Relational Contracts, Growth Options and Heterogeneous Beliefs: A Game-Theoretic Perspective on IT Outsourcing

Transcription

1 Relatonal Contrats, Growth Otons and Heterogeneous Belefs: A Game-Theoret Persetve on IT Outsourng Xaotong L College of Busness Admnstraton The Unversty of Alabama n Huntsvlle, AL Phone: ; E-mal: lx@uah.edu [Fnal Workng Paer Verson] L, Xaotong, Relatonal Contrats, Growth Otons, and Heterogeneous Belefs: A Game-Theoret Persetve on Informaton Tehnology Outsourng, Journal of Management Informaton Systems, Volume 3, Number 2, Fall 204, Abstrat More omanes have realzed that IT outsourng, one vewed as a ost reduton tool, ould faltate and even enable the transformaton of ther ore busness roesses. The benefts from a otental outsourng relatonsh exanson have strateg mlatons for relatonal nentve rovson. Modelng nformaton oahng n IT outsourng as an nentve roblem wth ontratblty onstrants, our analyss shows that ths roblem ould be mtgated n a reeated game where the outsourng lent and the serve rovder agree uon a relatonal ontrat. When the two artners share the belef that they an otentally beneft from a future relatonsh exanson, they are more lkely to behave ooeratvely durng the early stages of ther relatonsh. However, when they dsagree about the lkelhood of the future relatonsh exanson, they wll have dfferent referenes on a set of otherwse equvalent relatonal bonus ontrats. Sefally, they wll adot a relatonal ontrat wth large but nfrequent bonuses when the lent s more otmst than the serve rovder about the otental of ther relatonsh. Beause these results hold even when the sourng artners belefs are very lose to eah other, our analyss sheds fresh lght on the ssue of equlbrum seleton n relatonal ontrat theory. In the ontext of IT outsourng, our results suggest that, beause salent forms of relatonal bonuses are often not adoted, relatonal nentve rovson s lkely more ervasve than what we an observe. Keywords: ontratblty, equlbrum seleton, heterogeneous belefs, growth otons, relatonal ontrats, reeated games, IT outsourng.

2 Author s Short Bo Dr. Xaotong L s an assoate rofessor at the Unversty of Alabama n Huntsvlle. Hs researh has aeared n many major journals nludng Journal of MIS, Communatons of the ACM, Marketng Sene, IEEE Transatons and others. Hs urrent researh nterests are n behavoral game theory and marketng hannel oordnaton. He has been nvted to gve researh semnars at Unversty of Mnnesota MIS Researh Center, Rensselaer Polytehn Insttute and other major unverstes. He has refereed researh aers for many aadem journals nludng Journal of MIS, MIS Quarterly, Informaton Systems Researh and Management Sene. He won the best aer award from IEEE Transatons on Engneerng Management n He has served on the edtoral board of Marketng Sene. He s an assoate edtor of E-Commere Researh and Alatons.

3 Relatonal Contrats, Growth Otons and Heterogeneous Belefs Those whose ourses are dfferent annot lay lans for one another. - Confuus, The Analets a. 500 B.C.E. In most resets matters beome more dffult when there are no olemen to whom one an aeal, beause only self-olng agreements are then worth the aer on whh they are wrtten. -Ken Bnmore, Game Theory and Soal Contrat II 994, MIT Press,. 09. INTRODUCTION To ontnuously mrove suly han effeny n an nreasngly omettve global market, omanes have to roatvely ollaborate wth eah other. Very often busness ollaboratons neesstate transferrng valuable and roretary nformaton beyond omanes boundares. The rad advane n Informaton Tehnology and the ubquty of the Internet, manly through faltatng nformaton exhange among busness artners, have dramatally extended the soe of nterorganzatonal ollaboraton. An exellent examle s the ggant and radlygrowng IT outsourng marketlae, whh has been a major atalyst for many omanes amagns to revtalze ther suly hans. One smly vewed as a tool to redue IT osts, outsourng s evolvng qukly to enomass many asets of a omany s strateg ntatves, faltatng and sometmes even enablng the transformaton of ts ore busness roesses. Several reent emral studes have suggested that IT outsourng has substantally and onsstently nreased ndustry outut and rodutvty aross many dfferent ndustres [6, 38, 39]. As more and more omanes vew outsourng n a broader strateg ontext, they have realzed that the otental of an outsourng relatonsh ould be sgnfantly underestmated f they mantan the ost-uttng, rourement-based mndset n relatonsh develoment. In realty, many strateg outsourng artners nowadays have develoed hand-n-glove relatonshs enablng them to dynamally adjust the soe of ther ollaboraton through learnng and adataton. For examle, on Arl 6th 2009, IBM announed that Dash Bank n Jaan had extended ts outsourng ontrat wth exanded soe for an addtonal sx years. Whle for years IBM has Aordng to IBM s news release, the new ontrat wll extend the outsourng soe to nlude lannng suort, oeraton and mantenane for the nformaton system and alatons. Addtonally, IBM wll rovde entral roessng unt CPU and software resoures aordng to the manframe usage needed for aountng or nformaton related oeratons. The on demand model wll rovde otmal IT resoures and flexblty based on busness

