Business-Science Research Collaboration under Moral-Hazard

Transcription

1 Bsiness-Science Research Collaboration nder Moral-Hazard Isabel Pereira Universitat Atònoa de Barcelona, y United Nations Developent Prograe z Septeber 07, 2007 Abstract I analyze, in the context o bsiness and science research collaboration, how the characteristics o partnership agreeents are the reslt o an optial contract between partners. The nal otcoe depends on the strctre governing the partnership, and on the inorational probles towards the e orts involved. The positive e ect that the e ort o each party has on the sccess o the other party, akes collaboration a preerred soltion. Divergence in research goals ay, however, create con icts between partners. This paper shows how two di erent strctres o partnership governance (a centralized, and a decentralized ones) ay optially se the type o project to otivate the spply o non-contractible e orts. Decentralized strctre, however, always choose a project closer to its own preerences. Incentives ay also coe ro onetary transers, either ro partners sharing each other bene ts, or ro pblic nds. I derive conditions nder which pblic intervention is optial. JEL Classi cation: L21, L24, L31, L33, O31, O32. I a deeply gratel to Inés Macho-Stadler and David Perez-Castrillo or their spport and help. I also thank coents received dring the Microeconoics Workshop and the Indstrial Organization Inoral Seinar at IDEA-UAB. Sggestions ro Pedro Rey-Biel have been very helpl. I a also acknowledge Irina and Nadia Proko eva or all their wise and valable coents. Finally, nancial spport ro Fndação para a Ciência e Tecnologia (Portgal), BEC (Spain), and Centre Tecnològic Forestal de Catalnya (Spain) are gratelly acknowledged. All errors are y own responsability. y URL: z 304 East 45th Street, 12th oor, roo 12104, New York, NY 10017, USA. Eail: [email protected]. 1

2 Keywords: collaboration, basic research, applied research, project, rs, niversities, partnership governance. 2

3 1 Introdction Why do pro t rs collaborate with niversities in less applied research projects? Why do niversities collaborate with rs in less basic research projects? Firs and niversities belong to di erent instittional settings, with di erent approaches and objectives when condcting research (Dasgpta & David, 1994). Throgh research, rs ai to obtain proitable discoveries that increase the qality o their goods and services or their prodctivity, or that redce their prodction costs (Eropean Coission, 2004). For niversities, however, research is the ean to l ll their "coitent to society to create and sstain knowledge" (Argyres & Liebeskind, 1998). Despite these divergences in research goals, recent trends in partnerships show an increasing iportance o research collaborations between rs and niversities (NSF, 2006; Caloghiro et al., 2001). 1 The ain reason or sch trend relies on the recognition o tal bene ts ro this type o interaction. To y knowledge, the type o research projects that ay arise nder collaboration o instittionally di erent parties, however, has not received a satisactory explanation in the literatre. 2 The present paper contribtes with a new possible answer to this pzzling qestion, by showing that the otcoe o a partnership agreeent ay optially derive ro a contract between the partners. The ain point o the argent is that the characteristics o a collaborative research can act as an incentive tool or non-contractible resorces (hereater naed e orts). The choice o a research project closer to the interests o one o the parties, otivates a higher allocation o e ort ro that party, ths increasing the expected bene t o collaborating. The analysis also ephasizes how the collaboration otcoe depends on the strctre o partnership governance, by coparing a centralized decision aking process, to a decentralized one. Besides expanding the stdy o bsiness and science links, the theory developed in this paper contribtes to a deeper nderstanding o the organization o research activities. In the ost recent decades, special attention has been dedicated to collaborative research between rs and niversities. The reason or this special interest lays in the recognition o potential bene ts and costs ro this interaction. Several epirical stdies docent the bene ts accring to rs that have niversities as research partners (e.g., Lee, 2000; Caloghiro et al., 2001; Schartinger et al., 2001; Belderbos et al., 2004; Vegelers & Cassian, 2005). The coon actor in these stdies is the recognition that cooperation with niversities represents the access to a pool o highly qal- 1 Reering to US alliances registered at the US Departent o Jstice, the Cooperative Research (CORE) database recorded a signi cative increase o RJVs having at least one niversity as a partner (NSF, 2006): 6% in 1985 (3 RJVs in a total o 50), towards 15% in 2003 (133 RJVs in a total o 913). In Erope, nder the rst or Fraework Prograes o the Eropean Union, the percentage o RJVs with at least one niversity as partner, increased ro 56% in 1983, 5 RJVs ot o 9, towards 67% in 1996, 938 ot o 1401 (Caloghiro et al., 2001). 2 Soe possible explanations, aybe copleentaries o ine, can be ond in Rosenberg (1990). 3

4 i ed scientists, in a wide range o disciplines. These portolios o knowledge and technology becoe especially relevant to rs, as societies becoe ore developed and consers ore deanding. The need to accoplish with sophistication o the arkets as a way to aintain perorance is, in act, one o the ost plasible cases or the recent trends in the research strategy o the rs. 3 Fro the niversities perspective, it is also possible to capitalize bene ts ro cooperating with rs. First, copanies provide an extra sorce o onetary nds or niversities. With the otrnning o pblic available resorces or the niversities, the iportance o this nding coponent increases (Rosenberg, 2003; and Nowotny et al., 2003). Second, the access to copanies data, eqipent, and arket experience also bene ts acadeics own research. Firs skills and resorces are excellent tools to test existing theories, or to have insights or the developent o new theories (Lee, 2000). Fro a ore general perspective, several epirical evidence register a higher probability o achieving valable otcoes ro research, when entrepreners and acadeics work together (e.g., Labert, 2003; Zcker & Darby, 1995; Cockbrn & Henderson, 1998; Balconi & Laboranti, 2006). Advantages o collaboration, however, coe at a cost, which oten hinders the relation between rs and niversities. As Dasgpta & David (1994) reark, rs (belonging to the Real o Technology) and niversities (belonging to the Repblic o Science) have di erent cltres, goals, nors o behavior and reward systes. Distinct socioeconoic rles lead to di erent approaches and objectives when condcting research. On the one hand, niversities priary concern is to contribte or the advanceent o knowledge. Activities o research developed with this goal, de ne what is known in the literatre as basic research (OECD, 2002). On the other hand, the prpose o rs when doing research is to nd concrete soltions or practical probles, ths prsing what is identi ed as applied research (OECD, 2002). According to existing epirical evidence (e.g., Hall et al., 2001; Siegel, 1999; Hall, 1999; Brainard, 1999; Schartinger et al., 2001), these distinct instittional settings and, especially, the distinct objectives towards research, are a natral sorce o obstacles or the interaction o bsiness and science. The raework in this paper bilds on the two phenoena jst described: collaboration between rs and niversities is bene cial, since it increases the probability o obtaining a valable research otcoe or both partners; bt divergence in research goals ay raise tensions in the agreeent. Under these preises, I analyze how the characteristics o col- 3 Fro the beginning o the last centry ntil 1980s, the ost sccessl innovative rs were aking (all) their in-hose research at their (big) corporate laboratories, (e.g. General Electrics, AT&T, Kodak, Xerox, IBM). In the past two decades, however, the tendency has been towards an increased cooperation with other instittions, in particlarly, with niversities (Labert, 2003; Adretsch et al., 2002; Hall et al., 2001). 4

5 laboration change in two diensions: the strctre o the partnership governance, and the inorational constraints o who has the athority over the decision aking process. In ters o partnership governance, I copare two strctres, a centralized one and a decentralized one. Under a centralized strctre, an entity representing the aggregate interests o both collaborators, the Consorti, is responsible or deciding the characteristics o the coon project, and the aont o resorces that each party shall eploy. Under a decentralized strctre, one o the parties is epowered to ake those decisions. For each o these two strctres o governance, I consider alternative inorational scenarios that di er with respect to the veri ability o e orts, ths creating or not a oral-hazard proble. I start with a benchark where both partners contribte with veri able e orts (no oral-hazard). I then analyze how the characteristics o the coon project change, when e orts becoe non-veri able to the decision-aker (oral-hazard ro one or both partners). The ain reslts o this paper show that, althogh a decentralized decision-aker always preers a project closer to its own interests (coparing with the choice o a Consorti), both types o governance ay se the type o research as an incentive tool or e ort. This incentive echanis eans that, when the e ort o one o the parties, say, the University is non-veri able, the other party, the Fir, ay nd optial to collaborate in a less applied project. With sch less applied research, scientists o the University are willing to exert higher e ort in the joint project. This higher involveent akes a sccess ore likely, increasing the expected bene t also o the Fir. Nevertheless, the se o the type o project as an incentive echanis st satisy two reqireents. First, a sccessl project shold have a s ciently high arket vale or the Fir, when coparing with the scienti c vale that a sccess brings to the University. Second, the e ort o the University shold be s ciently relevant or the sccess o the project. By a siilar reasoning, when the Fir contribtes to the joint project with non-veri able e ort, it ay also be optial or the University to collaborate in a ore applied research project. This incentive argent o ers an alternative explanation or the evidence that rs and niversities tend to collaborate in ore basic research projects (Caloghiro, 2001; Vegelers & Cassian, 2005). Soe athors, e.g., Rosenberg (1990), jstiy the involveent o rs in collaborative projects o basic research, as an long-ter investent to acqire copleentary knowledge. Ultiately, they arge, this investent wold bring soe insights on how to better condct and evalate rs own research. The present paper shows another possible jsti cation or the interest o rs in collaborative basic research: it is a tool to otivate the spply o e ort o the niversities, whenever this e ort is s ciently iportant to obtain a sccessl valable otcoe. The predictions o y odel also o er insights with anagerial and policy relevant iplications. Fro the perspective o anageent, this paper ephasizes the iportance o coitting to a project that aligns the interests o the parties involved in the collaboration. 5

6 The ex-ante coitent on the project is specially valable, whenever they can not coit on the resorces to eploy. By choosing a project whose characteristics are closer to the interest o the parties, their otivation to collaborate is higher and, ths, is ore likely to obtain a sccessl reslt. At the level o the internal organization o research, in rs, it is also possible to derive soe anagerial iplications o y reslts. In order to otivate highly qali ed scientists or the Fir s projects, the Fir ay give to those scientists the possibility to contine pblishing and to se the reslts o research in their own scienti c agenda. This argent is consistent with the reslts o Cockbrn & Henderson (1998), who nd evidence that rewarding researchers in rs, on the basis o their standing in the pblic rank hierarchy, is associated with rs being ore prodctive than their rivals. Fro a policy perspective, this paper stresses the bene ts o prooting both a centralized partnership governance, and veri ability o the resorces involved in the coon project. When the oral-hazard proble ro at least one o the partners is the reason or a less e cient collaboration, it ay be socially desirable to increase the reward o a sccessl project, sing pblic nds. The conditions or the optiality o sch policy intervention rely, on the one hand, on a high expected gain ro the partnership and a high relevance o the non-contractible resorces to realize sch gain, and on the other hand, on the low cost o the pblic nds. The theory o this paper relates to three ain branches o literatre. First, y reslts have soe eatres o research partnership literatre that shows the e ciency gains o cooperation in R&D, in the presence o spillovers and low degree o copetition (e.g., Spence, 1984; Katz, 1986; D Aspreont & Jacqein, 1988; Kaien et al., 1992; De Bondt, 1996). Classiying as a spillover the positive externality o the e ort o a partner on the expected bene t o the other partner, y reslts are aligned with this literatre. In act, I ephasize, rst, that collaborating is preerred to developing research alone, and second, that a centralized strctre o governance delivers a ore e cient otcoe than a decentralized one. In contrast with this strea o work, I consider that there exists only one phase o interaction between partners, and that all bene ts ro collaboration accre to the partners. Frtherore, I take into accont the pecliarities o rs and niversities interaction, naely di erences in research goals, and the tensions that can arise de to these divergences. Second, y paper relates to the literatre o oral-hazard probles in teas (e.g., Holstro, 1982). As in this literatre, I ephasize the ine ciency in the allocation o resorces, when individally decided by tea ebers. Nevertheless, we di erentiate on the ain sggestion to redce the oral-hazard ipact. This branch o literatre ephasizes the role o the principal and a non-balanced bdget, to ensre that agents decisions are aligned with the e cient ones. In the present paper, I se the capacity to coit on the characteristics o project, as the echanis to otivate agents or a higher e ort (closer, bt not neces- 6

