti-competitiveorharmful,thegeneralconsensusisthatpoolsshouldberestricted toessentialpatentstopreventforeclosureofalternativetechnologiesforoptional features.

recognizingthecostofproductofferingcomplexity.Beforeafirm decidesonhowmuchtoproduce(ortrytosell)andhowmuchto charge,itfirsthastodecideexactlywhatitsells.Evenafterdeciding onitsgenerallineofbusiness,theproductsafirmoffersaretypically asmallsubsetoftheproductsandproductcombinationsitcould conceivablyoffer.Dellrevolutionizedthepersonalcomputer indus-trybyputtinginplacesystemstocustomizeorderstoconsumer specificationstoadegreethathadpreviouslybeenunimaginable. ButevenDell’shighlycustomizedofferingsdidnotincludeevery conceivableconfigurationand,moreimportantly,Dellandthe per-sonalcomputerindustryaretheexception.Ingeneral,companies donotandindeedcannotcustomizetheirofferingstotheprecise desiresofevery(or,forthatmatter,any)customer.

While Evans andSalinger didnot addresstheissueof tying patents,theframeworktheysuggestprovidesaplausible-indeed, obvious-explanationforwhypatenttyingissuchacommon phe-nomenon.Thekeyquestiontoaskinregardtoàlacartelicensing is,“Whatisthelimitingprinciple?”Somelargeinnovative com-panies thatlicensetheirtechnologyhave thousandsof patents. Yet,theymightoffertheminonlyahandfulofbundles,andthey mightnotofferanyofthemindividually.Foracompanywith1000 patents,thenumberofpossiblelicensingcombinationsofpatents isontheorderof10301_,_which_is_about_googol_cubed!_The_notion thatthelicensor isobligated tounbundleanyarbitrarysetand offeradiscountmeansthatit wouldhavetoset10301 _different pricesandthenmonitorandenforcecomplianceforallthose dif-ferentconﬁgurations.Asapracticalmatter,thenumberofdifferent combinationsthatlicenseesmightdemandwouldlikelybemuch smaller,butthereisnonethelessacostofhavingmorecomplex productofferings.Asaresult,patentlicensorsnecessarilyoffera smallsubset ofthe patentbundles that theycouldconceivably offer;anditshouldcomeasnosurprise(andshouldnotnecessarily beapublicpolicyconcern)ifmanylicenseesonlyuseasubsetof thepatentstheylicense.

Italsoshouldnotbesurprisingiflicenseeswantinclusive bun-dles. A licensee takes a license to(1) access useful technology and(2)avoidbeingsuedforpatentinfringement.Acompanythat licensesjust asubsetofthepatentsthat itneedstoimplement atechnologyrisksapatent-infringementsuitevenifitpaysthe royaltiesdueonthepatentsitdoeslicense.Asaresult,licensees might demand patents in an inclusive bundle that completely protects them from the threat of a suit (referred to as “free-domtooperate”licenses).Totheextentthatsuchbundlescover bothRAND-committedpatentsandnon-RANDcommittedpatents, includingallpatentsthatalicenseemightconceivablyuseisitself aformofcommitmentonthepartofapatentownernottobehave opportunisticallybysuingforpatentinfringementonanon-RAND committedpatentthatthelicenseeendsupinfringing.Boththe licensorand thelicenseecansave transactionandenforcement costsbylicensingatthetechnologyportfoliolevel.

3. TheGilbert-Katz(GK)model

Withthemotivesforpatentbundlinginmind,weturnnowto patenthold-up.TheGilbert-Katz(GK)modeladdressesthistopic inthecontextofpatentbundling.Thepossibilityofpatenthold-up addsa layerofcomplexitytotheimplicationsofthesingle-rent theorembecausetherearetwolevelsofrentstoconsider:theex anterentsbeforelicenseesengageinsunkinvestment(including R&Deffortstoinventaroundthepatents)andtheexpostrentsafter theydo11_.

11_We_start_our_analysis_from_the_point_in_time_that_the_patent_holder_has_already madeitsR&Dinvestmentandhasapatentinhand.Thus,inouranalysishere,“ex ante”referstothelicensee’sinvestment,notthepatentholder’s.

(4)

IntheformalsetupoftheGKmodel,theowneroftwo com-plementarypatents(“thepatentowner”)canlicensetoasingle licensee(the “manufacturer”). Thetechnologies covered bythe patents are strongly complementary. That is, the technologies createvalueonlyincombinationwitheachother.However,the patentsthemselvesarenotstronglycomplementaryasthe man-ufacturercaninvestinR&Dtotrytoinventaroundoneorboth patents.TheIPownerdoesnothavemanufacturingcapability,so itmustlicenseitstechnologytothemanufacturertocaptureany valuefromit.Thevaluethatcanberealizedfromthetechnologyis afunctionofthelevelofcomplementaryinvestment,whichonly themanufacturercanmake.Ifthemanufacturerdoesnotobtain alicensetothetechnologypriortoinvestingincomplementary assets,theIPownermightbeabletoexpropriatethecontribution ofthemanufacturer’sinvestment.Inotherwords,ifthe manufac-turerdoesnotobtainanearlylicense,thepatentholdercanpractice hold-up.

AsimplenumericalexampleillustratestheGKmodel,the intu-itionbehindit,andtheroleofpatenttyingintheGKframework. Supposethatwithoutanyinvestment bythemanufacturer,the patentedtechnologyyieldsavalueof20(unrealizablebythepatent holder,byassumption).Withefﬁcientinvestmentin complemen-taryassetsbythemanufacturer,thetechnologyembodiedinan endproductyieldsgrossbeneﬁts(i.e.,beforetakingaccountofthe costofthemanufacturer’sinvestments)of100(unrealizablebythe manufacturerabsenttheinitialcontributionbythepatentholder). Thecommercializationinvestmentsneededtogeneratethe addi-tionalvalue(theendproduct)haveacostof30,sothatthepotential netvalueofthecombinedtechnology(patentplusmanufacture) embodiedintheendproductis70.