4 Relatonal Contrats, Growth Otons and Heterogeneous Belefs been romotng the strateg value of transformatonal IT outsourng to ts outsourng lents, many Indan IT outsourng gants have reently started to reognze the otental of broadenng ther IT outsourng serve, aggressvely ometng for hgher-level and wder-rangng outsourng deals that usually go to ther major U.S. omettors nludng IBM, HP and Aenture [68]. Lke earler studes that romote otons thnkng n strateg IT deson-makng [7, 29, 46, 56], our aer advoates the vew that the growth otons assoated wth a relatonsh exanson ould mat nentve rovson and ontrat hoes ror to the exanson, thereby yeldng new mlatons for managng and develong outsourng relatonshs. Generatons of busness researhers have extensvely studed varous nentve roblems that lead to exhange oortunsm and ontratual hazards. Through the lens of modern ontrat theory and nentve theory, these studes have systematally examned the ageny roblem aused by asymmetr nformaton and the hold-u roblem aused by ontratual nomleteness [e.g., 35, 43, 55]. A sgnfant nentve roblem n strateg outsourng results from the vulnerablty of the transferred nformaton to msaroraton and exlotaton [8, 37]. 2 In the standard suly han or hannel ontext, nformaton merfeton reates nentve dstortons, and as a result most models fous on effetve ommunaton strateges [e.g., 3, 23, 53]. When a omany msarorates ts artners nformaton, ts nentves rmarly ome from the value of usng the nformaton for unauthorzed but roftable uroses. Beause msaroratng nformaton tends to harm owners of the nformaton, Clemons and Htt [8] desrbe t as oahng. In our aer, we use oahng, nformaton msaroraton and nformaton exlotaton nterhangeably. It s worth notng that nformaton oahng an be onsdered as an examle of losng ntelletual requrements. Ths suort by IBM Jaan wll hel Dash Bank aggressvely realze ts busness strategy to enhane roftablty and mantan a sound busness. The new agreement was sgned n Marh 2009 and follows the orgnal tenyear ontrat sgned n Arl Many IT outsourng lents, nludng some of the world s largest omanes, fnd t more and more dffult for them to exeute an otmal outsourng strategy n the very omlex and dynam global sourng market. Some of these omanes, nreasngly dssatsfed wth ther outsourng serve rovders, ndate that they are onsderng salng down ther future IT sourng atvtes or rematurely termnatng some ongong IT sourng relatonshs [2, 22, 75]. Fousng on a handful of outsourng strutural rsks, both Delotte s [2] and Weakland s [75] reorts ndate that many outsourng lents are serously onerned about nformaton onfdentalty, knowledge loss and ntelletual roerty roteton. 2

5 Relatonal Contrats, Growth Otons and Heterogeneous Belefs roerty through outsourng. Glass [32] develos a theoretal model fousng on the mat of ntelletual roerty roteton on the extent of outsourng. Several more reent studes have hghlghted defendng ntelletual roerty as a major onern for outsourng frms [e.g., 40, 66]. Our model an be readly extended to address the IP roteton ssue for many tyes of outsourng relatonshs. To study the nterlay between nentve rovson and relatonal adataton, we analyze the oahng roblem n an IT outsourng model where a lent omany she soures one of her nformaton systems funtons to an outsde IT serve rovder he. Our model dets an nomlete ontrat envronment where nformaton msaroraton s unverfable and so fato exlt ontratng on msaroraton s nfeasble. Beause of the ontratblty roblem, the IT serve rovder always has an nentve to exlot hs lent s transferred nformaton n a one-shot sourng transaton. Beng aware of hs nentve for nformaton exlotaton, she has to send some resoure to rotet the valuable nformaton to be transferred, whh onsequently bloks frst-best mlementaton and redues jont surlus. Examles of tehnal nformaton roteton nlude nformaton enryton, rodut/roess modularty and seedng dummy nformaton [8]. It s worth notng that frms an also rotet ther nformaton usng some non-tehnal method [e.g., 5]. For examle, nformaton montorng and audtng an mrove observablty, whh onsequently makes t vable to revent nformaton oahng through formal nentve ontrats. In some other stuatons, mehanst governane may rovde the arorate soluton [e.g., 70]. In our reeated sourng game whose stage game mathes the one-shot sourng game, oahng ould be avoded when the two forward-lookng sourng artners lay a more effent relatonal sourng equlbrum n whh the serve rovder never msarorates the lent s nformaton. Our analyss further suggests that the sourng artners, wth the ommon understandng that the soe of ther relatonsh ould be extended f warranted, are more lkely to adot a relatonal ontrat durng the early stages of ther relatonsh. Our study belongs to a theoretal lterature that uses reeated games to model self-enforng relatonal ontrats [4, 5, 6,, 7, 30, 52]. In the extant IS lterature, several studes have 3

6 Relatonal Contrats, Growth Otons and Heterogeneous Belefs hghlghted the sgnfane of relatonal governane and ontrat nomleteness n the ontext of IT outsourng [24, 47, 65]. Our study ontrbutes to ths lterature by formally analyzng how to use relatonal ontrats to rovde nentves n an nomlete ontrat envronment. Several eonoms aers have suggested that real otons models an be used to dede whh roorton to rodue n-house and whh roorton to outsoure [, 69]. Our study onsderably dffers from these studes by fousng on the growth otons rather than the embedded deferral otons assoated wth an outsourng relatonsh. In addton to nororatng otons thnkng nto the analyss of relatonal ontratng, our aer extends ths lterature by exltly studyng the role layed by nformaton struture roblems suh as heterogeneous belefs n nfluenng equlbrum oordnaton n long term busness relatonshs. 3 Sefally, when the sourng artners dsagree about the lkelhood of the future relatonsh exanson, they wll have dfferent referenes on a set of otherwse equvalent relatonal bonus ontrats. Consequently, the lent wll have an nentve to ay large but nfrequent bonuses when she s more otmst than the serve rovder about the otental of ther sourng relatonsh. Furthermore, our analyss shows that ths nentve wll not dsaear under a more general senaro where the lent s only margnally more otmst than the serve rovder. Deste the theoretal nature of our study, the man results of our model are emrally relevant n the ontext of relatonal outsourng. In the real busness world, t s not unommon for the duraton of a new outsourng ontrat to san more than fve years. Our model rovdes one ratonale for ths observaton: a sourng lent wth more otmst vew on relatonsh otental refers ontrats wth longer duraton beause they rovde the lent more flexblty to defer relatonal bonuses lowerng transaton osts s another ratonale for usng long-term ontrats. Our modelng framework also emhaszes that exogenous events often trgger mutually benefal ontrat renegotatons under long term ontrats. Aordng to a reent reort from Outsourng Journal [34], more than one-thrd 38 erent of the 92 outsourng relatonshs t studed n Chassang [7] roosed a relatonal ontrat model where nomlete nformaton leads to artal learnng and athdeendent equlbra. Unlke hs model that fouses on otmal learnng, our aroah emhaszes equlbrum refnement resultng from belef dsarty or nomlete nformaton. 4