7 sarily eqal, to the e cient level). Macho-Stadler & Perez-Castrillo (1993) also analyze a oral-hazard proble, considering a principal-agent odel with several agents. As in y setting, the strctre o incentives ais to elicit cooperation between agents, since it yields ore e cient otcoes. Nevertheless, we di er on the ain incentive echanis sed to redce oral-hazard ine ciencies. Their ocs is on how the capacity o the grop to coit on non-veri able variables, sch as e ort and tal help, can otivate agents to a higher involveent. My ocs is on how the proxiity o the qalitative characteristics o the activity towards the interests o the agents (the partners) can be the echanis enhancing the e orts. Moreover, while in Macho-Stadler & Perez-Castrillo (1993) the interest o the agents are aligned, in ine they are divergent, ths creating a trade-o when the decision-aker aces doble oral-hazard. Third, a ore recent branch o literatre ocses on bsiness and science interaction, ephasizing their instittional di erences, Aghion et al. (2005) and Lacetera (2006). As in y paper, Lacetera (2006) ocses on the distinct goals o each instittion: rs seek econoic pro ts, while niversities are interested in scienti cally valable knowledge. Siilarly to y reslt, a higher level o e ort translates in a larger probability o a sccessl otcoe. Nevertheless, Lacetera (2006) does neither consider a collaborative scenario where both, r and niversity, interact, nor does he consider the existence o inorational probles in the interaction. Instead, he analyzes the otsorcing o a project to acadeia as a coitent o the r not to terinate a project beore its copletion. That coitent otivates scientists e ort. Aghion et al. (2005) also discss the best allocation o a project between acadeia and the private sector, based on their instittional di erences. Their ain argent ephasizes the control rights over research decisions, with scientists praising their reedo in research, and the directness o private sector conveying a distility or researchers. As a reslt, acadeia shold develop projects with saller arket vale. My ain qestion di ers ro these two previos works. Considering bsiness and science as di erent instittions with their own established eatres, I analyze the characteristics o a siltaneos interaction. Rather than stdying who develops a project, I ask what kind o project is developed by both. The paper is organized as ollows. In the next section, I present the theoretical setting o the odel, with the objective nctions o both Fir and University, and the characteristics o the collaboration. In Section 3, I explain the collaboration eqilibri otcoes nder a centralized partnership governance as well as nder a decentralized one, and I copare the otcoes o these two strctres. In Section 4, I discss a policy intervention to spport the collaboration throgh sbsidies. In Section 5, I interpret the reslts o the odel and I address their anagerial and policy iplications. Conclsion rearks are in Section 6. All the proos are in the Appendix. 7

8 2 The Model Firs and niversities have di erent organizational settings and goals towards the prodction o knowledge. Consider a representative eber o each conity, naely one niversity (identi ed as the U niversity) and one r (identi ed as the F ir). When developing a project, the University seeks to contribte or the existent stock o knowledge. Following the literatre, basic research is de ned as the set o theoretical and experiental research activities aiing to advance knowledge (OECD, 2002). For the Fir, however, the interest o research relies on the potential applications that can be derived ro the new discoveries. Let applied research be the prodction o knowledge with the prpose o eeting a speci c recognized need. Stressing the di erence between these two research approaches, I represent the as opposite extrees o a line, as Figre 1a shows. Applied Research Basic Research Figre 1a: Applied Research and Basic Research. A research project is identi ed by a point in this line, representing a cobination o both goals. The otcoe o a project is either a sccess or a ailre. For the Fir, a sccessl project translates into an invention with arket vale, V F. The Fir receives all the bene ts ro the arket vale o the new discovery. For the University, a sccess represents a scienti c pblication with a certain scienti c vale, V U. The scienti c vale o the discovery, hence o the pblication, deterines the reward o the University. Both vales, V F and V U, depend on how applied (or syetrically, how basic) is the research. For siplicity, I consider the preerences o the two parties, Fir and University, towards the type o project, as single-peaked. Considering the two ost preerred projects (one or each party), I noralize the distance between the to one. I then identiy each party with its ost preerred project, respectively, at 0 and 1. Figre 1b represents the noralization. V F V U Applied Research 0 1 Fir University Basic Research Figre 1b: Noralization o the vales o a sccessl project. 8

9 Since, in reality, Fir s interests are closer to applied research and University s to basic research, these new extrees o the line are the ost applied and ost basic projects that are now relevant. Figre 1c represents the new project doain. 0 1 Fir s Applied Research University s Basic Research Figre 1c: Relevant range o research projects. A point x 2 [0; 1] in this new (shorter) line describes the type o a research project. x represents the relative iportance o the basic research eatres o the project, and (1 x) the relative iportance o its applied characteristics. Since, by de nition o the line, the highest possible bene t or the Fir coes ro project x = 0; and or the University ro project x = 1; it is possible to de ne the arket and the scienti c vales o all the projects in the range as ollows: V F (x) = B x; (1) V U (x) = B (1 x) ; (2) where B i represents the highest possible vale o a sccess, or party i (i = ; ), and the slope i indicates the arginal loss that i incrs when developing a research project that is arther ro its ost preerred option. I consider 1 B i < 1 and i 2 (0; 1) : The vale o i can also re ect the distance between the research goals o the Fir and the University. The closer the interests, the saller the vale o i. Ths, a saller is associated with ore science-base indstries, and a saller with acadeic departents whose interests are ore applied. As expressions (1) and (2) ake explicit, the sorce o con ict between the two parts lies on how applied is the research, in coparison with what is individally preerred. The type o project, x; then becoes an iportant decision variable, and the reslts depend on the relative vale o in coparison with : For the sake o siplicity, I consider < ; and discss how reslts change or the reaining cases ( = ; and > ). Also or qestions o siplicity in notation, M 0 = B B represents the ratio o arket-scienti c vales at x = 0; and S 1 = B B the ratio o scienti c-arket vales at x = 1: The arket vale V F, and the scienti c vale V U are, however, achievable only in the case o a sccessl otcoe or the research project. In the alternative scenario o a ailre, the project brings no vale or the partners. The probability o each otcoe depends on the e orts exerted by the partners. Throgh collaboration, each party bene ts ro the e ort exerted by the other party. Asse p is the probability o a sccess, while (1 p) the probability o a ailre, where p depends positively on the e orts that both collaborators 9

10 exert: p = ke + (1 k)e : (3) The variable e i denote the e ort exerted by party i, while the paraeter k represents the sbstittion rate o e by e. I consider e i 2 (0; 1) ; and k 2 (0; 1). Each instittion i bears a cost C i associated to a certain e ort level e i, given by: The cost coe cients c i 2 R + are sch that c > k (B + B c > (1 k) (B + B ~) ; with ~ = in ( ; ) : 4 For siplicity o notation, consider R U = (1 e ort relative to the Fir s e ort, while R F = 1 C F = c 2 e2 ; (4) C U = c 2 e2 : (5) k)2 c k 2 c R U : ~) and the bene t-cost ratio o the University s Using (1), (3), and (4), the Fir s expected gain ro developing a research project together with the University, E F, is described by: E F = pv F (x) C F : (6) Using (2), (3), and (5), the University s expected reward ro collaborating is: E U = pv U (x) C U : (7) As ar as the strctres or governing the partnership are concerned, I consider two possible alternatives: a centralized, and a decentralized ones. The ain di erence between these two strctres o governance relies on who decides over the ain characteristics o the collaboration (type o project, e orts): either one o the parties, decentralized strctre; or a third entity, which considers the aggregate interest o the two partners, centralized strctre. Under the centralized strctre, the Fir and the University (ater agreeing to collaborate) create a separate entity, the Consorti, to anage the collaboration. The Consorti chooses the best joint project x, and i possible also the aont o e ort that each partner shold exert in the project (e ; e ). Both, type o the project and resorces, are settled by contract. Nevertheless, inorational constraints ay prevent the contractibility o the e orts o the partners. I consider di erent scenarios, regarding the veri ability o e orts: both (e ; e ) are veri able, only one is, none is. Consorti s objective is to axiize the joint expected net bene t o the collaboration, EW = E F +E U : As explicit in this objective, I asse the Consorti gives eqal weight to each o the partners. 4 In this doain or c i we garantee that e and e always lay in the interval (0; 1) : 10

11 The seqence o the actions nder centralized strctre is: rst, the Consorti decides over the collaboration characteristics; second, partners exert e ort; third, Natre plays, deciding whether the project is sccessl or not, and nally each partner receives its revenes ro the research. Under the alternative decentralized strctre, the relation is prooted by one o the parties. Instead o a coon anager, it is now one o the collaborators who chooses the project to be jointly developed, and presents it to the other party. For siplicity o the analysis, I consider the e ort exerted by the party prooting the collaboration is always veri able. However, the e ort that the other party devotes to the coon project ay be contractible or not. I then consider two alternative scenarios: rst, when the e ort o the other party is veri able, and second when it is not. In the orer scenario, the prooter o the collaboration designs a contract de ning the project type, x; and the e orts. In the later scenario, the prooter only decides x and its own e ort. Once the collaboration proposal is accepted, each partner allocates its resorces to the coon project. Finally, Natre plays, deciding whether the project is sccessl or not, and each partner receives its revenes ro research. Table 1 presents the sary o the several contexts, as well as the notation sed aterwards to identiy each di erent sitation. Inoration / Manageent Consorti Fir s initiative University s initiative Both (e ; e ) veri able 1F G 1UG Only e veri able AU 2F G non applicable Only e veri able AF non applicable 2UG Both (e ; e ) non-veri able AUF non applicable non applicable Table 1: Di erent contexts to analyze. Under the anageent o the Consorti, or alternative contexts are taken into accont, naely sitations ( rst-best), AU; AF; AUF. When the Fir governs the collaboration, its e ort e is always assed veri able, and the only inorational change relates with the veri ability o e. As a conseqence, nder Fir s initiative there is only two relevant contexts: 1F G and 2F G: Siilarly, when is the University governing the collaboration, the two contexts to take into consideration are 1UG and 2UG: Otside option Instead o collaborating, each party has the possibility to develop the research by its own, alone. 5 Research alone, however, translates in a sall probability o 5 In a ore general setp, we cold jst consider as alternative or collaboration, a (general) action or each party, that wold yield a payo o i (also general). By considering the speci c case o doing research alone, we not only endogenize reslts, bt also gain soe insights on the coparison o the two research scenarios (alone and with collaboration). 11

12 sccess, or a higher cost, or both. When the Fir develops research alone, its choice solves the ollowing proble: ax E F = p F V F (x) C F ; (8) x;e g where p F = ke is the probability o a sccessl otcoe: In the optial soltion, the Fir develops the project type x = 0; exerts an e ort e ;alone = kb c ; and obtains an expected pro t o E F;alone = k2 B 2 2c : Siilarly, when the University perors research withot collaboration, it scceeds with probability p U = (1 k) e : The best soltion is to exert an e ort o e ;alone = or the project type x = 1: This yields an expected bene t o E U;alone = (1 k)2 B 2 2c : (1 k)b c Coparing (8) and (6), the University s e ort has a positive externality over Fir s expected gain (and vice-versa). Departing ro a sitation o doing research alone, collaboration represents an increase in the total expected gain, or a given project type x: The isse, however, is the opposite interests o the parties towards x: As a reslt, the decision o whether to collaborate or to develop research alone involves a trade-o : on the one hand, doing research alone enables to select the ost preerred project; on the other hand, nder collaboration, the partner contribtes to the sccess o the project. When the bene t-cost ratio o the University s e ort (R U ) is high, acadeics contribtion to the sccess is relatively high. In this case, we expect the Fir to be ore willing to collaborate. Conversely, the University preers collaboration when the e ort o the Fir is relatively iportant or a sccess, that is, when R F is high. The calcls con r this intition. The ai o this paper, however, is to ocs in the role o incentives on the otcoe o collaboration. Thereore, and or the sake o siplicity, I postpone the presentation and discssion o the exact participation constraints to the Appendix. In the next section, I present the collaboration otcoes, once adopting Sb-gae Perect Nash Eqilibri as the soltion concept. 3 Collaboration Otcoes 3.1 Consorti Governance The otcoe o the Consorti governance depends on the veri ability, hence contractibility, o the resorces that each partner devotes to the joint project. 12