Absentanyfrictions,themanufacturerwouldnotinvest30in complementaryassetswithoutobtainingalicenseforthepatented technology.Ifitdidso,theIPownercouldinsistonalicensefee of100(orjustbelowit)andthemanufacturer wouldrationally acceptthisoffer.TheIPownerhasanincentivetocommitupfront toalicensefeeofnomorethan70forthebundle(100–30),which allowsthemanufacturer torecover itsinvestment (andalsoto choosethemostefﬁcientlevelofcomplementaryinvestment)12_.

GKrefertolicensesenteredintobeforethemanufacturerinvests as“long-term”licensesandlicensessignedafterthemanufacturer investsas“short-term”licenses.Aswehaveargued,wecan inter-prettheirlong-termlicensesasRAND-committedlicenses.

Uptothispoint,whetherthetechnologyisbasedononepatent ortwoisirrelevant.Themanufacturerneedsboth.Thus,whether theIPowneroffersthepatentsseparatelyorinabundleisalso irrelevant.Itcanofferthepatentsasabundleatalicensefeeof70 oràlacartewithindividualpricesthataddtoacumulativelicense of70.Proﬁtsandconsumerwelfare(and,therefore,totalsurplus) areallthesameunderthevariousoptionsforchargingatotalof70. Theirrelevanceofbundlingundertheseconditionsisanapplication ofthesinglerentprinciple.Onepatentthatisessentialforaproduct givesthepatentholdertheabilitytoextractthesametotallicense feeasitcanwithtwosuchpatents.

ThefeatureoftheGKmodelthatmakesbundlingpotentially rel-evantistheabilityofthemanufacturertoinvestinR&Dtoinvent aroundoneorbothpatents.Theoutcomeofthemanufacturer’s R&Disrandom.Foragivenlevelofinvestment,themanufacturer

12 _A_simplifying_assumption_in_GK_is_that_the_IP_owner_makes_{take-it-or-leave-it} offerstothemanufacturer,whichimpliesthattheIPownerisabletocapturethe entireavailablesurplus.Astheyexplain,themodelwouldbemorecomplicatedifthe IPownerandmanufacturerbargainedovertheavailablesurplus,buttheriskwould remainthattheIPownerwouldexpropriatepartofthemanufacturer’sinvestment ifthemanufactureinvestedpriortoobtainingalicense.

decidestoinventaround“patent1,”“patent2,”both,orneither13_.

Themanufacturer’sincentivetoinvestinR&Ddependsonwhether ithaslicensedthepatentsonabundledoranàlacartebasis.If itlicensesthebundle,itonlyearnsareturnonitsR&Difit suc-ceedsininventingaroundbothpatents.Ifitlicensesonanàlacarte basis,thensuccessfullyinventingaroundjustoneofthepatents willlowerthelicensefeesitowestheIPowner.Thus,holdingthe totallicensefeeconstant,themanufacturerhasmoreofan incen-tivetoinvestinR&Dunderàlacartelicensingthanunderbundled licensing.TheIPownercanlimitthemanufacturer’sincentiveto investinR&Dtoinventarounditspatentsbylicensingthemsolely asabundle.IntheGKmodel,theadvantagetheIPholdergetsfrom patentbundlingisthatitdiscouragesattemptstoinventaroundits patents,andthatbeneﬁtistheIPowner’sincentivetoenterinto long-termpatentlicenses14_.

4. RANDcommitments:Thenoopportunismgame

Inthissection,wepresentamodeloftheNoOpportunismGame toclarifythemeaningofaRANDcommitmentonasinglepatent. ThemodelcloselymirrorstheGKmodelexceptthatthereisonly onepatenttobelicensedinsteadoftwo.

ConsiderapatentthatyieldsnetbeneﬁtsofBbutrequiresa commercializationexpenditureofsunkcostS15_._With_expenditure R,thelicenseecaninventaroundthepatentwithprobabilityp16_.

Table1 laysout thetimingof the“NoOpportunismGame.” At Time1,thepatentownersetsaroyalty,L.AtTime2,the manu-facturerdecideswhethertoinvestinR&Dtocircumventthepatent andincomplementaryinputs.IfthemanufacturerinvestsinR&D, theoutcomeisrevealedatTime3.AtTime4,themanufacturer decideswhethertoproduce.Thekeyfeatureofthegameisthatthe patentownersetstheroyaltybeforethemanufacturerinvestsin complementaryassetsorR&D.

At Time 1, there are three levels of royalties to consider: LE=B,LV=B−S, and LC=R/p. (Thesubscripts denote

“expropria-tion,” “value,” and “cost,” respectively17_.) _Since _our_interest _in

the No Opportunism Game is when the patent holder has an incentivetocommitnottoexpropriatethevalueofsunk invest-ments,werestrictattentiontoparametervaluesthatcreatesuch anincentive18_._Thus,_to_capture_the_effects _we_are_interested_in,

13_The_assumptions_and_the_phenomenon_that_the_GK_model_examines_are_similar tothoseexploredbyChoiandStefanadis(2001),discussedabove.

14_GK_assume_that_R&D_to_invent_around_the_IP-owner’s_patents_is_entirely duplica-tiveandthatitoffersefficientlicensingtermsthatdonotdistortproductprices. (Thatis,theyassumelump-sumlicensefees).Giventheseassumptions,theR&Dto inventaroundtheIP-owner’spatentsissociallywastefulandyieldsnoconsumer benefits.Inpractice,theR&Dtoavoidtheneedtolicenseoneormoreofthe IP-ownerspatentsmightyieldconsumerbenefits.Evenifthatisso,however,theGK resultsclarifywhyallowingpurebundlinginlong-termlicensingcanmakeanIP holdermorewillingtoengageinthelong-termlicensing(perhapsbymakingRAND commitments)neededtogeneratecomplementaryinvestment.

15_GK_allow_for_different_levels_of_S_and_for_B_to_be_a_function_of_S._The_levels_of_sunk costthatareoptimalforboththelicenseeandsocietyarethenpartofthemodel solution.WeassumeasinglepossiblevalueofSandB,whichcanbethoughtofas theoptimizedvalues.