7 Relatonal Contrats, Growth Otons and Heterogeneous Belefs and 2009 renewed ther deals early, before the orgnal ontrat renewal dates. The early ontrat renewal rate for IT outsourng deals was even hgher almost 50 erent. Our results also hghlght the role layed by the relatonsh exanson oton n nfluenng relatonal nentve rovson. Aordng to Delotte Consultng 2008 Outsourng Reort, 68% of the exeutves surveyed sad ther largest outsourng ontrats nluded the flexblty of hangng the soe of serves. Whether suh flexblty s assoated wth hgher degree of relatonal governane n the early stages of an outsourng relatonsh s aarently an emrally testable queston. The next seton of ths aer resents our model of one-shot sourng transaton between the lent and the serve rovder. In Seton 3 we onstrut a reeated sourng game and haraterze ts relatonal sourng equlbrum. A set of equvalent relatonal bonus ontrats wthn a renegng onstrant are also haraterzed. In the followng seton, we analyze how the roset of a relatonsh exanson nfluenes nentve rovson and relatonal ontratng. We allow the sourng artners belefs on the lkelhood of a relatonsh exanson to dffer ether sgnfantly or margnally n Seton 5, whh leads to some farly general results on equlbrum refnement. Seton 6 offers more dsussons and onludes the aer. THE ONE-SHOT SOURCING GAME We model the one-shot sourng transaton between the lent and the IT serve rovder as a one-shot sourng game that, as mentoned before, mathes the stage game of our reeated sourng game to be dsussed n the next seton. Two layers, the IT serve rovder and the lent, dede whether to engage n a one-shot sourng transaton. The nentve for the lent to outsoure omes from the ost advantages enjoyed by the serve rovder n mlementng an IT funton. The ost for the lent to nternally mlement the funton s S S>0 and the ost for the serve rovder to do the same job s normalzed to 0. So the maxmum surlus avalable from ths outsourng transaton s S. The lent offers the serve rovder m m 0 5 for hs serve. Uon hs aetane of her offer, she dedes whether to nur ost >0 to rotet her nformaton to be transferred to hm. Our model assumes that the serve rovder annot exlot the nformaton

8 Relatonal Contrats, Growth Otons and Heterogeneous Belefs one t s roteted. A more general assumton s that roteted nformaton s less lkely to be exloted by the serve rovder than unroteted nformaton. However, ths generalzaton does not alter any nsghts from our model and s therefore not adoted for notatonal smlty. If the lent hooses not to rotet her nformaton, the serve rovder has the oton to oah the unroteted nformaton. If he exerses ths oton, she wll lose L L>0 and he wll gan G. We assume that the benefts from oahng outwegh the osts assoated wth t.e., G>0. So reutaton onerns and otental legal osts are not suffent to sto the serve rovder from oahng n our model. We ntally assume that G s onstant and later extend the baselne model to analyze an merfet observablty senaro under whh the serve rovder an make some effort to make t less lkely for the lent to detet nformaton oahng. The serve rovder essentally faes an eonom tradeoff. He an make some effort to redue the lkelhood of deteton by hs lent. However, hs effort wll nur some osts and thereby redue hs gan. Many extant relatonal ontrat models am to study otmal nentve rovson n the lass ageny theory framework where the key ssue s for the rnal to ndue the otmal effort from the agent. Gbbons [30] suggests that relatonal ontrat theory should go beyond the lass ageny theory framework and dsusses ts otental for new alatons to nterfrm suly transatons. Unlke these relatonal ontrat models n labor eonoms, many nentve ontrat models n marketng hannel and suly han management fous on mtgatng busness artners oortunsm n strateg rng, nventory management or nformaton exhange. The rmary goal of our model s to study the role of relatonal ontrats n mtgatng one form of oortunsm. So the fous here s to analyze how relatonal nentve rovson mtgates the serve rovder s roensty to msarorate nformaton. In our model, nformaton msaroraton, as an nentve roblem, s always welfare damagng,.e., L>G. In addton, to avod the unnterestng senaro where rotetng nformaton s always a domnated strategy, we let < Mnmum L, S so that rotetng nformaton may otentally mrove effeny and faltate outsourng. Our model adots an nomlete ontrat aroah by assumng that nformaton msaroraton and the resultant loss L are ex ost 6

9 Relatonal Contrats, Growth Otons and Heterogeneous Belefs unverfable to a thrd arty e.g., the ourt, whh moses a severe enforeablty onstrant on exlt nentve ontratng. 4 The one-shot sourng game desrbed above s ommon knowledge, and ts order of lay and other detaled features are lsted n Table. It s worth notng that the struture of our game alloates vrtually all barganng ower to the lent, onsstent wth the fat that sourng markets n most ases are very omettve and many lent omanes are ndustry leaders lookng for ost-reduton oortuntes. Nevertheless, more omlated barganng mehansms an be used to enrh our model n those stuatons where barganng ower s more evenly dstrbuted between the two sourng artes. We wll dsuss the mlatons for more evenly dstrbuted barganng ower when we extend our model to onsder the mat of a growth oton assoated wth the relatonsh. [Insert Table Here] We use the onet of subgame erfeton to haraterze the erfet equlbrum for our one-shot sourng game. We solve ths fnte-horzon dynam game by bakwards nduton, the standard tehnque for solvng ths tye of game. Startng from ste 4 n Table, the serve rovder wll always exlot transferred unroteted nformaton beause m G m. Knowng ths and the fat that S S L, the lent wll always rotet her nformaton at ost before transferrng t to hm n ste 3. The rovder knows that he wll get m f he stays n the game and 0 otherwse, so he wll aet any offer m 0 n ste 2. Knowng ths, the lent wll always offer hm m=0 beause she has vrtually all the barganng owers she makes a take-t-or-leave-t offer n ste. Note that our mode mltly assumes m 0. Otherwse a seond equlbrum m=-g arses when > L G. We desrbe the equlbrum ath and the two artes strategy ombnaton n the followng rooston. Prooston The Perfet Equlbrum of One-Shot Sourng Game: The followng strategy ombnaton haraterzes the unque erfet equlbrum of the one-shot sourng game: The Clent s Strategy: offers m=0, always rotets her nformaton. 4 See Hart and Moore [42] for detaled dsussons of the ex ost nonverfablty assumton of nomlete ontrat theory. Tuna and Zenos [7] study the omettve dynams between rourement autons and relatonal ontrats n stuatons where nentve roblems arse beause of the nonverfablty of rodut or serve qualty. 7