13 3.1.1 First-best: both e orts are veri able In the rst-best scenario, the Consorti veri es the e ort o both partners and, thereore, incldes the in the collaboration contract. Knowing the ipact that the resorces o each partner has on the expected revene o the project, the Consorti asks e ort levels that eqate their arginal cost to their arginal revene. Proposition 3.1 presents the optial joint project. Proposition 3.1 When the e ort o both partners is veri able, their optial level depends on the total vale o a sccessl project: e = k c [V F (x) + V U (x)] ; e = 1 k c [V F (x) + V U (x)] : In this sitation, the axi joint expected gain ro collaboration is " # EW = 1 k 2 (1 k)2 + [B + B ( ) x] 2 : (9) 2 c c Considering > ; the best project is the one with the highest arket vale, that is, the ost applied research. At the optial level o e orts, the axi joint expected gain ro collaboration is convex in the type o project x; and thereore the optial joint project is located at one o the extrees o the line, x = 0 or x = 1: When > ; the stakes o the Fir are higher than o the University, eaning that the Fir looses ore ro a less applied project, than the University looses when deviating ro its ost preerred basic research. As a reslt, the s o the expected gains is axiized when the Consorti decides to ipleent the ost applied project. Figre 2 represents the sitation. EW * 0 1 x Figre 2: Joint expected gain with veri able e orts, when > : 13

14 In the opposite case, when <, the loss in the scienti c vale ro a less basic project wold be the largest, and the best choice wold be at x = 1: In a third (alternative) case o = ; any project in the interval [0; 1] wold be eqally preerred by the Consorti. The next corollary presents coparative statics reslts or the rst-best scenario. Corollary 3.1 In the rst-best collaborative scenario (Consorti, and veri ability o both e orts): 1. the optial research project does not change with the paraeters k; c i ; or B i (or i = ; ): As long as > ; the optial project is always the one with the highest arket vale; 2. the axi joint expected gain ro collaboration increases with: i) a greater relative iportance o the Fir s e ort or the sccess o the project, k; as long as k > c c +c ; ii) a saller cost coe cients, c i ; iii) a higher arket or scienti c vales, B i ; and iv) a saller arginal loss in the scienti c vale de to a less basic project, : When the e orts o the partners are contractible, the Consorti s decision internalizes the positive e ect that the e ort o each partner has on the expected gain o the other. The optial decision or the e orts, then, depends on the s o both arket and scienti c vales. This iplies that the optial type o project x only depends on how it a ects that s o vales, that is, on the relation between and : A change in the reaining paraeters does not a ect this reasoning. When k increases, the Fir s e ort becoes relatively ore iportant or the sccess o the project and, thereore, the optial e increases. Since an increase in k is eqivalent to a decrease in (1 k) ; or the University the opposite holds, that is, the optial e decreases. Considering the increase in Fir s e ort, it has both a positive ipact on the probability o sccess, and a negative ipact o enhancing the costs. The decrease in the University s e ort has opposite e ects. When k > c c +c () 1 k < c c +c, the positive e ects o the changes in the e orts doinate and, as a conseqence, EW increases. When one o the cost coe cients c i increases, the optial level o e i decreases. This translates into a saller probability o a sccess, and hence in a redction o EW : Also, when B i increases, a sccessl project brings a larger bene t, hence a larger expected gain EW : Finally, a University with ore applied interests, characterized by a saller ; gets a higher scienti c vale at the rst-best research project x = 0. As a reslt, the axi possible EW is higher. 14

15 3.1.2 At least one e ort is non-veri able When the e ort exerted by one or both o the parties is non-veri able, its choice o e ort dedicated to the coon project depends on its individal interest. At the rst stage, the Consorti takes into accont those interests o the partners, when choosing the type o project to be jointly developed. Considering the ollowing pairs o regions o paraeters, the next proposition states the reslt: Region 1 AU : M 0 > 1 and R U > ( )(M 0 +1) M 0 ( ) ; Region 2 AU : otherwise. Region 1 AUF : M 0 > 1 and R U > ( )M 0 + M 0 ( ) ; Region 2 AUF : otherwise. Proposition 3.2 The level o e ort that each party i exerts depends on its veri ability: i e i is veri able, e i = k i c i [V F (x) + V U (x)] ; i e i is non-veri able, e i = k i c i V i (x); where k i = k or i = F; or k i = 1 k or i = U. The best joint collaborative project chosen by the Consorti also depends on the (non) veri ability o the e orts, according to the ollowing rle: Optial project Non-veri able e ort x > 0 x = 0 only e Region 1 AU Region 2 AU. only e never always both e ; e Region 1 AUF Region 2 AUF Frtherore, in Region 1 AUF we have 0 < x AUF < x AU : Figre 3 plots the reslts related with the choice o the project: 15

16 R U Region 1 AU : x x AU AUF = x > 0, AF = = 0 Region 1 AUF : x AU > x AUF > x AF = 0 R = U ( ) M 0 + M ( ) 0 x AU = x AUF = x AF = 0 R U = ( )( M + ) M 0 ( ) 0 1 Figre 3: Consorti s optial project with e non-veri able (AU), with e non-veri able (AF ), and with both e and e non-veri able (AUF ). M 0 When resorces are non-contractible, the Consorti knows that the ore bene t a partner obtains ro a project, the larger is the aont o resorces it is willing to allocate to that project. When the non-contractible resorces o a partner are specially iportant or the expected joint bene t o the collaboration, the Consorti s best option is to deviate ro its rst-best project and to approach the interests o that partner. The increase in the probability o sccess copensates the decrease in the total vale o a sccessl otcoe, and hence the expected bene t increases. More speci cally: - when e is non-veri able, the University is not willing to devote as ch resorces or an applied project as it wold be jointly preerred. In Region 1 AU, the relative arket vale o the invention M 0 is s ciently high, eaning that a sccessl project brings a relatively high arket vale. Also in Region 1 AU, the bene t-cost o the University s e ort R U is s ciently high, eaning that the University s resorces are iportant or the sccess o the collaborative research. Both conditions ensre that the Consorti is sensible to acadeics preerences. Since a research project closer to the University s interests acts as an incentive or its e ort, the Consorti preers to select a less applied (ore basic) project than in the rst-best soltion; - when the Fir contribtes with non-contractible e ort or the joint project, it does not consider the positive externality that its e ort has on the University s expected gain. As a reslt, the Fir chooses to exert less e ort than it is jointly desirable. In order to redce as ch as possible the ipact o sch individalistic approach, the Consorti 16

17 preers a project closer to the Fir s interests. Given > ; the rst-best project is already the ost preerred o the Fir, ths no rther distortion can be ade. This eans that, nder > and veri ability o University s e ort, the best joint project is exactly the sae as in the rst-best scenario; - in the presence o a doble oral-hazard, the divergence o preerences creates an abigity on how to se the type o project as an incentive echanis. The reslt depends on whose e ort is ore iportant or the sccess o the project and how valable is sch sccess. In Region 1 AUF ; a sccessl reslt brings a s ciently high relative arket vale (high M 0 ); and the University is relatively iportant or sch otcoe (high R U ). Thereore, in Region 1 AUF ; University s interests doinate and x is ore basic than in rst-best. In the case o doble oral-hazard, the e ort o the Fir is also non-contractible. In order to otivate it, the Consorti chooses a ore applied project than in the case where only University s e ort is non-veri able. Figre 4 depicts the coparison o best projects or the Consorti as well as the expected joint bene t, nder the di erent inorational contexts, or paraeters in Region 1 AUF. EW * EW AF EW AU EW AUF x AUF 0= x AU 1 x = x* = x AF Figre 4: Optial joint expected gain nder rst-best (EW ), oral hazard ro one o the partners (Fir, EW AF ; University, EW AU ), and doble oral-hazard (EW AUF ). I now present soe coparative statics reslts or the collaboration otcoe, when University s e ort is non-contractible. 17

18 Corollary 3.2 Under non-veri ability o University s e ort, the best collaborative project in Region 1 AU becoes closer to the University s interests when: i) B increases, ths increasing the arket vale o the invention; ii) B decreases, ths decreasing the scienti c vale o the pblication; iii) the iportance o the Fir s e ort or the sccess, k; decreases; iv) the Fir s e ort becoes ore costly, higher c ; v) the University s e ort becoes less costly, saller c ; vi) the loss in the arket vale o a less applied invention, ; decreases; vii) the loss in the scienti c vale o a less basic pblication, ; increases. A higher arket vale, B, increases the iportance o the University s involveent in the research, to ensre a larger probability o sccess. The Consorti selects a project closer to University s interest, as an incentive echanis or e : Conversely, when B increases, the higher scienti c vale o the research already acts as a otivation or the University. The optial collaborative project can be ore applied, closer to the rst-best. When k decreases, the Fir s e ort becoes relatively less iportant or the sccess o the project, whereas or the University the opposite holds. In order to indce a higher e ; the Consorti chooses a less applied project. With a higher coe cient cost c, the optial level o Fir s e ort decreases. A saller e eans a saller probability o sccess. This redction ay, however, be partially copensated by increasing the University s e ort. In order to indce sch larger involveent o the University, the project becoes ore basic research, that is, x increases. The inverse happens, x becoes ore applied, when the University s e ort is ore costly, throgh a higher c. A saller arginal loss i eans that partner i experients a saller loss, when the project is di erent ro its ost preerred. When is saller, the ipact on the arket vale o the invention de to a less applied project is saller and, thereore, Consorti ay a ord to choose a project closer to the University s interests. Conversely, a saller is linked with a saller loss in the scienti c vale whenever the project is ore applied. In this case, the Consorti preers a ore applied project. When it is possible to establish transers between partners, the incentive or the involveent o a partner in the joint project ay also coe throgh a share in the revene o the other partner. The next proposition oralizes this reslt, or the case when only the University s e ort is non-veri able, and acadeics receive a share t 2 [0; 1) o the arket vale o a sccessl invention. We consider the two ollowing regions o paraeters: Region 1 AUT : M 0 > (2 t )t and R U > ( )(M 0 +1) [ (2 t )t ]M 0 ( ) ; Region 2 AUT : otherwise. 18

19 Proposition 3.3 With non-veri ability o the University s e ort, i the University receives a share o the arket vale ro a sccessl project, the joint optial project is closer to the rst-best. In particlar, in Region 1 AUT ; the joint preerred type o project is between the rst-best and the one chosen when no share is given. In Region 2 AUT ; the project is exactly the rst-best. When e is non-veri able; denote by x AUT the best project when the University receives a share t, and by x AU the best project when t = 0. Figre 5 presents the proposition, in Region 1 AUT : EW * EW AUT EW AU 0= x* x AUT x AU 1 x Figre 5: Joint expected gain in the rst-best (EW ), and nder University s oral-hazard (with transer, EW AUT ; withot transer, EW AU ). Region 1 AUT ephasizes the high arket vale o a sccessl research (high M 0 ), as well as the relative iportance o the University or sch sccess (high R U ). Under this region, the Consorti selects a less applied project than in the rst-best, in order to otivate acadeics e ort. Making the University also a bene ciary o a sccessl invention is an alternative way o otivating its scientists. As a reslt, the higher is t, the closer is the research to the rst-best. Nevertheless, the higher is t ; the lower is the reaining share or the Fir. The bondary level o Fir s expected gain that still akes it willing to collaborate dictates the opti vale o t : An alternative way o coparing both sitations, with and withot transer, is to analyze both regions 1 AUT and 1 AU : Since Region 1 AUT Region 1 AU ; the conditions ensring x AUT > 0 are ore restrictive than the ones or x AU > 0. 6 Siilarly, when only the Fir s e ort is non-veri able, it is jointly bene cial to transer a share o the University s revene to the Fir. This transer wold not change the optial 6 Figre 9, in the Appendix, represents these two regions. 19

20 project chosen by the Consorti (since it is already the rst-best x = 0), bt it increases the aont o e ort that the Fir is willing to exert in the collaboration. As sch, it enhances the joint expected gain. 3.2 Decentralized Governance Under a decentralized governance strctre, one o the parties involved, the Fir or the University, proposes to the other the joint developent o a research project. The governing party designs a contract with the characteristics o the relation, which the other party can accept or reject. Apart ro de ning the type o the coon project and the e ort o the party in governance, the contract ay also speciy the aont o resorces that the second party shold devote to it. This speci cation o e ort ay or not be possible, depending on their veri ability. I analyze both cases: when the e ort o the other party is veri able, and when it is not Fir s governance When e is veri able, the Fir proposes to the University a contract that speci es the type o project and the aont o e ort that the acadeics st exert. The reedo o the Fir in designing the contract is, however, liited by the otside option o the University. The ollowing proposition states the reslt, considering two regions o paraeters: Region 1P U : R F > Region 2P U : otherwise. 2 [2 (2B )+B2 ] 2 2 (B )[ (B )+ B ] ; Proposition 3.4 When University s e ort is veri able and the Fir designs the collaborative contract, the University earns as ch as in its otside option o developing research alone. In Region 1P U, the Fir proposes its ost preerred project x = 0: In Region 2P U, the Fir proposes a ore basic project, x > 0: De to divergences in the preerences and the existence o an otside option or the University, the Fir ay ace soe constraints in selecting its ost preerred project nder collaboration. As long as its contribtion or the sccess is relatively ore iportant than the University s contribtion (high bene t-cost ratio o the Fir R F, or eqivalently, low R U ), the Fir selects x = 0: This is the case in Region 1P U : There, the daage that an 7 Under the decentralized governance, the e ort o the party in governance is considered veri able. Introdcing non-veri ability o this e ort, wold indce an additional incentives contraint. Since this increase in coplexity o qalitative reslts wold not have a qalitative ipact, the veri ability assption is kept. 20