16_GK_allow_for_a_range_of_R_and_let_p_be_an_increasing_function_of_R._Just_as_we assumedsinglepossiblevaluesforSandB,wesimplifytheGKframeworkby assum-ingsinglepossiblevaluesforRandp.GKalsoassumethatthepatentholder’spatents havesomeprobabilityofnotbeingvalidorthatthetechnologydoesnotwork.They explicitlyconsiderthepossibilitythatthepatentownerwouldofferalong-term licensethatwouldobligatethepatentusertopayalicensefeeregardlessofwhether itusesthetechnology.Theythenderivetheresultthatthepatentownerwouldnot choosesuchalicenseifthereisasymmetricinformationaboutwhetherthe tech-nologyisgoodorthepatentsarevalid.Weassumethatthetechnologyisgoodand thepatentsarevalidandwerestrictlicensestothosethatrequirepaymentonly whenthemanufactureractuallyusesthepatents.

17_We_explain_why_R/p_is_cost-based_below.

18_An_alternative_modeling_approach_would_be_to_assume_that_the_manufacturer choosesSonlyafteritobservestheoutcomeofitsR&D.Underthatassumption,the

(5)

Table1

Noopportunismgame.

Time 1 2 3 4

Decisionmaker Patentowner Manufacturer Random Manufacturer

Decision SetroyaltyL R&D,complementaryinvestment R&Dsucceedsorfails Production

assume thatpB<R+S. WhenpB>R+S, themanufacturer would investinbothR&DandcomplementaryassetseveniftheIPholder choosesLEatTime1,andtheIPholderwould,forsomeparameters, chooseLEtochargeBwithprobability(1−p).ThesolutiontotheNo OpportunismGameistheRANDrate;dependingontheparameter values,thatratecanbeeitherLVorLC19.

Giventheaboveparameterrestriction(whichallowsustofocus onthechoicebetweenLVandLCatTime1),thesub-gameperfect

solutionofthegame isasfollows.AtTime4,themanufacturer produces ifit hasinvested ininvent-around R&D and theR&D succeeded.Alternatively, ifeither itdidnot investinR&D orif itinvestedand theR&D failed,itproduces ifL≤Lv=B−S.Since

thepatentholderonlygetsapositivepayoffifthemanufacturer produces,itwillchooseL=LvatTime1.Asaresult,the

manufac-turerwillproduceatTime4andinvestincomplementaryinputs atTime2.

If the manufacturer does not invest in R&D, its pay-off is B−S−L. If it does invest, its expected payoff is p(B−S−R)+(1−p)(B−S−R−L).ThevalueforLthatmakesthe manufacturerindifferentbetweeninvestingand notinvestingis LC=R/p20.

IfLC>LV,thentheIPownerchargesLV.InvestinginR&Dtoinvent

aroundthepatentisnotproﬁtableinthiscase,sotheIPownercan chargeavalue-basedroyaltyandnotfaceariskofhavingitspatent inventedaround.IfLC<LV,thentheIPownergetsanexpected

pay-offof(1−p)LVifitchoosesvaluelicensingandLCifitchoosescost

licensing.Itchoosescost-basedlicensingif: (B−S)≥R

p≥(1−p)(B−S), (1)

andL=Lv=B−Sotherwise.Ifp*istheprobabilitythatmakesthe

patentownerindifferentbetweenthevalueandcost-basedlicense fee,thentheconditionforp*_is_quadratic_with_roots:

p∗=

1±

1−4

R/(B−S)

2 (2)

Basedontheabovediscussion,wecanestablish:

Proposition1. AtTime1intheNoOpportunismGame,thepatent ownerchargesLv=B−SwhenB−S≤R/p.ItalsochargesLv=B−S

whenB−S>R/pandpiswithintherangegivenbyEq.(2). Other-wise,itchargesLc=R/p.

AccordingtoProposition1,theownerofasinglepatentwould, in seeking to negotiate license terms before the manufacturer incurssunkcostsordecideswhethertoinvestinR&D,choose cost-basedlicensesinsomecasesandvalue-basedlicensesinothers. Itwouldneverseektochargeabovethevalue-basedroyaltyeven whenthecost-basedishigherbecausethemanufacturerwould

IPownerwouldneversuccessfullychargealicensefeeofB.InSection5,however,we showthatwecaninterpretSastheopportunitycostofnotpursuinganalternative standard,andthatinterpretationisparticularlyrelevantforcaseswhenIPholders makeRANDcommitments.Underthatinterpretation,itwouldnotbereasonableto assumethatitispossibletodelaytheinvestmentdecision.

19 _The_condition_for_the_value-based_royalty_to_be_greater_than_the_cost-based roy-altyisB−S>R/p.NotethattheconditionpB<R+Sdoesnotruleoutthispossibility.

20_Given_that_the_patent_owner_is_not_going_to_charge_above_L

V,themanufacturer producesregardlessofwhetheritsR&Dsucceeds.Thus,theexpectedvalueofthe R&DispL.

neveragreetopaymorethanthevalue-basedroyalty.Onemight haveguessedthatlong-termlicensingwouldimplycost-based roy-altieswhenevertheexpectedcostofinventingaroundapatentis lessthan thevaluethepatentcreates(whenthepatent userin factpracticesit).AccordingtoProposition1,however,thepatent owner’schoicebetweenavalue-basedand cost-basedlicenseis moresubtle.

Figs.1and2illustratethispoint.Fig.1showsacasewhenEq. (1)hasnorealroots.Inthatcase,thepatentownerchoosesthe minimumofthecost-basedandvalue-basedfees(asonemight expect).

InFig.1,thehorizontallineisthevalue-basedroyalty,thecurve isthecost-based royalty,and thedownward-slopinglineis the patentowner’sexpectedroyaltyifitchargesavalue-based roy-alty.Forallvaluesofp,theexpectedcostofinventingaroundthe patentexceedsthepatentowner’sexpectedroyaltiesifitcharges avalue-basedroyalty.However,whentheexpectedcostof invent-ingaroundthepatentexceedsB−S,themostthepatent-holdercan chargeisLv=B−S.GiventheparametervaluesunderlyingFig.1,the

patentownermaximizesitsexpectedroyaltieswithvalue-based licensingwhenpisbetween0and0.3andwithcost-basedlicensing forvaluesofpabove0.3.

MattersaremorecomplicatedinFig.2,however,whereEq.(1) doeshaverealroots.AsinFig.1,thepatentownerchargesLv

when-everLc>Lv(again,becausethepatentuserwouldneveraccepta

licensefeeaboveLv).However,intherangebetweenthetworeal

rootsin Fig.2,thepatentownerchoosesLv eventhoughLc<Lv.