10 Relatonal Contrats, Growth Otons and Heterogeneous Belefs The Serve Provder s Strategy: aets any offer m 0, always exlot the transferred nformaton f t s unroteted. The Equlbrum Path: the lent offers the rovder 0, and he aets. She then hooses to rotet her nformaton before t s transferred, and onsequently he gets no hane to exlot the transferred nformaton. The Equlbrum Payoffs: the lent gets S-, and the serve rovder gets 0. Proof of Prooston : Prooston desrbes not only the strateges layed n the equlbrum but also the strateges off the equlbrum ath, whh makes the equlbrum well sefed n every subgame of the one-shot sourng game. It s easy to see that no layer wll be strtly better off by unlaterally devatng from the equlbrum ath, and t s even more straghtforward to onfrm that the relevant strateges sefed above onsttutes a Nash equlbrum n every subgame. Therefore, the equlbrum s subgame erfet. To rove ts unqueness, we need to rule out all other Nash equlbra as subgame erfet ones. Frst, m>0 wll not be layed n any Nash equlbrum beause some layer always has nentves to unlaterally devate under ths senaro. Seond, m=0 does suort two Nash equlbra, one of whh s the erfet equlbrum desrbed above. The other Nash equlbrum requres the serve rovder to rejet any offer m 0, whh s obvously not a redble threat off the equlbrum ath. It s therefore not subgame erfet. Q.E.D. Whle the maxmum surlus avalable from the one-shot sourng transaton s S, the jont surlus reeved by the serve rovder and the lent n equlbrum s S-. The serve rovder s nentve to msarorate the transferred nformaton redues the jont surlus by, the amount of money that the lent sends to rotet her nformaton. Ths effeny loss ours beause of the ontratblty onstrant mosed by the nomlete ontrat envronment. If nformaton exlotaton s ex ost verfable, ths nentve roblem an be easly solved. To aheve ths goal, the lent an use exlt ontngent ontrats that ether enalze oahng or reward good behavor. Unfortunately, n our one-shot sourng game where oahng s not ontratble, any threat of enalty or romse of reward deendng on ex ost verfablty s not redble. If ths oneshot sourng game aurately ortrays most real world sourng transatons, sourng lents should send sgnfant amount of resoures n safeguardng ther nformaton beause ther serve rovders always try to exlot t. In atualty, many lents do not send a lot of resoures to rotet ther nformaton, and many serve rovders rarely msarorate ther lents nformaton. Ths one-shot game fals to reognze the fat that, as tehnologal advane ontnues 8

11 Relatonal Contrats, Growth Otons and Heterogeneous Belefs to redue the transaton osts for nterfrm ollaboratons, more and more sourng transatons are exeuted by omanes wth endurng and hand-n-glove sourng relatonshs. These sourng artners, relyng on mlt and self-enforng relatonal agreements, usually nterat reeatedly and behave ooeratvely under the shadow of the future [9, 48]. THE REPEATED SOURCING GAME We develo a reeated sourng game hereafter alled the baselne model to analyze relatonal sourng and the assoated mlt ontrats. The man results from our baselne model Proostons & 2 are very smlar to the major nsghts from revous theoretal studes that use reeated games to model self-enforng relatonal ontrats [4, 6,, 7, 30, 52]. Eonomsts have long beleved that reeated nteratons an sgnfantly nfluene nentve strutures and onsequently the market dynams [, 49, 58, 67]. Moreover, reent exermental evdene strongly suorts game theorsts belef that reeated games are very effetve n studyng reurrent market nteratons wthout thrd arty enforement [9, 0]. The reeated sourng game develoed here s an nfntely reeated game, wth our one-shot sourng model as ts stage game. We study statonary relatonal ontrats n the stable stage of the sourng relatonsh we wll desrbe the three stages of the sourng relatonsh later. Beause of the stat nature of the reeated sourng game, the relatonal nentve ontrats haraterzed here won t be hstory-deendent. Nevertheless, we wll analyze relatonal nentve rovson under two hstory-deendent senaros later n ths aer. After eah sourng transaton onludes, the reeated game ontnues wth robablty and ends wth robablty -. Ths robablty of ontnuaton nely atures the noton that no sourng relatonshs last forever n the real busness world and ther termnaton dates are mostly unertan. In many reeated game models, s substtuted by a ommon dsount fator. 5 Informaton msaroraton by the serve rovder ontnues to be unverfable n our 5 We assume rsk neutralty to avod nessental analytal omlatons aused by. We an easly dro ths assumton by relang ths robablty wth a ommon dsount fator or by exressng all strategy ayoffs n terms of ther von Neumann-Morgenstern utltes. In the reeated game lterature, there are two nterretatons of. It an be 9

12 Relatonal Contrats, Growth Otons and Heterogeneous Belefs reeated sourng game, whh effetvely rules out thrd arty enforement. In addton, we assume that transferred nformaton s ershable so that the serve rovder annot msarorate the transferred nformaton that was not exloted n any revous transaton we wll later relax ths assumton to analyze a more general senaro where the transferred nformaton doesn t ersh for N rounds of transatons. The reeated sourng game s order of lay and other detaled features are lsted n Table 2, and they are ommon knowledge. [Insert Table 2 Here] We frst analyze a benhmark senaro where there s no roset for a relatonsh exanson. In our reeated sourng game, the lent and the serve rovder mltly agree to ooerate to attan the maxmum jont surlus S,.e., the serve rovder romses never to msarorate the lent s nformaton, and she agrees to share the surlus wth hm by offerng hm m for eah transaton. In ths model, the two sourng artes an easly oordnate on the mlt agreement through hea talk see [28] and [53] for dsussons of the hea talk game and ts alaton to nterfrm oordnaton. It s worth notng that ths mlt agreement a relatonal ontrat annot be enfored by a thrd arty n our model and so fato must be self-enforng. To enfore ther mlt agreement, they lay trgger strateges to unsh any devaton from a relatonal sourng equlbrum haraterzed n the followng rooston. Prooston 2 The Relatonal Sourng Equlbrum: In the reeated sourng game that extends the one-shot game ndefntely wth robablty, the two artes an both be better off n a relatonal sourng equlbrum. In the equlbrum the lent always offers the serve rovder m G and hooses not to rotet her nformaton, and he never exlots her unroteted nformaton, thereby nreasng both artes exeted ayoffs over the one-shot game. Ths Pareto mrovement an be aheved f G. The trgger strateges are haraterzed below. The Clent s Trgger Strategy: she offers the serve rovder m G for eah transaton and hooses not to rotet her nformaton. However, f she observes that the serve rovder exloted her unroteted nformaton, she wll lay her erfet equlbrum strategy of the one-shot sourng game forever. nterreted as a ommon dsount fator or as a ontnuaton robablty. The two nterretatons are equvalent under rsk neutralty. 0