21 applied project cases to the University is copletely copensated by the increase in the probability o sccess when collaborating with the Fir. 8 When e is non-veri able, the Fir s best contract takes into consideration not only the participation constraint o its partner, bt also the role o incentives o a ore basic project towards indcing a higher e : Considering the two ollowing regions, the next proposition states the reslt: Region 1 F G : M 0 > and R U > M 0 M 0 ; Region 2 F G : otherwise. Proposition 3.5 Under non-veri ability o University s e ort, the Fir ay propose a less applied project than its ost preerred one, to increase University s involveent. This is the case in Region 1 F G ; where x > 0: In Region 2 F G ; the Fir chooses exactly its ost-preerred project, x = 0. In Region 1 F G ; a sccessl research brings a s ciently high relative arket vale (high M 0 ), and the relative contribtion o the University or sch sccess is signi cantly high (high R U ). Under sch conditions, the Fir chooses a less applied project than its ost preerred, that is, x > 0; to otivate University s e ort University s governance When e is veri able, the collaboration contract that the University designs is only constrained by the willingness o the Fir to participate in sch joint project. When the relative iportance o the Fir to have a sccessl project is high (high R F ), its participation constraint indces the University to choose a less basic project than its ost preerred. Otherwise, the University proposes the joint developent o x = 1, and a level or e that akes the Fir (alost) indi erent between collaboration and its otside option. When e is non-veri able, the choice o the project becoes an instrent to otivate Fir s involveent in the coon project. Considering the two ollowing regions, the next proposition states the reslt. Region 1 UG : S 1 > and R F > S 1 S 1 ; 8 As stated in the Model section, in this paper the ocs is the role o incentives or the otcoe o collaboration. As Proposition 3.4 shows, however, participation constraints can also a ect the otcoe o collaboration. Ftre work ay enlarge this discssion. 21

22 Region 2 UG : otherwise. Proposition 3.6 When the University governs the collaboration and Fir s e ort is nonveri able, the chosen project ay not be the University s ost preerred, as a way to otivate Fir s e ort. In Region 1 UG the project is ore applied than the University s ost-preerred, x < 1. In Region 2 UG ; the University chooses x = 1. In Region 1 UG, the relative scienti c vale o a discovery (S 1 ), as well as the Fir s iportance or sch sccess (R F ) are high enogh to ake the University sensible to Fir s interests. As a reslt, the best option or the acadeics is to propose the joint developent o a less basic project than its ost-preerred. By doing so, the University gives an incentive to a higher e ort o the Fir and, hence, increases its own expected gain. 3.3 Coparison o otcoes: Centralized vs Decentralized governance Fro the previos analysis, we ay conclde that the type o research nder collaboration can be sed as an incentive tool, both nder centralized and decentralized strctres o governance. Nevertheless, the optial project is not always the sae or both strctres. In act, when the Fir governs the collaboration and selects a less applied project than its ost-preerred (and rst-best), it is also tre that a Consorti acing oral-hazard ro the University also preers x > 0: Taking into accont the conditions that ensre x > 0 or the centralized context with either oral-hazard ro the University (sitation AU) or doble oral-hazard (sitation AU F ), and or the decentralized context with Fir s initiative (sitation F ), we conclde that: Region 1 F G Region 1 AUF Region 1 AU : Frtherore, the ollowing corollary holds: Corollary 3.3 In the Region 1 F G ; it is possible to establish the ollowing coparison between optial research projects: 0 < x F < x AUF < x AU : Figre 6 below presents this corollary as well as the expected joint gain or the di erent scenarios, considering paraeters in Region 1 F G. 22

23 EW * EW AU EW AUF EW F x F x AUF x AU 0 =x* 1 x Figre 6: Joint expected gain nder Consorti (EW ; EW AU ; EW AUF ), and nder Fir s governance with non-veri able e (EW F ). A siilar reasoning can be developed or x = 1: Coparing University and Consorti governance, having the University choosing a less basic project than individally it wold preer, is a s cient condition or all the reaining projects being also saller than 1. 4 Policy Intervention: Prize Fro the previos section, it is clear that inorational asyetries on the aont o e ort that each partner decides to allocate to the coon project, a ect the otcoe o sch collaboration. In order to redce the negative ipact o a oral-hazard proble, the governor o the relationship (either the Consorti or one o the partners) ay decide to deviate ro its ost preerred project. An additional way to redce ine ciencies arising ro the oral-hazard proble is to allow a onetary transer between partners. In this section, I analyze a third echanis to otivate the partners to dedicate ore resorces or the collaboration: throgh (pblic) prizes. Given that raising pblic nds is costly, society is only willing to give an extra-reward or the collaborative research, when the associated bene ts ore than copensate. 9 In the case o a research project, these bene ts can be several. In the raework o the present paper, all the bene ts are already considered in the vales o the project. Nevertheless, society ay still be interested in prooting a ore e cient otcoe by increasing the reward o a 9 As explicit in the odel and coon in the literatre, the cost o pblic nds relates not only to the decrease o resorces soewhere else, bt also to distortions that sch decrease creates (La ont & Tirole, 1993). 23

24 sccessl project developed nder collaboration, that is, by giving a prize. The conditions presented here nder which this pblic intervention is optial, ay then be consider as a lower bondary or those cases where other bene ts or society ay exist. The previos analysis o collaboration otcoe considers two alternative governance strctres: centralized and decentralized. It has been shown that the centralized strctre allows to obtain a higher joint expected gain and, hence, leads to a ore e cient otcoe. The conditions nder which society preers to give an extra-reward or the collaboration with centralized governance, are then s cient to ensre that society also preers to intervene nder a decentralized strctre. Thereore, I only ocs on giving an extra-reward (prize) or research collaboration with Consorti governance. Let z 0 represent the prize or the research that is already collaborative, and 2 R + be the cost o sch pblic nds: Considering that both arket and scienti c vales re ect all the bene ts ro a research project, a Social Planner s objective nction is represented by: ES = p (V F + V U + z) C F C U (1 + ) zp = p (V F + V U z) C F C U : The probability o sccess p; the arket and scienti c vales o a sccessl otcoe, V F and V U ; and the cost o resorces involved, C F and C U ; are the sae as de ned in the Section 2 (expressions (3), (1), (2), (4), and (5), respectively). Let s consider the case where the Social Planner has the capability to de ne both the total aont o the prize, z; and the raction that each party receives: 2 [0; 1] is the raction or the Fir, whereas (1 ) the raction or the University. Ater observing the Social Planner s decision, the Consorti decides on the type o project to develop, and on the aont o resorces to allocate, in a siilar way as beore. The objective nctions or the Fir, the University, and the Consorti are now, respectively: E F = p (V F + z) C F ; E U = p [V U + (1 ) z] C U ; EW = E F + E U : When both e orts are veri able and, hence, contractible, the Consorti chooses the project x = 0; whether there is or not a prize. Since the Consorti s decision does not consider the cost o the pblic nds, ; the possibility o having a prize leads to excessive levels o e ort, ro the social point o view. Thereore, in the syetric inoration case, the best social soltion is not to give a prize to collaboration. 24

25 When the involveent o at least one the collaborators is non-contractible, however, it ay be optial to give a prize or sch partner. The prize not only otivates the noncontractible e ort, bt also allows to choose a project that is closer to the rst-best. Next proposition states the reslt. Proposition 4.1 When the e ort o at least one o the partners is non-veri able, its e ort is s ciently iportant or the sccess o the project, the sccess o the project is s ciently valable, and the cost o pblic nds is not very high, it is optial to give a prize to sch partner. 10 In case o a doble oral-hazard, either = 0 or = 1; that is, it is never socially optial to siltaneosly give a prize to both partners. Frtherore, with a prize, the optial project coes closer to the rst-best. When only University s e ort is non-veri able, the Consorti ay otivate the University or a higher involveent by choosing a project closer to its ost-preerred, as seen in the previos section. Under sch scenario, the prize has the doble ipact o increasing the resorces involved in the research, and o approxiating the project type to the rst-best (x = 0): When the cost o collecting pblic nds is not very high, the socially optial soltion is to attribte a prize to the University, which acts as an incentive sbstitte o a ore basic research. When only Fir s e ort is non-veri able, the Consorti chooses the ost applied research, independently o the existence or not o a prize. When the cost o pblic nds is not very high, however, it ay be socially desirable to attribte a prize to the Fir. Sch intervention increases the involveent o the Fir in the collaborative research to an aont closer to the rst best, ths iproving the probability o a sccessl otcoe. When the e orts o both partners are non-veri able, the previos argents jstiy the allocation o a prize or their involveent on the collaborative project. Nevertheless, only one o the two partners shold receive the extra-reward. When R U is high, the University e ort is relatively ore iportant or a sccessl otcoe. Giving a prize to acadeics increases the aont o resorces that they are willing to devote or the collaboration project and, hence, the expectation o a joint gain enlarges. Conversely, when R F is high, the prize shold be given to the Fir. 10 In the Appendix, the proo o the proposition akes explicit the pper bondary o copatible with the prize o each partner. 25

26 5 Generalization In this section, I show that the reslts o the previos Sections 3 and 4 are robst to ore general speci cation o the odel. As beore, let s consider one University and one Fir, with single-peaked preerences over the type o research projects. The two ost preerred projects (one or each party) are the two extrees o a line o nitary easre. A point x 2 [0; 1] in this line identi es a research project. In case o a sccessl otcoe, a project developed nder collaboration translates in an invention or the Fir and in a scienti c pblication or the University. The invention has a arket vale V F (x) ; and the scienti c pblication has a scienti c vale V U (x) : V F is a decreasing nction o x, while V U is an increasing nction o x, and each o these nctions V i is non-convex on x; F < U > V i 0 or i = @x 2 In case o a ailre, the projects brings no vale or any o the two parties. The probability o sccess depends on the e ort that each party exerts to the project, p (e ; e ), and non-convex in each o the i > p 2 i For exerting an e ort e i, party i has a cost C i (e ; e ), i C i 2 i As ar as second-order e ects are concerned, let s consider three alternative cases: copleentarity o e orts, both in the probability o sccess and in the costs: 2 C j < 2 j > 2. sbstittability o e 2 j < 2 C j > 0; 3. independence o e 2 j = 2 C j = 0: The reain strctre o the odel, naely in ters o governance and veri ability o e orts, is the sae as beore. Consider, rst, a centralized strctre o governance. When both e orts are veri able, the decision proble o the Consorti is: ax EW = p (e ; e ) [V F (x) + V U (x)] C F (e ; e ) C U (e ; e ) ; x;e ;e g 11 The two initial alternatives (copleentarity, and sbstittability) are de ned in strict sense (with strict ineqality). The reslts or the weak copleentarity and weak sbstittability (with weak ineqality) can, aterwards, be easily dedced. 26

27 sbject to the participation constraints o both parties. When sch constraints are satis ed, collaboration is preerred to a sitation where both parties do research alone. The soltions or the Consorti proble ollow as: i : (e ; e ) [V F (x) + V U (x)] i (e ; e ) j (e ; e ) ; i : p (e ; e U = 0; where i; j = F; U, and i 6= j: With the speci c nctional ors o Section 2, naely assing linearity o the vales V i towards the type o project x, the best research is either a corner soltion or ndeterined. Nevertheless, as condition (11) ephasizes, once we leave the linearity assption, it ay also appear interior soltions x 2 (0; 1). When the e ort o one o the parties is non-contractible, its level is individally decided by that party: e i : (e ; e ) V i (x) i (e ; e ) i The optial decision o the Consorti becoes: e Ai j (e ; e ) [V F (x) + V U i (e ; e ) V j j j (e ; e ) i (e ; e ) ; j x : p (e ; e @e (e ; e ) V j (x) = 0: (13) Coparing (12) and (13) with the previos (10) and (11), respectively, is visible the existence o a new ter (hereater, called external e ect), de to the in ence o the choices o the Consorti on the non-contractible e ort o party i. The ollowing proposition then holds: Proposition 5.1 Asse the e ort o party i is non-contractible. When the external e ect o e i in the choice o project is strong enogh, the Consorti distorts its rst-best decision towards the ost preerred project o party i. When both e orts are non-veri able (doble-oral-hazard), the distortion o the project is towards the preerences o the party casing the higher external e ect. In ters o e orts, i only e ort i is non-contractible, the Consorti chooses an e ort or j that is: 27