Whenitdoesso,itsacriﬁcesgettingthecost-basedroyaltywith cer-taintyinordertogetthevalue-basedroyaltywithsomeprobability lessthan1.

OnecandebatewhatthisresultimpliesaboutRANDroyalties. Ontheonehand,Proposition1formalizestheprincipleofsetting anon-opportunisticlicensefeeasanyroyaltythatdoesnotexceed whatthepatentholderwouldhavesoughtunderlong-term con-tracting.Ontheotherhand,somemightargueforastricterviewof RANDasacommitmentnottochargearatethatleavesan incen-tivetoinventaroundthepatent.Underthisstricterview,RAND wouldbethelesserofthevalue-basedandcost-basedroyalties. Inthecontextofstandard setting,thepatentholderissettinga ratethatwouldallowitspatentedtechnologytobechosenforthe standard.Ifitsetsaratetoohigh,anotherSDOmember(licensee inourmodel)willattempttodevelopitsowntechnologytodeﬁne thestandardortheSDOmemberswillselectanalreadyavailable alternative,inwhichcasethepatentholderwouldnotbechosen forthestandard.(Wediscussthisinterpretationmoreformallyin thenextsection.)

5. Exantecompetitiontobethestandard—Analternative interpretationofBandS

An important context for the debate over patent tying is standardsetting.Inparticular,technologiestypicallycompeteto deﬁnea standard and RANDcommitments can play an impor-tantroleinthatcompetition.Manyformalstandarddevelopment organizationsrequest RANDcommitments,and even outsideof suchformaleffortsunilateralRANDcommitmentscanbecrucial insecuringindustrysupportforinformalstandardcompetitions withinamarket(seefootnote4).Thissectionaddressesthis con-text,interpretingthemodelasdeﬁningtechnologiescompetingto

(6)

Fig.1.Cost-basedvs.value-basedroyalties(norealrootstoEq.(1)).

becomeastandardandconsideringhowthatcompetitionimpacts theresultingRANDroyaltyrate.

Thetwoessentialfeaturesgivingrisetotheneedforstandards are(1)competingtechnologies,eachofwhichcouldserveasthe standard,and(2)networkexternalities.TheGKframeworkdoesnot explicitlycapturethoseelements,butcanbeextendedto accom-modate them. The “Standards Competition Game” introduced belowcapturesbothoftheseessentialfeatures;herethe manufac-turer’ssunkcostsintheNoOpportunismGamearereinterpreted astheopportunitycostofnotadoptinganalternativetechnology asthestandard.

Supposethattherearetwocompetingtechnologies,˛andˇ, andthattherearethreetypesofcustomers,I,II,andIII. Correspond-ingly,therearethreetypesofmanufacturerstocatertoeachtypeof customer.LetBi

jkbetheperpersonbeneﬁtthatGroupi(i∈I,II,III)

getsfromtechnologyj(j∈˛,ˇ)giventhatthestandardis technol-ogyk(k∈˛,ˇ).GroupIprefers˛toˇbutisaboveallinterestedin standardization,soBI

˛˛>BIˇˇ>BI˛ˇ.Incontrast,GroupIIisloyal to˛andwillchooseitevenifitisnotthestandard,whileGroup IIIissimilarlyloyaltoˇ.Thatis,BII

˛ˇ>BˇˇII andBˇ˛III >B˛˛III.LetII

andIIIbetheproportionofcustomersinGroupsIIandIII(with

theproportioninGroupIbeing(1−II−III)).

Tokeepmatterssimple,weassumethatthereisnoadditional costofadoptingastandardotherthantheopportunitycostofnot adoptingthealternativetechnologyasthestandardandthatthe probabilityofinventingaroundthepatent(s)is0.Table2laysout thetimingofthegame.AtTime1,theownersofbothtechnologies eachofferaroyalty(L_˛andL_ˇ,respectively)conditionalonbeing acceptedasthestandard.FurtherassumethatonlyTypeI manufac-turersparticipateinthestandardsettingeffort,sothatTypeIIand

(7)

Table2

Standardscompetitiongame.

Time 1 2 3 4

Decisionmaker Patentowners TypeImanufacturers Ownerofnon-standardpatent Manufacturers

Decision SetroyaltyL˛,Lˇ Setstd.on˛orˇ SetroyaltyL˛’orLˇ’ Produceorshutdown

TypeIIImanufacturerssimplytakethestandardsettingoutcome asgivenandhavenovoiceinthecooperativedevelopmentofthe standard.Therefore,atTime2,theTypeImanufacturerschoose whichtechnologytoadoptasthestandard.AtTime3,theownerof thetechnologynotselectedasthestandardcanchoosealicensefee (notboundedbyRAND).AtTime4,manufacturersdecidewhether toproduce.

AswiththeNoOpportunism Game, weassume a sub-game

perfectNashequilibrium.Thesolutiontothegameisasfollows. SupposetheTypeImanufacturerschoose˛atTime2.ThenTypeIII

manufacturersproduceatTime4(usingthe_ˇtechnology,outside ofthestandard)ifLˇ≤BIII_ˇ˛andshutdownotherwise.TypeIand TypeIImanufacturersproduce(usingthestandard˛technology). AtTime3,theowneroftheˇtechnologychoosesLˇ=BIII_ˇ˛(and earnsIIIBIII_ˇ˛).Attime2,TypeIproducersselect˛ifBI˛˛−L˛≥ BI

ˇˇ−Lˇ,andselectˇotherwise.