13 Relatonal Contrats, Growth Otons and Heterogeneous Belefs The Serve Provder s Trgger Strategy: he does not exlot the lent s unroteted nformaton as long as she offers hm m G. If her offer s ever below G, he wll always exlot her transferred nformaton f t s not roteted. Proof of Prooston 2: We frst rove that m satsfy both layers nentve omatblty IC onstrants. The lent s exeted ayoff wll be S equlbrum strategy n the reeated game. So her IC onstrant s f she hooses to lay her erfet S m. The S m serve rovder wll exlot the unroteted nformaton only f hs short-term gans from oahng m outwegh hs long-term ayoffs from ooeraton. So hs IC onstrant s G m G.Note that m s the resent value of all the future re remums that he an gan n the relatonal sourng equlbrum. It s easy to see that m satsfes both IC onstrants when G. Next we rove that both layers, gven ther trgger strateges, have no nentve to devate from the equlbrum ath. The lent wll not be better off by offerng more than m. If she offers below m, the serve rovder wll exlot her unroteted nformaton. He also annot be better off by exlotng her nformaton when her offer s m. Q.E.D. When G, the lent s IC onstrant s volated and the two sourng artes wll reeatedly lay ther erfet equlbrum strateges of the one-shot sourng game, whh onsequently redues the total exeted surlus from S to S. It s easy to see that, regardless of the values of and G, the relatonal sourng equlbrum an be sustaned as long as s suffently lose to. In our reeated sourng settng, ths mles that when the two sourng artes ereve ther sourng relatonsh as very stable ths senaro usually arses when there s hgh level of mutual trust between the two artners, they should always behave ooeratvely and not msarorate transferred nformaton. When s not lose to, ether a sgnfant nrease n G benefts from oahng or a sgnfant derease n osts of rotetng nformaton ould destroy the vablty of the relatonal sourng equlbrum. Interestngly, lower nformaton roteton ost may not lead to a more effent outome n our model. Ths s beause lower nformaton roteton ost redues the nentve for the lent to ooerate wth the serve rovder.

14 Relatonal Contrats, Growth Otons and Heterogeneous Belefs In our baselne model, we mltly assume that nformaton oahng an always be deteted by the lent. A natural extenson of the model s to onsder the senaro where the rovder an make some effort to redue the lkelhood of beng deteted by hs lent as an nformaton oaher. Denote the rovder s effort, hs net gan from oahng nformaton osts of hs effort subtrated and the lkelhood for the lent to detet nformaton oahng as e, Ge and He resetvely, where Ge and He both monotonally derease n e. Prooston 2. shows that, under ths senaro the two artes ould aheve Pareto mrovement n a relatonal sourng equlbrum that s qualtatve very smlar to the one haraterzed n Prooston 2. Nevertheless, we obtan several new nsghts nto the role layed by the serve rovder s effort to redue the lkelhood of deteton. Prooston 2. The Relatonal Sourng Equlbrum-An Extenson: In the reeated sourng game that extends the one-shot game ndefntely wth robablty, the two artes an both be better off n a relatonal sourng equlbrum. Ths Pareto mrovement an be aheved when G e / H e, where. In the equlbrum the lent always offers the serve rovder m G e / H e and hooses not to rotet her nformaton, and the serve rovder never exlots her unroteted nformaton. Proof of Prooston 2.: In ths model extenson, the lent s IC onstrant remans S m S. Beause the serve rovder an make some effort to redue the m m H e lkelhood of deteton, hs IC onstrant beomes G e m G e / H e It s easy to see that m satsfes both IC onstrants when G e / H e. Next we rove that both layers, gven ther trgger strateges, have no nentve to devate from the equlbrum ath. The lent wll not be better off by offerng more than m. If she offers below m, the serve rovder wll exlot her unroteted nformaton and make effort e to redue the lkelhood of deteton. Q.E.D. Comarng the analytal results of Proostons 2 and 2. yelds some nterestng observatons. Frst of all, these results are qualtatvely very smlar. However, t beomes muh harder to sustan a relatonal sourng equlbrum when the serve rovder s efforts an sgnfantly redue the lent s deteton robablty. Beause m m, the arameter range that an sustan the relatonal sourng equlbrum has beome smaller. Consequently, ths model 2

15 Relatonal Contrats, Growth Otons and Heterogeneous Belefs extenson generates several new manageral nsghts. For examle, our results suggest that relatonal sourng s more lkely for those IT outsourng relatonshs wth effetve montorng mehansms that make t very ostly for the rovders to avod deteton. Moreover, eters arbus, a lent wth a stronger deteton aablty enjoys more benefts from engagng n relatonal sourng. These benefts nlude better hane to aheve Pareto mrovement through relatonal sourng and lower re remum ad to the serve rovder. Interestngly, the serve rovder may not neessarly beneft from a stronger aablty of exertng efforts to avod deteton. Whle he an gan a hgher re remum n the relatonal sourng equlbrum, he may end u losng the entre relatonal remum when the relatonal sourng equlbrum beomes nfeasble beause of the more strngent IC onstrants. Beause nororatng the serve rovder s effort nto our model does not qualtatvely affet the relatonal sourng equlbrum, we use G as a onstant n the remander of ths aer for notatonal smlty. One noteable feature of the relatonal sourng equlbrum, as omared to the erfet equlbrum n the one-shot sourng model, s that the lent always offers the serve rovder somethng more than zero. Why does the lent wllngly share rents wth the serve rovder deste that fat that she an make a take-t-or-leave-t offer at the begnnng of eah transaton? Our model suggests that ths re remum s neessary to make the mlt relatonal ontrat between the two sourng artes self-enforng although onstruted n dfferent settngs, some revous eonom models yelded very smlar nsghts, [e.g., 4, 49, 67]. Ths result s onsstent wth the argument n [8] that usng omettve bddng mehansms s lkely to exaerbate the oahng roblem. [Insert Fgure Here] Fgure llustrates three stages of the outsourng relatonsh analyzed n our model. Whle the relatonal sourng game we have develoed so far the baselne model s a reasonable haraterzaton of the stable outsourng relatonsh n Stage 2, t s hard to be mlemented durng the relatonsh buldng stage. As the outsourng artners are more lkely to ontnue ther relatonsh when they have a suessful relatonsh for a longer erod of tme, t s reasonable to 3