28 higher than in rst-best, when e orts are copleentary, saller than in rst-best, when e orts are sbstittes, eqal to the rst-best, when e orts are independent. Consider now the decentralized strctre o governance. Party j is responsible to de ne the characteristics o the research collaboration and its own e ort e j, bt the e ort o party i is non-contractible. The optial decision o party j is given by: e jg j (e ; e ) V j i (e ; e ) V j j j (e ; e ) ; (14) x jg : p (e ; e @e (e ; e ) V j (x) = 0: (15) When the decentralized governance aces oral-hazard ro its partner, the external eect is present. Nevertheless, since nder decentralized governance the decisions are individally taken, the vale o the external e ects are saller than with Consorti s governance. This iplies the ollowing reslt. Proposition 5.2 Asse that the e ort o party i is non-contractible. When the external e ect o e i in the choice o project is strong enogh, party j s governance ay distort its rstbest decision towards the ost preerred project o party i. Nevertheless, coparing with a Consorti governance, the decentralized governance o j always choose a project closer to j 0 s preerences. 6 Discssion and Iplications o the Reslts Research collaboration between rs and niversities brings tal gains throgh enhancing the probability o achieving discoveries valable or both partners. Cltral and goals divergences ay, however, becoe obstacles or the interaction o the two parties. The reslts in the present paper help to predict the sstainability and otcoes o collaboration, in the presence o those divergences. These reslts ocs on or ain ideas. First, when the resorces o a partner are non-contractible, choosing a project closer to the interests o this partner is a way o indcing it to exert a higher e ort or the coon project. With ore resorces being devoted to the project, a sccessl otcoe is ore probable. Althogh the initial distortion o the characteristics o the project cold a ect negatively the 28

29 vale o the otcoe, the increase in the probability o a sccess ay copensate that. As a reslt, the expected retrn o the project ay be higher. My analysis shows that distortion o the characteristics o the project is worth when two conditions are satis ed: rst, when the ipact o non-veri able e ort is relatively ore iportant or obtaining a sccess than the e ort o the other partner; second, when the vale o a sccessl otcoe is s ciently large, in particlar or the partner whose interests are daaged de to the change in project. Second, changing the characteristics o a project is an incentive echanis that ay enhance the expected gain o the collaboration, both nder a centralized and a decentralized strctre o governance. Nevertheless, nder a decentralized strctre, the otcoe is always closer to the interests o the partner prooting the collaboration. As a conseqence, nder decentralization, the collaboration holds a saller expected gain than in the case o centralization. Third, besides changing the characteristics o the project, an alternative echanis o otivating the spply o e ort can be the establishent o a transer between the partners. In particlar, when the partner whose resorces are non-contractible receives a share o the revene o the other partner, the negative ipact o the oral-hazard decreases. As a reslt, the type o the project can be closer to the rst-best. Forth, society ay be interested in giving an extra-reward to the collaboration, in order to redce the ine ciency cased by oral-hazard. This is the case when the non-contractible resorces o one o the partners are relevant to obtain a sccessl reslt, and when the vale o a sccessl project is s ciently high to jstiy policy intervention. My clais spport the epirical evidence that niversities and rs tend to collaborate in ore ndaental, general-prpose research (e.g., Vegelers & Cassian, 2005; Caloghiro et al., 2001). Scientists dedication and e ort to research is sally di clt to veriy (Cockbrn & Henderson, 1998), and thereore a niversity ay be nable to coit on the resorces that it allocates or collaboration. The niversity s involveent ay, however, be highly relevant or the sccess o a project. As sch, y reslts show that it ay be optial to develop a project whose characteristics are closer to acadeics interests. This incentive echanis is particlarly sitable when the goals o the two partners are ore aligned (saller arginal losses i, in the langage o the odel). When that is the case, the saller is the redction in the vale o one partner by changing the characteristics o a project towards the other s interests, the saller is the con ict o interests in the partnership. For exaple, in the research agreeent started in 1994 between the Massachsetts Institte o Technology (MIT) and the pharacetical r Agen, this alignent o interests is perceived as the ain reason or the viability o the relation. Initial dobts on how di erent instittions wold be able to jointly develop a project that wold be bene cial or both partners, were not aterialized de to the proxiity o interests. In 2002, however, the reverse happened. The shit in the goals o the r towards a greater ephasis on 29

30 arketing, raised serios concerns on the collaboration persistence (Lawler, 2003; Lacetera, 2006). In y raework, I consider that the otcoe o a sccessl research renders both arket and scienti c vales, respectively or a r and a niversity. The analysis does not directly deal with the probles that partners ay ace in appropriating those vales. The ain jsti cations or taking sch approach is twoold. First, y ai is to ocs on how inorational probles can a ect the otcoe o a collaborative research between two dierent instittions. Second, there is no clear pattern on how intellectal property rights a ect collaboration between rs and niversities. Soe athors nd no evidence that concerns abot appropriating the bene ts o new knowledge are an obstacle to the relationship (e.g., Vegelers & Cassian, 2005), while other athors nd that those concerns ay be a barrier to collaboration (e.g., Hall et al., 2001). Nevertheless, this isse can be addressed in y raework. In the odel, the variable x represents the basic research eatres o a project that is valable or the University. Acadeics knowledge prodction is by natre open to society, with no rivalry in its se, and oten non-excldable (the "intellectal coons" concept o Argyres & Liebeskind, 1998). Thereore, an additional interpretation or x is to consider it a easre o how non-excldable is new knowledge o the project. As x becoes saller than one, the knowledge prodced becoes ore excldable (so rther ro University s ain goal), bt with higher valable coercial applications. As Argyres & Liebeskind (1998) ention, biotechnology is an exaple o sch type o research, where excldability increases the private vale o the knowledge, while decreasing the aont o knowledge pblicly available. Considering this alternative interpretation or x; y reslts are also consistent with the ndings o Zcker & Darby (1995). Analyzing cooperation between star bioscientists and biotechnology enterprises, they nd evidence that as the expected coercial vale o the research increases and scientists receive a share ro that vale, they decrease the di sion o the discoveries to other scientists. In the langage o y odel, this corresponds to the reslt o Proposition 3.3: when University receives a share o the arket vale o the otcoe, the optial type o project is closer to Fir s interests (optial x decreases). 6.1 Managerial Iplications The reslts o this paper bring concrete anageent insights or the collaboration between rs and niversities. First, when a partner cannot coit on the aont o resorces it dedicates to a coon project, it ay be optial to change or a type o research closer to the interests o that partner. This is particlarly so, when its involveent is relatively iportant to obtain a sccessl otcoe and the sccessl otcoe brings a s ciently high vale, in particlar 30

31 or the partner eeling the external e ect. Second, in case the change in the characteristics o the project is too costly and partners do not agree on it, bt still nd it worth to collaborate, the proble o non-coitent o resorces can be redced by a higher interaction between the partners. This eans that, rather than considering the veri ability o e ort, we ay reer to the capacity o coitent on a certain level o e ort. This is also the conclsion o the head o the pharacetical r Agen, Gordon Binder, whose experience o sccessl collaboration with MIT was based on reglar joint research between Agen s researchers and MIT s scientists: "What doesn t work is to give a niversity a ton o oney and then sit back to wait or sel retrns" (Lawler, 2003, page 331). Despite other bene ts that tea work ay have, when acadeic scientists and the researchers o the r work reglarly together, it ay be possible to redce the inorational probles on the resorces eployed. Developing research in a tea environent, increases the possibilities o each partner to onitor the aont o resorces that the other partner devotes to the coon project. When sch higher accontability is cobined with a higher bargaining power o the partner whose interests are hared with the non-veri ability o resorces, then tea work increases the expected gains o the collaboration. This reasoning ay explain the recent trend in copanies collaboration strategy, when oving ro large-scale agreeents to contracts with individal scientists (Lawler, 2003). Fro the point o view o the Fir, the research collaboration with individal scientists ay also be interpreted as a way to adopt a decentralized anageent strategy, nder the Fir s initiative. As the reslts o the odel show, in this scenario, the Fir is able to ipleent a project closer to its interests. Three ore exaples o research collaboration between a r and a niversity reinorce the relevance and application o y raework (the rst two exaples are also discssed by Lacetera, 2006). Exaple 1, Novartis and Berkeley University: In Noveber 1998, the Swiss pharacetical Novartis established an agreeent with Berkeley University, Caliornia, nder which the copany paid $25 illion over 5 years to the niversity. In exchange, the copany had access to niversity s plant and icrobial biology departent labs and to scienti c discoveries coing ro the niversity. In ters o y raework, this corresponds to a collaborative relation where the e ort o the r is veri able (oney), bt the resorces o the niversity are not. In act, there was no explicit coitent ro the niversity to devote its resorces or a coon project, rst and above all, becase there was no exact de nition o a coon project, in particlar there was no exact goal that the niversity shold l ll. In this scenario, it is natral to dedce that acadeic researchers wold be 31

32 work on projects closer to their own research interests, rather than to the interests o the r. In case o divergence o objectives between the two partners, we cold expect the otcoe o the cooperation wold be ore valable to the niversity than to the r. The reality con red those expectations. According to several coents both ro Berkeley University and ro otsiders, the arrangeent was a "terri c (good) deal or the niversity" (Robert Price, Berkeley s associate vice chancellor or research, in Lawler, 2003) and "a bad deal" or the copany (Lawrence Bsch, Michigan State University in East Lansing). Exaple 2, DPont and MIT Alliance, DMA: In 2000, the Aerican copany DPont and MIT established an agreeent in the areas o aterials, cheical and biological sciences. The initial agreeent o ve years involved an investent o $35 illion to develop new aterials and processes at bioelectronics, biosensors, bioietic aterials, and alternative energy sorces. The sccess o this rst interaction jsti ed its renewal in 2005 or additional ve years and to new areas as nanocoposites, nanoelectronic aterials, and alternative energy technologies. Two ain reasons or the sccess o sch collaboration were given: on the one hand, the proxiity o interests between the two partners (what in the odel is considered as a sall vale o the arginal loss i ); on the other hand, the working ethodology where both MIT aclty and DPont colleages de ne together research opportnities (a Consorti anageent, which as the odel shows axiizes the aggregate bene ts o the project). Exaple 3, Rolls-Royce and Psan National University (PNU): The power systes provider r Rolls-Royce established a research collaboration agreeent in Janary 2006 with PNU, to develop ltra-light weight heat exchangers. The goal is to, jointly, develop technologies that will be applied to Rolls-Royce s engines or the aviation, arine and energy sectors. The ost iportant headqarters o the joint research are the existing Rolls-Royce University Technology Centres (UTCs), and the r expects the activity o PNU to be aligned with the one at the UTCs (Rolls-Royce, 2006). In the langage o y raework, this corresponds to a decentralized governance, nder the initiative o the r. As expected, the prpose o the project is closer to the interests o the r. Nevertheless, the proxiity o interests o the two parties (sall i ), and a work ethodology based on teas ored by researchers ro both partners are key ingredients or the sccess o this project. Besides the insights on the anageent o collaboration between rs and niversities, the reasoning o y raework can also be applicable towards a better nderstanding o the internal organization o research in the Fir. When developing research in-hose, the 32

33 Fir recrits scientists specialized in the eld. Nevertheless, the ost qali ed scientists are oten not very otivated to work in private rs, where they ay ace restrictions on pblishing and di clties to prse their acadeic research paths (Aghion et al., 2005). An incentive echanis to involve these scientists in the projects o the Fir, ay then allow the to contine pblishing and se the Fir s research reslts (at least partially) or the developent o their own acadeic agenda. In the langage o the odel, this corresponds to a project whose characteristics are closer to acadeic scientists interests (higher x). As a reslt, the saller vale o the otcoe or the Fir (higher x iplies saller arket vale V F ), ay be copensated by an increase in the probability o sccess, de to a higher involveent o the scientists (higher e ). 6.2 Policy Iplications Fro the policy point o view, y analysis delivers soe iplications. First, in the presence o non-veri able resorces in the collaboration between rs and niversities, the negative ipact o the oral-hazard can be redced by giving a prize to the collaborative research. This is an optial strategy when the cost o pblic nds is sall as copared with the expected bene ts o the project. Second, as discssed, working in teas ay increase the onitoring o partners e ort. Policy easres prooting the interaction o researchers ro both instittions (or enhancing their obility between rs and niversities) ay then have a positive ipact on the expected gains o collaborative research. Third, the aggregate expected gain ro collaboration is axiized nder a centralized governance, rather than a decentralized one. Policy easres that give incentives to the orer have a clear bene t or society. 7 Conclsion This paper stdies how instittional di erences between bsiness and acadeia a ect the otcoe o their collaboration in research. Distinct research goals is a sorce o disagreeent on the type o project to be jointly developed. When the aont o resorces that one o the parties shall eploy is non-veri able, it ay be optial or the other party to agree on a research that is not its ost preerred type. The party with non-veri able resorces is willing to enhance its contribtion, when collaboration is on a project closer to its interests. The optiality o this incentive echanis is conditional on two reqisites. First, a s ciently high vale o a sccessl otcoe or the party eeling the externality e ect. Second, a relatively high iportance o the non-contractible e ort or the sccess. In coparative 33