NowconsiderTime1.Theowneroftheˇtechnologycan guar-anteeitselfIIIBIII_ˇ˛evenifisnotchosenasthestandard.Ifitoffers

aroyaltythatinducestheproducertoacceptitasastandard, how-ever,itcanincreaseitssharefromIIIto(1−II).Thelowestroyalty

itiswillingtooffertobethestandardis: ˜

Lˇ=₁₋III IIB

III

ˇ˛. (3)

Iftheowneroftheˇtechnologyoffers ˜Lˇ,thentobecomethe

standardtheowneroftechnology˛wouldhavetooffer: L˛=˜Lˇ+B˛˛I −BIˇˇ=BI˛˛−

BI ˇˇ−L˜ˇ

(4) aslongas:

BI ˛˛−

BI ˇˇ−˜Lˇ

(1−III)>IIBII_˛ˇ. (5)

Iftheowneroftechnology˛offeredanyroyaltyabovethatgiven inEq.(4),theowneroftechnologyˇwouldundercutitinorder toinduceproducerstoacceptitasastandard.Thus,given(5),no royaltyfor˛canexceedthevaluegivenbyEq.(4).Sincewehave alreadyestablishedthattheowneroftheˇtechnologywillnotoffer aroyaltybelowthatgivenbyEq.(3)andthattheroyaltygivenby (4)isthebestresponsebytheownerofthe˛technologytothe royaltygivenbyEq.(3),wehaveestablished:

Proposition2. AtTime1intheStandardsCompetitionGame,the owneroftechnology˛offerstheroyaltygivenbyEq.(4)andthe owneroftechnologyˇofferstheroyaltygivenbyEq.(3).TheType Imanufacturerschoosethe˛technologyasthestandard,andthe ownerofthe_ˇtechnologysetsaroyaltyof_BIII

ˇ˛atTime3.

Sincewehaveassumedawaythepossibilityofinventingaround thestandard, thepricing at Time 1 in the Standards Competi-tionGamecorrespondstovaluepricingin theNoOpportunism Game,withBI

˛˛correspondingtoBandtoBIˇˇ−L˜ˇcorresponding toS.Notethattheopportunitycostofnotadoptingthe alterna-tivestandardisthevaluenetoftheroyalty(ratherthantheentire value).Introducinginvent-aroundinvestmentwouldyieldresults conceptuallyanalogoustothosepresentedabove.Theintuitioncan beeitherthatthe˛technologyiseasytoinventaroundforthe currentstandard,orthatitcouldbereplacedinthenext genera-tionofthestandard.SinceweformulatedthegamewithBertrand competitionatTime1,theroyaltythattheownerofˇisassumed

tocommandrequiresthatˇhavesomevalueevenifitisnotthe standard.Ifeachpatenthasnovaluewhenitisnotthestandard, thenundertheStandardsCompetitionGame,patentholderswould bewillingtoofferaroyalty-freelicenseatTime1.Moregenerally, ifthepatentownerscompeteagainsteachothertobeincluded inmultiplestandards,licensingcompetitioninpracticemightbe “softer”thanwhatwehavemodeled.Inpractice,competitionmay beovertechnologieswithsomeoutsidevalueandhencepatent ownersareunlikelytosettheirratesatroyaltyfree.

6. RAND-committedandnon-RANDcommittedpatents: Thesomeopportunismgame

HavingformalizedthemeaningofaRANDcommitmentona sin-glepatent,wecannowanalyzetyingaRAND-committedpatentto anon-RANDcommittedpatent.Tokeepmatterssimple,weassume asunkcostofcomplementaryinputs(asinSection4)without spec-ifyingwhethertheyareout-of-pocketcostsortheopportunitycost ofnotadoptinganalternativetechnology.

6.1. Analysis

Assumethat thepatentownerownspatentsover two tech-nologies needed to capture value B with investment S into complementaryinputs(asinGK).LetR1andR2betheR&Dexpenses neededtoinventaroundeachpatentandp1andp2bethe respec-tiveprobabilitiesofsuccess.Supposethepatent-ownermakesa RANDcommitmentonpatent1butnotpatent2.

Table3laysoutthetimingofthe“SomeOpportunismGame.”At Time1,thepatentownersetsthelicensefeeforpatent1.AtTime 2,themanufacturerdecideswhethertoinvestinR&Dwithrespect toeachpatentandwhethertoinvestincomplementaryinputs.It cantrytoinventaroundbothpatents,patent1,patent2,orneither. AtTime3,theresultsoftheR&Dbecomeknown(byeveryone).At Time4,thepatentownerthengetstochoosealicensefeeforpatent 221_._At_Time_5,_the_manufacturer_decides_whether_to_produce.

The manufacturer’schoiceat Time5 limitswhat the Patent OwnercanchargeatTime4,butitdoesnotpreventhold-up. Sup-posethatatTime4themanufacturerneedsalicenseforpatent2, buthasinventedaroundpatent1.Inthatcase,thepatentowner cansetthelicensefeeforpatent2atB.If,ontheotherhand,the manufacturerneedsa licensetobothpatents,thepatentholder cansetthelicensefeeforpatent2atB−L1.Eitherway,thepatent holderearns Bandthemanufacturerloses allitssunk costs(in complementaryinputsandanyR&Ditperformed).

At Time2, the manufacturer in principle has eight possible choices.Withoutsuccessfulinventionaroundpatent2,however, thepatentownercanexpropriateanycoststhatthemanufacturer incursatTime2;wecanthereforeimmediatelyruleoutanychoice thatdoesnotentailinvestinginR&Dtoinventaroundpatent2.As aresult,themanufacturerhasonlythreerealisticoptionsto con-sideratTime2.ItcaninvestincomplementaryassetsandR&Dto

21_Assuming_that_the_manufacturer_can_wait_to_learn_the_outcome_of_its_R&D_before decidingwhethertoinvestincomplementaryinputswouldnotaltertheresults qualitatively.Here,weassumethatthemanufacturedecideswhethertoinvestinthe complementaryinputsatthesametimethatitmakesitsR&Ddecisionsto accom-modatetheinterpretationofSastheopportunitycostofnothavingselectedan alternativepossiblestandard.

(8)

Table3

Someopportunismgame.

Time 1 2 3 4 5

Decisionmaker PatentOwner Manufacturer Random PatentOwner Manufacturer

Decision SetroyaltyL1 R&Dforeachpatent,complementaryinvestment R&Dsucceedsorfails L2 Produceorshutdown

inventaroundbothpatents,itcaninvestincomplementaryassets andR&Dtoinventaroundpatent2only,oritcannotinvestatall. Withtheﬁrstoption,therearefourpossibilitiesfortheresolution ofuncertainty.Withthesecondoption,thereare2.