16 Relatonal Contrats, Growth Otons and Heterogeneous Belefs assume that the relatonsh ontnuaton robablty nreases over tme n Stage. Assumng the blateral relatonsh advanes nto the seond stage after k rounds of sourng transatons, we an model the relatonsh n Stage as a fntely reeated game. Beause nreases over tme n stage, mlementng a relatonal ontrat wth a bonus ayment after eah round of transaton may nur sgnfant ontratng and mlementaton osts t essentally requres that both artners know the exat value of relatonsh ontnuaton robablty after eah round of transaton. Instead, a sngle relatonal bonus ayment ayable to the serve rovder at the end of Stage s a muh more onvenent and ost-effetve way for nentve rovson. Denotng 0 as the relatonsh ontnuaton robablty at the begnnng of Stage, a sngle relatonal bonus n the amount of G k 0 wll be suffent to overome the serve rovder s nentve to oah nformaton durng Stage. Beause the resent value of ths one-tme bonus s always greater than or equal to G, t guarantees that at any tme the rovder wll not be better by oahng nformaton. Note that ths bonus may be more than enough f we know exatly how nreases over tme durng Stage. In many real world stuatons L>>G and L>>S. So unless the lent has very reous nformaton about how evolves an unlkely senaro durng Stage, she needs to ay a bonus bg enough to avod the ossblty of sufferng a major loss from nformaton oahng. Reall that our model assumes that the transferred nformaton ershes after eah transaton. Otherwse the serve rovder an oah the aumulated nformaton. Under ths senaro, the serve rovder s gans from oahng nformaton may qukly nrease over the frst few transatons durng the frst stage as shown n Fgure and then stablze over tme. We analyze ths ase n the followng rooston. Prooston 2.2 Relatonal Pre Premum when Informaton Persh after N Rounds: When N G, the lent always offers the serve rovder m N G rotet her nformaton, and he never exlots her unroteted nformaton. N and hooses not to 4

17 Relatonal Contrats, Growth Otons and Heterogeneous Belefs Proof of Prooston 2.2: We frst rove that mn satsfes both layers nentve omatblty IC onstrants. The lent s exeted ayoff wll be S erfet equlbrum strategy n the reeated game. So agan her IC onstrant s S m N S m N f she hooses to lay her. The serve rovder wll exlot the unroteted nformaton only f hs short-term gans from oahng outwegh hs long-term ayoffs from ooeraton. Moreover, f he dedes to exlot unroteted nformaton, he an oah nformaton aumulated over N rounds of transatons beause nformaton only ershes after N rounds. So hs IC onstrant s N N m N m N G G G 2... G G [ ] m N N N G N easy to see that mn satsfes both IC onstrants when G. Q.E.D. N. It s Informaton aumulated over tme, as Prooston 2.2 suggests, makes t more dffult for the two artes to engage n ooeratve relatonal sourng. Essentally, the serve rovder an msarorate nformaton aumulated over many rounds of transatons. As a result, the lent has to share the surlus more generously to satsfy hs more restrtve IC onstrant. However, beause of her oton to lay unooeratvely by rotetng her nformaton at ost, she wll never ay hm more than, whh makes the relatonal sourng equlbrum unlkely to hold when transferred nformaton does not ersh over many rounds of transatons. Therefore, a sourng lent wth low nformaton roteton ost wll lkely to rotet her nformaton n stuatons where large amount of transferred nformaton ould aumulate over tme. Beause s assumed to be stable durng the seond stage, we an haraterze a seres of ayoff-equvalent relatonal bonus ontrats. For notatonal smlty, we mantan the assumton that nformaton ersh after one round through the remander of the aer. Beause the offered ayment an be ostoned usng bonus ontrats, a renegng roblem may emerge when the lent has an nentve not to honor the ayment offered to the serve rovder beause nformaton oahng s assumed to be an unverfable event ex ost, any ayment ontngent on ths event annot be enfored by a thrd arty, whh justfes the renegng rsk n relatonal 5

18 Relatonal Contrats, Growth Otons and Heterogeneous Belefs ontratng. 6 The lent s renegng onstrant beomes a key nentve ssue when we mlement the relatonal sourng equlbrum usng relatonal bonus ontrats, arguably the most ommonly studed ontrat hoe n relatonal ontratng lterature e.g., Gbbons [30] demonstrates that the dea of relatonal bonuses s readly alable to nterfrm suly transatons. In our baselne model, t s reasonable to assume that relatonal sourng wll not survve the lent s renegng on romsed ayments. So the lent has no nentves to renege on a romsed bonus ayment unless the reneged ayment s greater than what she an gan from relatonal sourng. Prooston 3 haraterzes a seres of relatonal bonus ontrats under ths renegng onstrant. Prooston 3 The Relatonal Bonus Contrats: The two sourng artners an agree uon a relatonal bonus ontrat as long as G. Under the ontrat, after every {, 2,... J } rounds of transatons wthout oahng, the lent ays the serve rovder a bonus m G, where J satsfes G / G G J J. These relatonal bonus ontrats are ayoff equvalent. Proof of Prooston 3: When the lent ays the serve rovder a relatonal bonus after every rounds of transatons, the serve rovder s IC onstrant beomes m G m G. Beause G S S G G relatonal bonus ayment when m, the lent s IC onstrant beomes. In addton, the lent wll have an nentve to renege on the m / G. As m nreases exonentally n, t s easy to see that there s a threshold J above whh the renegng onstrant wll be bndng. These bonus ontrats are ayoff equvalent beause the two sourng artners exeted ayoffs are the same,.e., for any {, 2,... J }, we have m G. Q.E.D. 6 Dutta and Radner [26] ont out that ths ssue s artularly roblemat n reeated moral hazard ontrats sne at some ont the rnal has an nentve to renege on hs ommtment. Consequently, most relatonal ontrats models exltly haraterze the rnal s renegng onstrant [e.g., 4, 6, 30]. Levn [52] larfed ths ssue by ontng out that beause ontngent omensaton s merely romsed, there s a temtaton to renege on ayments. Both Baker et al. [4] and Gbbons [30] haraterze relatonal ontrats as non-ourt-enforeable ontrats subjet to renegng onstrants. In our model, nformaton oahng s unverfable behavor and thus the romsed bonus ayments are non-ontratble note that the ontratble art of the outsourng ayment has been normalzed to zero, a smlar modelng tehnque was used n [30]. Suose that the lent offers the serve rovder a ourt-enforeable ayment of $00 after eah transaton. In addton, the lent romses the rovder a $20 bonus after eah transaton wthout nformaton oahng ths s essental a relatonal bonus. Can the lent renege on the $20 bonus when stuaton warrants? Yes. Ths s beause no thrd arty e.g., the ourt an enfore the relatonal bonus.e., no thrd arty an verfy whether the rovder has oahed the lent s nformaton or not. 6