34 statics ters, the odel predicts that when collaboration involves a ore scienti c-base r, the best joint project becoes closer to the ost preerred o the niversity. Conversely, when a niversity has ore applied interests, the optial research is less basic. In the presence o a oral-hazard proble ro at least one o the partners, incentives ay also coe by eans o onetary transers. Withot policy intervention, the collaborator with non-veri able e ort shold receive a share o the reward o the other party. This is the best option, when the non-veri able resorces are s ciently iportant or the sccess o the project. When the payent o transers between collaborators is not possible, a policy intervention ay be in the interest o society. A prize to the non-contractible involveent is welare iproving when the cost o pblic nds is not too large. Pblic intervention has two positive e ects or collaboration: it increases partners e ort, and it approaches the type o project to the rst-best. By increasing the expected bene t o collaboration, the intervention redces the negative ipact o a oral-hazard sitation. The bene ts ro basic research ay have a long-ter horizon. In y static odel, possible tre gains ro research are already taken into accont, when we interpret both arket and scienti c vales o a sccessl otcoe as the present vale o a strea o gains. An interesting extension o this analysis wold be to consider a dynaic raework with several periods o tie, and yopic partners interacting in each period o tie. I the type o project today in ences the otcoe toorrow, there wold be interteporal e ects probably not internalized by partners. The design o policy wold then be particlarly iportant or the achieveent o socially desirable reslt. The present paper ocs on incentives isses or a collaborative relation, that is already ored. Frther developents ay bring interesting insights or a previos stage, when partners select with who they will develop sch collaboration. Epirically, also soe work is still to be done. First, in ters o the predictions o the crrent odel. The general setting sed enables the discssion o the characteristics o the collaboration, in the presence o inorational probles between partners who have di erent interests. The direction o the predictions depends, however, on the vale o the paraeters. Data on speci c indstries and on the pro le o acadeics departents wold allow to concretize the reslts or particlar cases. Second, on the role that the type and reqency o interaction between partners ay have on the otcoe o the relationship. In act, the reslts o the present paper stress the role o the veri ability o the e orts in obtaining a higher expected gain. Following the basic ndaents o contract theory, veri ability (and hence, contractibility) o e orts is essential to garantee their enorceent, dring the period o interaction. In everyday s lie, however, enorceent o e orts ay also be related with the capacity o the parties to coit on that level o e orts. Under sch preises, a higher and ore reqent interaction between partners ay avor this coitent capacity, ths redcing the ipact o a oral-hazard proble. 34

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36 Hall, B. (2002): On Copyright and Patent Protection or Sotware and Databases: a Tale o Two WorldsGrandstand. Hall, B., A. Link, and J. Scott (2001): Barriers Inhibiting Indstry ro Partnering with Universities: Evidence ro the Advanced Technology Progra, Jornal o Technology Transer, 26, Holstro, B. (1982): Essays in Econoics and Manageent in Honor o Lars Wahlbeckchap. Managerial Incentive Probles. Swedish School o Econoics, Helsinki. Kaien, M., E. Mller, and I. Zang (1992): Research Joint Ventres and R and D Cartels, Aerican Econoic Review, 82(5), Katz, M. (1986): An Analysis o Cooperative Research and Developent, RAND Jornal o Econoics, 17(4), Lacetera, N. (2006): Di erent Missions and Coitent Power in RandD Organization: Theory and Evidence on Indstry-University Alliances, MIT Sloan Working Paper, Laont, J.-J., and J. Tirole (1993): A Theory o Incentives in Procreent and Reglation. The MIT Press, Cabridge, Massachsetts. Labert, R. (2003): Labert Review o Bsiness-University Collaboration, Final report, HM Treasry UK Governent, London, UK. Lawler, A. (2003): Last o the Big-Tie Spenders, Science Magazine, 299, Lee, Y. (2000): The Sstainability o University-Indstry Research Collaboration:an Epirical Assessent, Jornal o Technology Transer, 25, Macho-Stadler, I., and D. Perez-Castrillo (1993): Moral Hazard with Several Agents, International Jornal o Indstrial Organization, 11, Nowotny, H., P. Scott, and M. Gibbons (2003): Mode 2 Revisited, the New Prodction o Knowledge, Minerva, 41, OECD (2002): Frascati Manal. Proposed standards practice or srveys on research and experiental developent. OECD, Paris. Rolls-Royce (2006): Rolls-Royce signs a research collaboration agreeent with Psan National University, Press Release. Rosenberg, N. (1990): Why do Firs do Basic Research (With Their Own Money)?, Research Policy, 19,

37 (2003): Aerica s Entreprenerial Universities, in The Eergence o Entreprenership Policy, ed. by D. Hart. Cabridge University Press. Schartinger, D., A. Schibany, and H. Gassler (2001): Interactive Relations Between Universities and Firs: Epirical Evidence or Astria, Jornal o Technology Transer, 26, Siegel, D., D. Waldan, and A. Link (1999): Assesssing the Ipact o Organizational Practics on the prodctivity o University Technology Transer O ces: and Exploratory Stdy, NBER Working Paper, Spence, M. (1984): Cost Redction, Copetition, and Indstry Perorance, Econoetrica, 52(1), Vegelers, R., and B. Cassian (2005): Research and Developent Cooperation between Firs and Universities. Soe epirical evidence ro Belgian anactring, International Jornal o Indstrial Organization, 23, Zcker, L., and M. Darby (1995): Virtos Circles o Prodctivity, Star Bioscientists and the Instittional Transoration o Indstry, NBER Working Paper, Appendix Proo o Proposition 3.1. When the e orts o both collaborators are veri able, the Consorti decides over x, e ; and e in order to axiize the joint bene t o the research project, EW: The soltion or the e orts is: e = k c (V F + V U ) = k c [B + B ( ) x] ; e = 1 k c (V F + V U ) = 1 k c [B + B ( ) x] : These optial level o e orts ake EW a convex nction o x and, as a conseqence, the best joint project is at one o the extrees, 0 or 1. By >, the best choice is x = 0, the Fir s ost preerred project: This soltion yields an expected gain or each collaborator o: E F = (B + B ) c k 2 (B B + ) + 2c (1 k) 2 B 2c c ; E U = (B + B ) 2c k 2 (B ) + c (1 k) 2 (B B ) 37 2c c :

38 The Fir s participation constraint is satis ed when R U is s ciently high: E F E F;alone, R U c (B ) 2 2c B (B B + ) : That is, when the role o the University s e ort or the sccess o the project is s ciently iportant, the Fir preers to collaborate rather then to develop research alone. Conversely, the University s participation constraint is satis ed when: E U E U;alone, R F c B 2 + (2B ) 2c (B ) (B B + ) : Proo o Corollary When both e orts are veri able, the joint expected gain ro the collaboration is convex on x: As a reslt, the corner soltion that axiizes EW only depends on the relation between and : When > holds, the rst best choice is always x = 0; no atter how the paraeters o the odel change inside their doain. 2. When both e orts are veri able, the axi joint expected gain ro the collaboration is " # EW (0) = 1 k 2 (1 k)2 + (B + B ) : 2 c c Fro this, we can veriy (0) = k2 2c = = [k (c + c ) c ] (B + B ) 2 c c ; which is positive when k > (B + B ) < 0; (1 k)2 2c = 1 2 = 2 " k 2 + c c c + c ; (B + B ) < 0; " # k 2 (1 k)2 + c c # (1 k)2 c < 0: > 0; Proo o Proposition 3.2. separate. The proo is ade or each inorational context, in 38

39 Scenario 1: Only e is non-veri able. When the Consorti cannot contract on e, the University s best choice is given by: ax E U = [ke + (1 k) e ] V U C U : e g The soltion to this axiization proble is e AU = 1 k c V U = 1 k c (B + x) < e : Anticipating this decision, the Consorti axiizes the total collaboration gain by choosing: e = k c (V F + V U ) = k c [B + B ( ) x] ; x AU = c k 2 ( ) (B + B ) + c (1 k) 2 [( ) (B ) B ] c k 2 ( ) 2 c (1 k) 2 : (2 ) The best research projectin this context, x AU ; is positive (ore basic than in the rst-best) whenever B > 1 (B ) () M 0 > 1 and R U > ( )(B +B ) () R B ( )(B U > ( )(M 0 +1) : Frtherore, ) M 0 ( ) R U > ( )(M 0 +1) M 0 ( ) is also s cient or having EW AU concave on x; and thereore, the soltion is a axiizer o EW AU. Figre 7 represents the sitation. R U Region 1 AU : x AU > 0 x AU = 0 R U = ( )( M + ) M 0 ( ) 0 1 Figre 7: Consorti s optial project when e U is non-veri able, x AU : M 0 When R U < ( )(B +B ) (B ) ( )B ; we additionally have x AU saller than 1. This eans that, althogh the optial project is less applied than in the rst-best, it does not go to the 39

40 opposite extree. The University is iportant to ensre the sccess o the research, bt its contribtion is not s ciently strong to convince the Consorti to choose x = 1: With the soltion e ; eau ; x AU ; the collaborators reward is: E AU F = E AU U = [ B + (B )] 2 (1 k) 2 2c k2 c ( ) 2 (1 k) 2 c (2 ) 2 +2 (1 k) 4 c 2 ( ) (1 k) 2 k 2 c c ( 2 ) 2 ; [ B + (B )] 2 (1 k) 2 2c k2 c ( ) 2 (1 k) 2 c (2 ) 2 n (1 k) 2 c + k 2 2 o c 2 k 4 c 2 : 2k 4 c 2 ( ) + The Fir s participation constraint is satis ed when (1 k) 6 c 2 2 ( ) [R F + R U ] ( 2 ) 2 B k 2 c ( ) 2 (1 k) 2 c (2 ) 2 [ B + (B )] 2 : This eans that the Fir is ore willing to collaborate when k is saller (University s contribtion or the sccess is larger), and B is saller (the opportnity cost ro not developing its ost preerred project is not too large). Conversely, the individal rationality constraint o the University is satis ed when [R U + 1] 2 B k 2 c ( ) 2 (1 k) 2 c (2 ) 2 k 2 c [ B + (B )] 2 ; that is, or sall k (University s higher iportance or the sccess akes the choice ore avored to its own preerences), and or sall B (the opportnity cost ro not developing University s ost preerred project is not too large). Scenario 2: Only e is non-veri able. At the second-stage, Fir s optial choice is e AF = k c V F = k c (B x) : At the rst stage, the Consorti decides on University s e ort e = 1 k c (V F + V U ) = 1 k c [B + B ( ) x]. The joint expected gain becoes EW AF = k2 (1 k)2 V F (V F + 2V U ) + (V F + V U ) 2 : 2c 2c Depending on the vale o the paraeters, EW AF can either be convex or concave. The two possible sitations are: 40

41 1. i > 2 or R U > (2 ) ; EW AF is convex on x; and the best project chosen ( ) 2 by the Consorti can only be one o the extrees. At x = 0 and x = 1; we have, respectively, EW AF (0) = k2 (1 k)2 B [B + 2 (B )] + (B + B ) 2 2c 2c " # k 2 (1 k)2 = + (B + B ) 2 k 2 (B ) 2 ; 2c 2c 2c EW AF (1) = k2 (1 k)2 (B ) (B + 2B ) + (B + B ) 2 2c 2c " # k 2 (1 k)2 = + (B + B ) 2 k 2 B : 2c 2c 2c Given >, the best research project is x = i < 2 and R U < (2 ) ; EW AF is concave on x: The type o project ( ) 2 that axiizes EW AF is then x = ck2 [( )B + (B )]+c (1 k) 2 ( )(B +B ) ; which is negative and c (1 k) 2 ( ) 2 c k 2 (2 ) ot o the decision doain. Coparing EW AF (0) with EW AF (1), we conclde that the best option is x = 0: This eans that, whether EW AF is convex or concave on x; the optial project is always x = 0 (as long as > ). At x = 0; the expected gain o both parties is E AF F = k2 B 2c + (1 k)2 B (B ) c ; E AF U = k2 B (B ) c + (1 k)2 (B ) 2 2c : Since E AF F University willing to participate in the collaborative research project, it is necessary that > k2 B 2c ; the participation constraint o the Fir is satis ed. For having the E AF U > (1 k)2 B 2c, R U < 2(B ) (2B ) : Scenario 3: Both e and e are non-veri able. At the second stage o this doble oralhazard sitation, each partner chooses its ost preerred e ort: the Fir chooses e AUF = k c V F ; and the University e AUF = 1 k V U : Given >, the joint expected c 41