SupposethemanufacturerinvestsonlyinR&Dtocircumvent patent2,whichimpliesthatitwillneedtopayL1ifitchoosesto produce.IftheR&Dis successfulanditproduces, the manufac-turer’spayoffisB−S−L1−R2.Thepatent owner’spay-offisL1. Ifthemanufacturer’sR&Disnotsuccessful,thepatentownersets

L2=B−L1.Inthiscase,thepayofftothemanufactureris−S−R2and thepayofftothepatentholderisB.Themanufacturer’sexpected payoffifitinvestsincomplementaryassetsandjustpatent2R&D isp2(B−L1)−S−R2.

NowsupposethemanufacturerinvestsinR&Dtogetaround both patents. If both R&D efforts succeed, the manufacturer does not need either license. Its payoff is B−S−R1−R2 and thepatentownergets0.Ifitsuccessfullyinvestsaroundpatent 2 only, the manufacturer needs a license to patent 1. In this case,its payoffisB−S−R1−R2−L1 and thepatentownergets

L1.If themanufacturer’s patent 2R&D fails then,regardless of whetherits patent 1 R&D succeeds, the patent owner chooses anopportunisticlicensefeeforpatent2.Thepatentownergets total license fees of B and the payoff to the manufacturer is

−S₋R1−R2.Themanufacturer’sexpectedpayoffif itinvests in complementaryassets and both patent 1 and patent 2 R&D is

p1p2B+(1−p1)p2(B−L1)−(S+R1+R2). Let Lv

1=B−(S+R2)/p2. With L1=Lv1, which is value-based licensingforpatent 1,themanufacturer’sexpectedreturnfrom investinginbothcomplementaryassetsandpatent2R&Dequals itsexpectedreturnfromnotinvestingatall.LetLc

1=R1/p1p2.If

Lc

1<L1,thenthemanufactureris indifferentbetweeninvesting andnotinvestinginpatent1R&DwhenL1=Lc1,whichiscost-based licensing.

Asin the No Opportunism Game, thepatent owner cannot

charge more than the value-based license fee for the RAND-encumbered patent. Thus, the cost-based license fee is only a consideration when it is less than the value-based license fee. When it is, the condition for the patent holder to get equal expected payoffs from value-based and cost-based licensing is [B−(S+R2)/p2](1−p1)=R1/p1p2,whichhasroots:

p∗

1=

1±

1−4

R1/(p2B−(S+R2))

2 (6)

Thus,wecanstate:

Proposition 3. At Time 1 in the Some Opportunism Game, thepatentownerchargesLv

1=B−(S+R2)/p2forpatent1when

B−(S+R2)/p≥R1/p1p2. It also charges L1v=B−(S+R2)/p2 for patent1whenB−(S+R2)/p>R1/p1p2andp1lieswithintherange deﬁnedbyEq.(9).Otherwise,itchargesLC

1=R1/p1p2forpatent1. AtTime4,thepatentownerchargesBforpatent2ifthe manufac-turerhassuccessfullyinventedaroundpatent1andB−L1ifithas not.

6.2. Interpretation

Proposition3summarizesourresultsaboutthemeaningofa RANDcommitmentononepatentwhenthelicenseeneedsaccess toa secondtechnologytoreapcommercialvaluefromtheﬁrst

patent.AsinProposition1,theRANDroyaltyissometimes cost-basedandsometimesvalue-based.However,theneedforaccessto thesecondtechnologyaffectsbothlicensefees.

Thevalue-basedRANDroyaltyisB−(S+R2)/p2ratherthanB−S. Ineffect,thetechnology2R&Dbecomesanothersunkcostneeded tocommercializepatent1.Theexpectedcostofsuccessful technol-ogy2R&DisR2/p2andnotjustR2becauseoftheriskthattheR&D fails.Moreover,givenourassumptionthatthemanufacturermust investincomplementaryassetsandpatent2R&Datthesametime, theriskthatthetechnology2R&Dwillfailalsocreatesariskthat themanufacturerwillnotbeabletorealizeanyvaluefromitssunk investmentincomplementaryassets.Asaresult,thevalue-based licenserequiressubtractingoutS/p2ratherthanSfromB22.

Theneedtoinvestinriskytechnology2R&Dalsoaffectsthe cost-basedlicenseforpatent1.InProposition3,thecost-based roy-altyisR1/p1p2whereasitisR/pinProposition1.Ifitdoesnotmake aRANDcommitmentonpatent2,thepatentownercanchargean opportunisticroyaltyofBforpatent2.Asaresult,the manufac-turer’sinvestmentinpatent1R&Donlysavesitthecostofapatent 1licensefeewhenitsuccessfullyinvestsaroundbothpatents.

AsinProposition1,themanufacturercannotchargemorethan thevalue-basedfeebecausethemanufacturerwouldneveraccept it.However,forsomeparametervalueswhenthecost-based roy-altyislessthanthevalue-basedroyalty,thepatentownermight stilloptforthehighervalue-basedroyaltywithprobability(1−p1) thanthelowercost-basedroyaltywithcertainty.

6.3. ComparisonwithRANDroyaltyonbundleof RAND-committedpatents

IfthepatentownermakesRANDcommitmentsonbothpatents 1and2andlicensesthemtogetherasabundle,thenwecan inter-pretProposition1toindicatewhat theRANDroyaltywouldbe foralicensetoabundleofthetwopatents.WecaninterpretR inProposition1asR1+R2andpinProposition1asp1p2.Inthat case,thevalue-basedroyaltywouldstillbeB−Sandthecost-based royaltywouldbe(R1+R2)/p1p223.

Thevalue-basedlicensefeeforpatent1intheabsenceofaRAND commitmentonpatent2islessthanthevalue-basedlicensefee forthebundleofpatents1and2givenRANDcommitmentson both.Asaresult,ifapatentownerdoesofferlicensestoits RAND-committedpatentsonlyinbundlesthatincludelicensestoits non-RAND-committedpatents,itcannotjustifyitsproposedlicensefee onthegroundsthatitwouldhavebeenRANDhaditmadeRAND commitmentsonboth.