19 Relatonal Contrats, Growth Otons and Heterogeneous Belefs Prooston 3 demonstrates that, as long as the renegng onstrant s not bndng, the outsourng artners an oordnate on any relatonal bonus ontrat among a seres of ayoff equvalent ones. Nevertheless, the vablty of these relatonal bonus ontrats requres that the lent s ost to rotet her nformaton s not too small. Otherwse, she would always rotet her nformaton. As we wll show n the followng seton, the sourng dyads are more lkely to use a relatonal ontrat when they share the belef that the soe of ther relatonsh ould be sgnfantly exanded n the future. THE SHADOW OF FUTURE RELATIONSHIP GROWTH To embrae the noton that strateg outsourng relatonshs usually have the otental to be sgnfantly exanded as omanes adat to ever-hangng busness ondtons, we extend our baselne relatonal sourng model to analyze the mat of a relatonsh exanson that searates Stages 2 & 3 n our modelng framework. In an nsghtful aer, Fhman [29] onetually demonstrates the nteratons among organzatonal learnng, adataton and the real otons assoated wth tehnology latform adoton. L [54] analyzes the nterlay among these fators n a ontnuous-tme stohast model. In our generalzed three stage model, the two outsourng artners start ther outsourng relatonsh wth the shared belef that ther relatonsh ould be exanded when some exogenous event ours n the future. However, beause exandng the soe of ollaboraton usually entals transferrng sgnfant amount of hghly senstve and valuable nformaton, the nentve roblem aused by nformaton msaroraton ould be onsderably exaerbated. Early studes have long onted out that nformaton oahng beomes an nreasngly ostly nentve roblem as the soe of nformaton-ntensve ollaboraton exands [8, 9, 37]. We assume that the lent wll not be better off n an exanded relatonsh where sgnfant resoure has to be sent to rotet the addtonal nformaton that needs to be transferred. So the exanded outsourng relatonsh has to be sustaned by some relatonal sourng equlbrum that does not ental nformaton roteton. In our model, the sourng artners ntally ollaborate on a relatvely small soe beause the 7

20 Relatonal Contrats, Growth Otons and Heterogeneous Belefs exeted jont surlus from the relatonsh exanson s too small to sustan any relatonal sourng equlbrum. However, the soe of ther ollaboraton ould be exanded n a mutually benefal way sometme n the future. To haraterze the shadow of future relatonsh growth, we extend our model by ntrodung a varable [0,]. We use to haraterze the robablty of the emergene of some exogenous event that favors relatonsh growth and thus justfes a relatonsh exanson. The outsourng artners may fnd a relatonsh exanson mutually benefal when any of the followng three tyes of exogenous events ours. Frst Tye: events that dretly result to nrease n the exeted jont surlus. Examles of these events nlude sgnfantly favorable movement n foregn exhange rates, sgnfant dro n IT osts e.g., sgnfant dro n bandwdth re, IT hardware/software osts. Seond Tye growth otons related: events that generate hgh varane oortuntes. Examles nlude major tehnology breakthroughs that faltate/ enable larger sale of IT outsourng EDI, Internet/Web tehnologes, ERP, CRM and more reently, loud omutng [62] and moble omutng; major ndustral regulaton hanges/deregulaton. The outsourng artners have stronger nentves to exand ther relatonsh as the growth otons assoated wth the exanded relatonsh beome more valuable. The extant real otons lterature also suggests that growth otons beome more valuable wth the emergene of hgh varane oortuntes [e.g., 29, 59]. Thrd Tye also growth otons related: events that trgger hgher omettve ressure or nrease the lkelhood of new entrane. As onted out by Cahon and Harker [2], ndustry ometton lays a major role n nfluenng frms outsourng strateges. The outsourng artners wll have an nentve to exand ther relatonsh when suh exansons an lead to strateg reemton whh, as emhaszed by Kulatlaka and Perott [50], wll nrease the value of growth otons n the future. For the seond and the thrd tyes of events, t s reasonable to assume that multle relatonsh exansons may our after the frst relatonsh exanson. Our framework aommodates ths ossblty by fousng on the future growth otons assoated wth 8

21 Relatonal Contrats, Growth Otons and Heterogeneous Belefs the frst relatonsh exanson. So for a hghly unstrutured envronment lke stage 3, we thnk that t s reasonable to onetualze future exanson oortuntes the seond and the thrd tyes dsussed above as growth otons. Reall that the outsourng relatonsh ontnues wth robablty n our reeated sourng game. In our extended model, wth robablty the sourng artners have no nentve to exand ther relatonsh and thus ther relatonsh ontnues wth the same soe. After eah round of transaton, wth robablty an exogenous event ours and the sourng artners fnd t mutually benefal to exand ther relatonsh. Under ths senaro, the lent has to transfer sgnfant amount of new nformaton. Durng eah erod after the relatonsh exanson, the serve rovder an gan G G f he dedes to oah the transferred nformaton so G reresents the addtonal gans from oahng the newly transferred nformaton. After the relatonsh exanson, the jont surlus from eah transaton s endogenously determned. There are at least two reasons why we model hstory-deendent gans from the relatonsh exanson. Frst, revous studes from the marketng lterature have suggested that, as a busness relatonsh matures, the levels of trust and ommtment grow and farness beomes a more mortant onern [2, 20]. Consequently the serve rovder exets to beneft more from a relatonsh exanson that ours later. Seond, revous studes from the management lterature have shown that, as a busness relatonsh matures, artners tend to develo stronger relatonal aabltes to exlot new busness oortuntes [e.g., 27]. So t s reasonable for the two sourng artners to exet to gan more from a later relatonsh exanson. We haraterze the hstory-deendent gans from the relatonsh exanson as. As a result, the serve rovder s exeted gan asymtotally aroahes βs over tme, where β s the serve rovder s share of surlus S every erod after the exanson. It s easy to see that the lowest exeted gan wll be f the exanson ours after the frst round.e., T=. We frst analyze the senaro where the serve rovder s gans from oahng the transferred nformaton may be overwhelmed by hs exeted gans from ooeratng wthout oahng. 9