42 gain EW AUF is concave on the type o the project or R U > ( 2 ). In this range (2 ) o paraeters, the Consorti selects x AUF = 1 c k 2 ( 2 ) c (1 k) 2 (2 ) c k 2 [B ( ) + (B )] + c (1 k) 2 [( ) (B ) B ] : )M 0 + When R U > ( and M M 0 ( ) 0 > 1 (Region 1 AUF ), the project is ore basic than in the rst-best: x AUF > 0: Figre 8 presents this reslt. R U Region 1 AUF : x AUF > 0 x AUF = 0 R U = ( ) M 0 + M ( ) 0 Figre 8: Consorti s optial project nder doble oral-hazard. M 0 At x AUF ; the expected pro ts o the partners are: E AUF F = [ B + (B )] 2 k 2 c + (1 k) 2 c ( ) 2c c k2 c (2 ) + (1 k) 2 c ( 2 ) 2 2 (1 k) 4 c k4 c 2 (1 k) 2 k 2 c c ( ) ; E AUF U = [ B + (B )] 2 k 2 c ( ) + (1 k) 2 c 2c c k2 c (2 ) + (1 k) 2 c ( 2 ) 2 2k 4 c 2 + (1 k) 4 c 2 + (1 k) 2 k 2 c c ( ) : To have both participations constraints satis ed, we st have < R U < R R U ; where R solves E AUF U > (1 k)2 B 2c ; and R U solves E AUF F > k2 B 2c : 1. The best joint project nder doble oral-hazard is less basic than the one chosen 42

43 with only oral-hazard ro the University, since x AU x AUF = k 2 c (1 k) 2 c k 2 c ( ) k2 c (2 ) (1 k) 2 c (2 ) [ B + (B )] k2 c ( ) 2 (1 k) 2 c (2 ) : and, thereore, x AU x AUF > 0 in Region 1 AUF : Proo o Corollary 3.2. Fro the Consorti best choice when only University s e ort is non-veri able, the optial project or Region 1 AU is: x AU = c k 2 ( ) (B + B ) + c (1 k) 2 [( ) (B ) B ] c k 2 ( ) 2 c (1 k) 2 : (2 ) Fro this expression, we can derive how the interior soltion x AU changes with respect to the di erent paraeters: - x AU is increasing in = - x AU is decreasing in = c k 2 ( ) c (1 k) 2 c k 2 ( ) 2 c (1 k) 2 (2 ) > 0; [c k 2 +c (1 k) 2 ]( ) c k 2 ( ) 2 c (1 k) 2 (2 ) < 0; - x AU is decreasing = 2(1 k)kc c ( )[ B + (B )] hc k 2 ( ) 2 c (1 k) 2 (2 ) i 2 < 0; - x AU is increasing in = (1 k)2 k 2 c ( )[ B (B )] hc k 2 ( ) 2 c (1 k) 2 (2 ) i 2 > 0; - x AU is decreasing in = (1 k)2 k 2 c ( )[ B + (B )] hc k 2 ( ) 2 c (1 k) 2 (2 ) i 2 < 0; - x AU is decreasing in AU = hc k 2 ( ) 2 c (1 k) 2 (2 ) i 2 (1 k) 4 c 2 (2B + B ) k 4 c 2 ( ) 2 (B + B ) (1 k) 2 k 2 c c [ (3B + 2B 2 ) + (B ) 2 (B + B )]g < 0; 43

44 - x AU is increasing in = [c k 2 +c (1 k) 2 ] hc k 2 ( ) 2 c (1 k) 2 (2 ) i 2 c k 2 ( ) 2 (B + B ) + +c (1 k) 2 [2 B + (B + B ) ( + 2B )] > 0: Proo o Proposition 3.3. When the University receives a share t 2 (0; 1) o the arket vale, in case o a sccessl invention, the University s choice or its e ort is given by: ax E U = [ke + (1 k) e ] (t V F + V U ) C U : e g Fro this, we obtain the optial soltion e AUT 2 e AU ; e ; with e AUT = 1 k c (t V F + V U ) = 1 k c (t B + B (t ) x) : Taking into accont the University s behavior, the soltion to the Consorti s axiization proble coes: e = k c (V F + V U ) = k c [B + B ( ) x] ; x AUT = 1 c k 2 ( ) 2 c (1 k) 2 ( t ) [(2 t ) ] c k 2 ( ) (B + B ) + +c (1 k) 2 [( ) (B ) ( t (2 t )) B ] : The expected gain to the Fir is then E AUT F = [ B + (B )] 2 (1 k) 2 2c k2 c ( ) 2 (1 k) 2 c (2 ) 2 2k 4 c 2 ( ) ( t ) + +2 (1 k) 4 c 2 ( ) ( t ) (1 k) 2 k 2 c c [(1 + t ) 2 ] 2 : The Fir is willing to collaborate when E AUT F q At t = 1 1 q t 2 0; 1 1 is at least eqal to k2 B 2c : ; this restriction is still not satis ed and, thereore, : Considering this interval or t ; the best joint project is still less applied than in the rst best, x AUT > 0; when ( )(B +B ) R U > () R ( )(M 0 +1) [ (2 t )t ]B ( )(B U > and ) [ (2 t )t ]M 0 ( ) 44

45 B > ( )(B ) () M (2 t 0 > : The rst condition ephasizes the iportance o e or the sccess o the project, whereas the second condition relates with the vale )t (2 t )t that a sccess has or the Fir (hence, to the Consorti). For these range o paraeters, the joint expected gain EW AUT is concave on x; garanteeing that x AUT is actally a axiizer or EW: In act, the condition or a concave EW AUT is R U > satis ed whenever x AUT > 0; becase ( ) 2 ( t ) [(2 t ) ] ; ( ) (B + B ) [ (2 t ) t ] B ( ) (B ) For t 2 0; 1 q 1 rst-best. This happens when: ( ) 2 ( t ) [(2 t ) ] > 0:, the selected collaborative project can still be eqal to the i) EW AUT is concave, bt we are in Region 2 AUT. In this case, we atoatically have x AUT < 0; and thereore the best possible project is x = 0; ii) EW AUT is convex, bt EW AUT (0) > EW AUT (1), which happens when the Fir s contribtion or the sccess o the project is relatively ore relevant than the University s: R F > (2B ) + 2 (B B ) t (2B ) (2 t ) : The proo that x AUT < x AU or Region 1 AUT < 0; = (1 k)2 c (D T ) 2 2 (1 t ) v (B D T + v N T ) where D T (=denoinator o x AUT ) < 0; and N T (=nerator o x AUT ) < 0: Figre 9 bellow shows Consorti s optial project when e is non-veri able, both with transer t (sitation AUT ) and withot transer (sitation AU). As told in the ain text, Region 1 AUT Region 1 AU. 45

46 R U Region 1 AUT : x AU x > AUT > 0 ( 2 t ) t x AU x = AUT = 0 AU x > 0, ( )( M ) R U = AUT [ x = 0 (2t ) t ] M0 ( ) R U ( )( M + ) = M 0 ( ) 0 1 ( 2 t ) t Figre 9: Consorti s optial project when e U is non-veri able. With transer t : x AUT ; withot transer: x AU : M 0 Proo o Proposition 3.4. When the Fir governs the collaboration and the University s e ort is veri able, the design o the contract coes ro the ollowing optiization proble: ax E F = [ke + (1 k) e ] V F C F ; x;e ;e g ( E s.t. U = [ke + (1 k) e ] V U C U (1 k)2 B 2 2c ; 0 x 1: The rst-order conditions or this constrained axiization are: e = k c (V F + 1 V U ) ; (16) e = 1 k (V F + c 1 V U ) ; (17) [ke + (1 k) e ] ( 1 ) = 3 2 ; (18) 1 = 0 or E U = (1 k)2 B 2 ; 2c (19) 2 = 0 or x = 0; (20) 3 = 0 or x = 1; (21) i > 0; i = 1; 2; 3: (22) where i are the Lagrangian ltipliers o the constraints. 46

47 Searching or the soltions o this proble that are relevant or the proo o the proposition, several cases are possible: case 1. 0 < x < 1 : Fro conditions (20) and (21), 2 = 3 = 0: Replacing in (18), it coes 1 = > 0: Conditions (16) and (17) then state the optial vale or the e orts levels: e = k B + B ; c e = 1 k B + B : c By condition (19): 1 > 0; which eans that the participation constraint o the University is biding: E U = (1 k)2 B 2 2c : The sbstittion o the soltions or e and e in this sitation gives the optial type o project: x = 1 2 k2 c + (1 k) 2 c [ (B ) + B ] (1 k) 2 c 2 2 (2B ) + B 2 2k 2 c 2 (B ) [ (B ) + B ] : when k 2 c > (1 k) 2 c 2 [ 2 (2B )+B2 ] 2 2 (B )[ (B )+ B ] that is, paraeters are in Region 1P U; this soltion is negative x < 0 which is ot o the doain o x: In Region 2P U, x > 0 and the only concern is to copare this vale o x with 1 (the pper bond in the doain o x). In any case, in Region 2P U, 0 < x 1: case 2. x = 0 : Fro condition (21): 3 = 0. Replacing in condition (18), it coes Two alternatives then appear: alternative 1. E U > (1 [ke + (1 k) e ] ( 1 ) = 2 : (23) k)2 B 2 2c : In this alternative, by condition (19), 1 = 0: Bt then, (17) gives e = 1, which is ipossible. alternative 2. E U = (1 k)2 B 2 2c : 47

48 Fro this participation constraint, it is possible to obtain an expression o e as a nction o e : q e = (1 k) (B ) + 2kc (B ) e (1 k) 2 (2B ) : c Replacing this expression in E F (e ; x = 0) and axiizing in order to e, we obtain the optial level o Fir s e ort. Proo o Proposition 3.5. Under University s oral-hazard and Fir s governance, at the second stage, the University chooses its level o involveent in the collaboration, by solving: ax E U = pv U C U : e g The optial rle is e = 1 k c V U = 1 k c (B + x) : Anticipating this behavior, when the Fir prposes the collaboration, it chooses the project and its level o e ort according to ax E F = [ke + (1 k) e ] V F C F : x;e g Fro what we obtain: e = k c V F = k c (B x). When R U > 2, E F nction o x, and its axi given by: is a concave x F = c k 2 B + c (1 k) 2 [ (B ) B ] k2 c 2 (1 k) 2 c : x F > 0 or M 0 > and R U > Region 1 F G : B () M 0 B (B ) ; that is, or paraeters in M 0 Since M 0 M 0 > 2 ; the condition R U > M 0 M 0 is s cient to ensre concavity. Proo o Proposition 3.6. Under Fir s oral-hazard and University s governance, at the second stage, the Fir chooses its level o involveent in the collaboration, by solving: ax E F = pv F C F : e g The optial rle is e = k c V F = k c (B x) : 48

49 Anticipating this behavior, when the University prposes the collaboration, it chooses the project and its level o e ort according to ax E U = [ke + (1 k) e ] V U C U : x;e g Fro what we obtain: e = 1 k c V U = 1 k c (B + x). For R F > 2, E U concave nction o x, and its axi given by: is a x U < 1 or x U = c k 2 [ (B ) B ] c (1 k) 2 (B ) c (1 k) 2 2c k 2 : B B > or paraeters in Region 1 UG : () S 1 > k and 2 c > S (1 k) 2 1 c S 1 () R F > S 1 S 1 ; that is, Since B > B (B ) 2 ; the condition R F > concavity. B B (B ) is s cient to ensre Proo o Corollary 3.3. Fro Proposition 3.2, 0 < x AUF < x AU in Region 1 AUF : Since Region 1 F G Region 1 AUF, then it trivially coes that 0 < x AUF < x AU in Region 1 F G : Frtherore, in Region 1 F G it also holds that x F x AUF < 0; since 2! 3 x F x AUF = [ B + (B )] 4 k2 (1 k) 2 2 (1 k)2 k : c c c c Proo o Proposition 4.1. Ater observing the Social Planner s choice o the prize and the Consorti s choice o the type o project, the partner with non-veri able e ort decides on its level o e ort. By backward indction, we obtain the eqilibri soltion. Regarding the non-veri ability o e orts, we ay have three di erent scenarios. The analysis, below, regards each o these scenarios. Scenario 1. Only the e ort o the University is non-veri able. At the last stage, the University s proble ax e g E U = [ke + (1 k) e ] [V U + (1 ) z] C U ; has the soltion e = (1 k) c [V U + (1 ) z]. 49