Atﬁrst,thisresultmightseemparadoxicalbecauseitsuggests thataparticularroyaltyforalicensetoabundleoftwopatents canbereasonableinsomecircumstancesbutnotinothers.Butthe resultisnotparadoxicalatall.AnalyzingRANDroyaltiesentailsin effectgoingbackintimetoimaginewhattermsthepatentowner andmanufacturerwouldhavereachediftheyhadcontractedatan earlierdate.Answeringthatquestionrequiresanunderstanding

22_If_the_manufacturer_can_delay_its_investment_in_S_until_after_it_learns_whether_its technology2R&Dissuccessful,thevalue-basedroyaltywouldbeB−S−R2/p2.

23_GK_in_effect_impose_the_restriction_(R1₊_R2)/p1p2_>_B₋_S,_which_implies_that bun-dlelicensesintheirmodelarevalue-based.Wedonotimposethisrestrictionand believethatthedistinctionbetweenvalue-basedandcost-basedRANDroyaltiesis animportantone.

(9)

ofwhattheexpectationsofbothpartieswouldhavebeenatthat earliertime.ThepresenceorabsenceofaRANDcommitmenton patent2affectsexpectationsandthereforethemeaningofaRAND commitmentonpatent1.AbsentaRANDcommitmentonpatent 2,themanufacturerwouldexpecttoneedtoinventaroundpatent 2inordertocommercializepatent1;andthatexpectationwould limitwhatthemanufacturerwouldbewillingtopayforalicense forpatent1.

Onemightwonderwhythepatentownerwouldnotmakea RANDcommitmentonpatent2ifdoingsowouldincreasethe roy-altyitcouldcommandfrompatent1.Assumingthepatentowner hasa choice ofwhether or notto commit toRAND for patent 2,thelogicfordoingsoisidenticaltothepossiblerationalefor choosingvalue-basedlicensefeeswhenthecost-basedfeewould belower.In thiscase,thechoiceforthepatentownerentailsa trade-offbetweenalower-feewithcertaintyandahigherfeewith someprobabilitybelow1butabove0.Inthecontextofa coop-erativestandard,however,thepatentownermayhavenochoice: itmayneedtocommittoRANDifthepatentisdisclosedforuse inthestandardunderdevelopment.Alternatively,patent2may benon-essentialforstandardcomplianceinatechnicalsense,but stillcomplementaryandhighlyusefulfromacommercialsense,in whichcasethepatentownerneednotmakeaRANDcommitment.

7. Conclusionsandpolicyimplications

Thequestionwesetouttoansweriswhetherapatentowner honorsaRANDcommitmentifitoffersitsRAND-committedpatent inabundlewithnon-RAND-committedpatents.Thequestionis, however,inherentlyincomplete.

Firstofall,offeringabundleofRAND-committedpatentsand non-RAND-committedpatentsdoesnotviolateaRAND commit-mentifthepatentowneralsoofferstheRAND-committedpatent separatelyonRANDterms.Giventheseparateofferingof RAND-committedpatents,theRANDcommitmentplacesnoadditional restrictiononthelicensefeethepatentownercanseekforbundles thatincludetheRAND-committedpatents24_.

Evenifwe restrict attentiontothepurebundling of RAND-committed and non-RAND-committed patents, however, the questionwesetouttoanswerremainsincomplete.Forexample, eventhoughRANDcommitmentsarenotcommitmentstooffer royalty-freelicenses,apatentownerwouldhonoritsRAND com-mitmentbyofferingaroyalty-freelicensetoabundleofpatents that includesboth RAND-committedand non-RAND-committed patents.Moreover,aswearguedinSection2,bundling(and espe-ciallypurebundling)canreducetransactionandlitigationcosts; andsomepatentusersmaydemandmoreinclusivelicenses.Thus, the issue toaddress is not pure bundling in and of itself but, rather,thetermsonwhichapatentownercanofferapurebundle ofRAND-committed andnon-RAND committedpatents.In par-ticular, canthe patent ownertake a credit for the valueof its non-RAND-committedpatentstodetermineanimplicitlicensefee foritsRAND-committedpatentsandthenclaimtohonoritsRAND

24 _Strictly_speaking,_“mixed_bundling”_entails_offering_all_the_components_of_a bundleseparatelyinadditiontothebundle.IntheGKmodelandoursimpliﬁed extensionofit,mixedbundlingwouldentailofferingnotonlyalicenseforthe bun-dleandastand-alonelicenseforpatent1,butalsoastand-alonelicenseforpatent2. Movingawayfromthesesimplemodels,however,apracticalapplicationofmixed bundlingwouldentailofferingalicensetotheportfolioofRAND-patentsalone, offeringasecondlicensetothenon-RANDpatents(eitherasaportfolioorin ratio-nalsubsets),andofferingathirdlicensewithabundleoftheRANDandnon-RAND patentstogether,ratherthanhavingtoofferindividuallicensesofeach RAND-patentandeachnon-RANDpatent,fortheproductofferingcostreasonsweexplain above.

commitmentifthisimplicitlicensefeeisRAND?Forthreereasons, ouranswertothisquestionis,“No.”

First, thereason a RANDcommitmentnottoimpose oppor-tunistic license terms is important is precisely because of the anticipationthatthepatentownerwillhaveanincentivetoimpose opportunistic licenseterms afterthelicensee sinks investment. TheopportunitytobundleotherpatentswithRAND-committed patentsandclaimcreditfortheirvalueindeterminingRANDterms forthebundlecreatesaclearriskofusingbundlingtocircumvent thecommitment25_.

Second,thecreditgivenforthenon-committedRANDpatents wouldrequireanassessmentoftheirvalue.AbsentaRAND com-mitmentonthosepatents,however,thepatentownercanclaim anopportunisticvalueforsuchpatentsastheirmarketvalue.The patentowneriswithinitsrightstoclaimsuchastand-alonevalue foranon-RAND-committedpatent,butforcingthemanufacturer topaysuchafeeinordertoaccesstheRAND-committedpatent wouldamounttorenegingonthecommitmentnottoimposean opportunisticlicensefee.