22 Relatonal Contrats, Growth Otons and Heterogeneous Belefs Prooston 4 Relatonal Bonus Unneessary when Exanson Provdes Suffent Inentves: When, the lent does not need to ay any relatonal bonus to the serve rovder before the relatonsh exanson, and the serve rovder has no nentve to oah the transferred nformaton. Ceters Parbus, ths ondton beomes less restrtve as α or β nreases. Proof of Prooston 4: Suose that the exanson ours after T rounds of transatons. The serve rovder s exeted gan wthout dsountng from the exanson s. Gven the ontnuaton robablty, we an alulate the resent value of the serve rovder s exeted gan from the otental relatonsh exanson as. Ths resent value must be greater than G to overwhelm the serve rovder s nentve to oah nformaton. The last art of ths rooston an be roved usng the omaratve stats results and. Q.E.D. Preoston 4 suggests that relatonal bonus s unneessary when the serve rovder exets to gan sgnfantly from the otental exanson. Moreover, a serve rovder exetng a more equtable relatonsh n the future s less lkely to oah nformaton oortunstally. A serve rovder s also less lkely to behave oortunstally f the two artes exet to develo ther aabltes more qukly to exlot the full otental of the relatonsh exanson. For the remander of our aer our analyss fouses on the senaro where, after the relatonsh exanson, the serve rovder s exeted gans from oahng the transferred nformaton domnates hs maxmum exeted gans wthout oahng,.e., S G G. As haraterzed n Prooston 2, the exanded relatonsh an be sustaned by a relatonal sourng equlbrum where the serve rovder s exeted ayoff from the exanded relatonsh s G+G note that the serve rovder an gan G+G by oahng the lent s nformaton. To omensate hm for not oahng nformaton, the lent has to ay hm at least G+G. The followng rooston demonstrates how otons thnkng on relatonal adataton mats the sourng artners strateges ror to the relatonsh exanson. 20

23 Relatonal Contrats, Growth Otons and Heterogeneous Belefs G Prooston 5 The Relatonal Sourng Equlbrum ror to the Exanson: When G, the lent does not need to ay any relatonal bonus to the serve rovder before the relatonsh exanson, and the serve rovder has no nentve to oah transferred nformaton. When n G G G G G, the lent ays the serve rovder a bonus after eah transaton and he never oahes the transferred nformaton n equlbrum. Proof of Prooston 5: Beause the serve rovder s exeted ayoff at the tme of relatonsh exanson s G G, hs exeted ayoff from the relatonsh exanson an be shown as G G G G 0 he has no nentve to oah the lent s transferred nformaton when G G G G G. It s easy to see that, before the relatonsh exanson,. Otherwse the lent has to ay hm a relatonal bonus after eah transaton wthout nformaton oahng. Denote the relatonal bonus as n. For the lent not to rotet her nformaton, n has to be less than the lent s nformaton roteton ost. Takng advantage of the reursve struture of our model, we have the followng ondton under whh no oahng ours n equlbrum: Q.E.D. G n G G G n G G One mmedate mlaton for the above rooston s that a ooeratve outsourng relatonsh, durng Stage 2, may not ental any form of relatonal bonuses or alternatvely re remum as long as busness artners understand that they may both beneft from otental relatonsh exansons n the future. Moreover, the roset for a sgnfant relatonsh exanson ould make t hghly lkely for the outsourng artners to behave ooeratvely and engage n relatonal sourng. Reall that Prooston 2 shows that relatonal sourng equlbrum annot be sustaned when t osts the lent very lttle to rotet the transferred nformaton. Prooston 5 suggests that, when t s lkely for the soe of an outsourng relatonsh to be exanded, even an outsourng lent wth very low nformaton roteton ost may not have nentves to rotet her transferred nformaton. In stuatons where future relatonsh exanson s not very lkely or the serve rovder exets lmted gans from an exanded relatonsh, 2

24 Relatonal Contrats, Growth Otons and Heterogeneous Belefs 22 relatonal sourng wthout nformaton roteton s stll lkely to our beause relatonal equlbrum an be sustaned by smaller relatonal bonuses. As shown n Prooston 3, when the frequeny of relatonal bonus ayments s endogenzed, the outsourng artners an oordnate on a set of ayoff equvalent relatonal bonus ontrats. Can they oordnate on a set of relatonal bonus ontrats wth dfferent ayment frequenes when they both understand that there s some lkelhood for a future relatonsh exanson? The followng rooston rovdes a ostve answer. Prooston 6 The Relatonal Bonus Contrats Pror to the Exanson: The two sourng artners an agree uon a relatonal bonus ontrat when G G 0. Under the ontrat, after every {, 2,... K } rounds of transatons wthout oahng, the lent ays the serve rovder a bonus ] [ ] [ n n, where G G n. These relatonal bonus ontrats are ayoff equvalent. Proof of Prooston 6: When the lent ays the serve rovder a relatonal bonus after every rounds of transatons, the serve rovder s IC onstrant leads to the followng equlbrum equaton note that we here take advantage of the reursve struture of our model: G G G n G. Rearrangng the equaton, we have ] [ ] [ n G G n. To rove ayoff equvaleny, we need to show that the exeted total amount of bonus ayments ror to relatonsh exanson s ndeendent of ayment frequeny note that under all these relatonal bonus ontrats the artners have the same exeted ayoff after the relatonsh exanson. For a bonus ontat wth ayment frequeny, the exeted total amount of bonus ayments ror to relatonsh exanson s G G n n, whh s ndeendent of. In addton, these bonus ontrats are vable only when the lent s IC onstrant s satsfed as G G S G G G S. Beause n nreases exonentally n, t s easy to see that there s a threshold K above whh the lent s renegng onstrant wll be bndng. Q.E.D. It s worth notng that, beause the relatonsh exanson nreases the lent s total exeted ayoffs, her renegng onstrant beomes less restrtve omared to her onstrant