50 At the previos stage, axiizing the joint expected gain, EW, the Consorti best options are e = k c [V F + V U + z] and x AU 1 = c k 2 ( ) 2 c (1 k) 2 (2 ) c k 2 ( ) (B + B + z) + +c (1 k) 2 [( ) (B ) B z ( (1 ))] : When M 0 > 1 and R U > ( )(M 0 +1) M 0 ( ) ; we have xau (z = 0) > 0: This eans that, withot the prize, the Consorti chooses a less applied project than in the rstbest, as an incentive echanis or the University s involveent in the collaboration. Anticipating Consorti s reaction, the Social Planner s objective nction becoes ES = (1 k) 2 (1 k) 2 c + k 2 c DF 2c c k 2 ( ) 2 c (1 k) 2 (2 ) ; where D = (z + B )+ [(1 ) z + B ] > 0; and F = D+2z (1 + ) : On a second-order condition or z at the ax ES, we z = < 0; where (1 k) 2 (1 k) 2 c + k 2 c c c k 2 ( ) 2 c (1 k) 2 (2 ) [(1 ) + ] [ (2 + 2) (1 )] : Since c k 2 ( ) 2 c (1 k) 2 (2 ) < 0 when x AU (z = 0) > 0; the previos axiizing condition is satis ed or (2 + 2) (1 ) > 0: Fro the rst-order condition or z; = 0 () zau = [(1 ) (1 + ) ] [ B + (B )] ; [(1 ) + ] [ (2 + 2) (1 )] which is strictly positive or (1 ) (1 + ) > 0 () () < (1 ) 1 : Considering the optial or having the = (1 k) 2 z (1 k) 2 c + k 2 c ( ) G c c k 2 ( ) 2 c (1 k) 2 (2 ) ; where G = D z (1 + ) ; with G > 0 or < (1 ) 1 Since c k 2 ( ) 2 c (1 k) 2 (2 ) < 0 when x AU (z = 0) > 0; this rst derivative is always negative, that is, ES is decreasing on : The soltion or is, then, at the corner = 0: This eans that all the prize : 50

51 z AU = [ (1+) ][ B + (B )] ; positive or [2 (1+) ] 2 1 < < given to the University. As a conseqence, the social bene t is: 1, shold be ES AU = (1 k) 2 (1 k) 2 c + k 2 c [ B + (B )] 2 H 8 (1 + ) 2 c c k 2 ( ) 2 c (1 k) 2 (2 ) ; where H = + (1 + ) (2 3)+2 (1 + ) 2 : Frtherore, the best project is ore applied with a prize than withot it, since x AU = 0; z AU < x AU (z = 0) : Scenario 2. Only the e ort o the Fir is non-veri able. At the last stage, the Fir s proble has the soltion e AF ax E F = [ke + (1 k) e ] (V F + z) C F ; e g = k c (V F + z). At the previos stage, axiizing the joint expected gain, EW, the Consorti best options are e = 1 k c (V F + V U + z) and x AF = 0: Anticipating Consorti s reaction, the Social Planner s objective nction becoes ES = k2 B (B + z) c 2 + B + z + 2 (1 k)2 B + B + (B + B + z) + 1 z : c 2 2 Fro the rst-order condition = 0 () zaf = (1 k)2 c (B + B ) + k 2 c [ (B ) B ] (1 + 2) (1 k) 2 c + ( + 2) k 2 c : The rst-order condition to have an interior soltion o that axiizes = 0 () k2 z 2 [B z ( + )] c = 0: Sbstitting z by the previos expression o z AF ; we obtain that either z AF = 0; or AF = 2 k 2 c B + (1 k) 2 c (1 + ) 2 (B ) + 2 B (B + B ) (1 k) 2 c + k 2 c < 0: Since AF soltions: < 0 is ot o the doain or ; we copare the three possible extree 51

52 i) or AF = 0; the rst-order condition or z gives z AF = (1 k) 2 c (B + B ) + k 2 c B (1 + 2) (1 k) 2 c < 0: ii) Since, by doain z AF 0; the closest soltion to be considered is z AF = 0: or AF = 1; the rst-order condition or z gives z AF 1 = (1 k)2 c (B + B ) + k 2 c (B B ) (1 + 2) (1 k) 2 c + k 2 c : When < B B and R U < B B B +B ; z AF > 0: In this case, the expected social gain ro collaboration is where ES x = 0; AF = 1; z1 AF = H 2 (1 + 2) c c (1 k) 2 c + k 2 c ; H = (1 k) 4 c 2 (1 + ) 2 (B + B ) 2 + +k 4 c 2 [B + (1 + ) B ] (1 k) 2 k 2 c c (B ) (1 + ) B [(1 + ) B + 2 (2 + ) (B )]] : iii) or z AF = 0; the expected social gain ro collaboration is ES x = 0; z AF = 0 = 1 2c c k 2 c B (B B ) (1 k) 2 c (B + B ) : Coparing ES x = 0; AF = 1; z1 AF with ES x = 0; z AF = 0 ; we obtain that the orer is socially preerred. In rese, when the Fir s e ort in the collaborative project is non-veri able, the best social soltion is to choose the ost possible applied research x AF = 0: When the cost o pblic nds is s ciently sall < 1M0 and the Fir s e ort is relatively iportant or the sccess o the project R U > M M 0 ; a prize z1 AF = (1 k)2 c (B +B )+k 2 c (B B ) (1+2)[(1 k) 2 c +k 2 c ] 0 shold be given. In this case, however, only the Fir s participation shold receive the extra-reward AF = 1 : Scenario 3. Both e orts o the University and o the Fir are non-veri able. 52

53 At the last stage, ro the individal axiization proble o each partner, we obtain the aont o resorces that they are willing to allocate or the joint project: e AUF = (1 k) c [V U + (1 ) z] ; e AUF = k c (V F + z) : Anticipating these choices, at the previos stage, the Consorti best option to axiize the joint expected gain, EW, is x AUF = 1 c k 2 (2 ) + c (1 k) 2 (2 ) c k 2 [( ) B + (B ) + z ( )] + +c (1 k) 2 [ B ( ) (B ) + z ( (1 ))] : When M 0 > 1 and R U > ( )M 0 + M 0 ( ) ; we have xauf (z = 0) > 0: This eans that, withot prize, given the iportance o the University or the joint project, the Consorti preers to choose a project closer to the acadeics interests. Thereore, the chosen project is less applied than in the rst-best. By backward indction, at the rst stage, the Social Planner s objective nction becoes ES = (1 k) 2 k 2 DI 2 c k 2 (2 ) + c (1 k) 2 (2 ) ; where D = (z + B ) + [(1 ) z + B ] and I = D + R U [z (2 + 2) D] + 1 R U [2z ( + ) D] : Fro the second-order conditions o ax ES; with respect to 2 2 z < 0 () () (1 k) 2 k 2 [(1 ) + ] J c k 2 (2 ) + c (1 k) 2 (2 ) < 0; where J = (1 ) + 1 R U [( ) ] + + R U [(2 + 2) (1 ) ] : When x AUF (z = 0) > 0; we have c k 2 (2 ) + c (1 k) 2 (2 ) > 0, and thereore, the previos condition is satis ed or J > 0: Fro the rst-order condition o ax ES; with respect = 0 () zauf = [ B + (B )] L ; [(1 ) + ] J 53

54 where L = (1 ) + 1 R U [( + ) ] + +R U [(1 + ) (1 ) ] : Given that J > 0; a positive soltion or z AUF exists whenever L > 0: Since the second derivative o ES with respect to is given 2 2 = z2 (1 k) 2 k 2 c c + k 4 c 2 + (1 k) 4 c 2 ( ) 2 c c c k 2 (2 ) + c (1 k) 2 (2 ) > 0; ES is non-concave with respect to : As a conseqence, the optial vale or st be at one o the corners, = 0 or = 1: The best social choice with respect to z and is given by the coparison o ES nder the three possible alternatives: i) at AUF = 0; the rst-order condition or z gives z0 AUF = [B + (B )]L 0 ; [(1 ) + ]J 0 where L 0 corresponds to the vale o L when = 0; and J 0 to the vale o J when = 0: With sch vales or z and ; the expected social gain ro collaboration is (1 + ) 2 k 4 c 2 ES0 AUF AUF = 0; z0 AUF + (1 k) 4 c 2 = 2c 2 c2 (1 k) 2 k 2 [ B + (B )] 2 c k 2 (2 ) + c (1 k) 2 (2 ) ; J 0 2 ii) at AUF = 1; the rst-order condition or z gives z1 AUF = [B + (B )]L 1 ; [(1 ) + ]J 1 where L 1 corresponds to the vale o L when = 1; and J 1 to the vale o J when = 1: With sch vales or z and ; the expected social gain ro collaboration is (1 + ) 2 k 4 c 2 ES1 AUF AUF = 1; z1 AUF + (1 k) 4 c 2 = 2c 2 c2 (1 k) 2 k1 2 [ B + (B )] 2 c k 2 (2 ) + c (1 k) 2 (2 ) J ; 2 iii) at z AUF = 0, the expected social gain ro collaboration is ES AUF z AUF = 0 = h i (1 k) 2 k 2 c c [ B + (B )] R U + R U 2 c k 2 (2 ) + c (1 k) 2 (2 ) : Then, the social best choice nder non-veri ability o e ort ro both partners is: 54

55 - to give a positive prize z0 AUF only to the University AUF = 0 when < and R U 2 R U ; R ~ 0 ; where R 0 is the ini vale o R U that satis es both conditions R U 1 (1 + 2) > (24) R U and R U 1 (1 + ) + 1 > 1 ; (25) R U and R ~ 0 is the axi vale o R U that still satis es R U 1 2 (1 + ) + 1 < 1 (1 + 2) : (26) R U R 0 garantees that the relative iportance o the University is s ciently high, so that its e ort or the collaboration receives a prize (positive vale o z): ~ R0 creates an pper bondary or R U ; above which the existence o a prize or the University has an ipact in the cost o its e ort greater than the ipact on the expected revene. As a conseqence, below R 0 the best is to sbsidize the Fir, whereas above ~ R 0 the best is to settle z = 0: - to give a positive prize z1 AUF only to the Fir AUF = 1 when > and R F 2 that satis es both conditions R F (1 + 2) R F and R 1 ; ~ R 1 ; where R 1 is the ini vale o R F > 1 + (27) R F 2 (1 + ) (1 + 2) > 1; (28) R F and R ~ 1 is the axi vale o R F that still satis es R F (1 + ) < 1: (29) R F R 1 garantees that the relative iportance o the Fir is s ciently high so that its collaboration receives a prize with a positive vale o z: ~ R1 creates an pper bondary or R F ; above which the existence o a prize or the Fir has an ipact in the cost o its e ort greater than the ipact on the expected revene. 55

56 Proo o Proposition 5.1. Coparing conditions (13) and (11), i > 0; it becoes clear that the Consorti distorts its choice or the project towards the preerences o party i; whenever the external e ect cased by e i ; i ; e ) V j over p (e ; e F U when only ei is non-veri able; or over p (e ; e F U + j ; e ) V i (x) ; when both e i and e j are non-veri able. When only e i is non-contractible, coparing conditions (12) and (10), we easily conclde that: when e orts are copleentaries, i s reaction nction e i (e j ) is sch j this case, the Consorti chooses a higher e j than in rst-best; < 0, Consor- when e orts are sbstittes, i s reaction nction e i (e j ) is sch j ti chooses a saller e j than in rst-best; > 0: In = 0, Con- when e orts are independents, i s reaction nction e i (e j ) is sch j sorti chooses the sae e j as in rst-best. Proo o Proposition 5.2. Coparing conditions (15) to (11), non-contractability o e i creates an external e ect, on j 0 s decision on the type o project. In this sitation, the governing party j is willing to distort its ost-preerred project towards i s interests, whenever the external i ; e ) V j (x) doinates over p (e ; e j : Nevertheless, conditions (15) and (13), it is visible that de to p (e ; e < p (e ; e F U, a decentralized governance always distorts less its rst-best project than a Consorti does. 56