Third,imposing a reasonableness requirementon thecredit given forthenon-RAND-encumberedpatent doesnot solvethe problem. Aswe show,theRANDlicenserateonpatent1when thereisnoRANDcommitmentonpatent2islessthanwhatthe RANDratewouldbeonthebundleifbothpatentshadRAND com-mitments.HadthepatentownermadeaRANDcommitmenton patent2,itwouldhavereassuredthemanufacturerthatitdidnot needtodevelopthetechnologycoveredbypatent2onitsown andcouldthussavetheexpenseandriskofmakinginvestments todo so.Nothavingmadea RANDassurance, it is not reason-ableforthepatentownertoextractthesamevalueasifithad. Putdifferently,ifthepatentholderiswillingto“throwin”other patents–eithernon-RANDcommittedpatentsorpatentsthatare committedforseparateanddistinctstandards–“forfree,”suchthat thelicensingtermsforthebundlewouldbeRANDwithorwithout theinclusionoftheadditionalpatents,themereinclusionof addi-tionallicensesdoesnotnecessarilyharmconsumers.Thisisnota meretheoreticalpossibility:giventhetransactioncostsinvolved inenforcinglicenseagreements,aswellasthecomplementarities acrosspatentsinagiventechnologyportfolio,licensorsmaywell ﬁnditisintheirbestintereststoaddinrelatednon-RANDpatents “forfree.”Symmetrically,licenseescannotdemandadiscountfor RAND-onlylicenses,ascomparedtoRAND-pluslicenses,without ﬁrstestablishingthatthebroaderportfoliolicenseratesandterms arehigherthantheRAND-onlyratesandterms.Asapractical mat-ter,however,thecomplexitiesof establishingthat aRAND-plus licensehasRANDtermsandconditionsmaypushlicensorsmore towardmixedbundling,butthedoortoRAND-committedpatent tyingshouldnonethelessremainopen.

We view our results as clarifying and extending the GK argumentsfortoleratingpatentbundlingratherthaneither contra-dictingorevenqualifyingthem.TheGKargumentisthatallowing patent bundling encourages long-term patent licensing. To the extentthatRANDcommitmentsareaformoflong-term licens-ing(or areanalogoustosuchlicenses),allowingpurebundling ofRAND-committedpatentsencouragespatentownerstomake RAND commitments. Restricting the ability to increase licens-ingfeesonRAND-committedpatentsby claimingcreditfor the value of non-RAND-committed patents that they bundle with their RAND-committed patents forces patent holders to honor thosecommitments.Lastly,ourmodelclariﬁestheargumentsthat licenseescanandcannotmakeinpressingforaRANDlicenseoffer.

25_Farrell_and_Weiser₍₂₀₀₃₎_refer_to_a_similar_exception_to_the_single_rent_principle asthe“Baxterexception.”

(10)

Acknowledgments

WethankJorge Contreras,BernhardGanglmair,RichGilbert, Georgvon Graevenitz,JohnHarkrider, ElizabethWangand two anonymousrefereesforhelpfulsuggestions.WethankJonathan Kowarskiforresearchassistance.WearealsogratefultoGooglefor ﬁnancialsupportforearlyversionsofthisresearch.Theopinions representtheviewsoftheauthorsandnotthoseofany organiza-tion.

References

Bowman,WardS.,1957.Tyingarrangementsandtheleverageproblem.YaleLawJ. 67,19–36.

Choi,JayPil,Stefanadis,Christodoulos,2001.Tying,investment,andthedynamic leveragetheory.RandJ.Econ.32,52–71.

Contreras,Jorge,2015.AmarketreliancetheoryforFRANDcommitmentsand otherpatentpledges.UtahLawRev.2015,479–558.

Elhauge,Einer,2009.Tying,bundleddiscountsandthedeathofthesingle monopolyproﬁttheory.HarvardLawRev.123,397–481.

Elhauge,E.,2015.TreatingRANDcommitmentsneutrally.J.Compet.LawEcon.11 (1),1–22.

Evans,DavidS.,Salinger,MichaelA.,2005.Whydoﬁrmsbundleandtie?Evidence fromcompetitivemarketsandimplicationsfortyinglaw.YaleJ.Regul.22, 37–89.

Evans,DavidS.,Salinger,MichaelA.,2008.Theroleofcostindeterminingwhen ﬁrmsofferbundlesandties.J.Ind.Econ.56,143–168.

Farrell,Joseph,Weiser,PhilipJ.,2003.Modularity,verticalintegration,andopen accesspolicies:towardsaconvergenceofantitrustandregulationinthe internetage.HarvardJ.LawTechol.17,85–134.

Gilbert,RichardJ.,Katz,MichaelL.,2006.Shouldgoodpatentscomeinsmall packages?Awelfareanalysisofintellectualpropertybundling.Int.J.Ind.Org. 24(5),931–952.

Harkrider,J.,2013.REPsnotSEPs:areasonableandnon-discriminatoryapproach tolicensingcommitments.AntitrustChron.(10),

https://www.competitionpolicyinternational.com/reps-not-seps-a-reasonable-and-non-discriminatory-approach-to-licensing-commitments/. Layne-Farrar,Anne,2014.MovingpasttheSEPRANDobsession:somethoughtson

theeconomicimplicationsofunilateralcommitmentsandthecomplexitiesof patentlicensing.GeorgeMasonLawRev.21(4),1093–1110.

Lerner,Josh,Tirole,Jean,2004.Efﬁcientpatentpools.Am.Econ.Rev.94,691–711. Krattenmaker,ThomasG.,Salop,StevenC.,1986.Anticompetitiveexclusion:

raisingrivals’coststoachievepoweroverprice.YaleLawJ.96,209–293. Nalebuff,Barry,2004.Bundlingasabarriertoentry.Q.J.Econ.119,159–187. Quint,Daniel,2014.Poolingwithessentialandnon-essentialpatents.Am.Econ.J.:

Microecon.6(1),23–57.

Shapiro,Carl,2001.Navigatingthepatentthicket:crosslicenses,patentpools,and standardsetting.In:Adam,Jaffe,Lerner,Josh,Stern,Scott(Eds.),Innovation PolicyandtheEconomy,1.MITPress,Cambridge,MA.

Swanson,DanielG.,Baumol,WilliamJ.,2005.Reasonableandnondiscriminatory (RAND)royalties,standardsselection,andcontrolofmarketpower.Antitrust LawJ.73,1–58.

Whinston,Michael,1990.Tying,foreclosure,andexclusion.Am.Econ.Rev.80, 837–859.