UNIVERSITÀ DEGLI STUDI DI PADOVA. Dipartimento di Scienze Economiche Marco Fanno

Transcription

1 UNIVERSITÀ DEGLI STUDI DI PADOVA Dipatimento di Scienze Economiche Maco Fanno DUAL LICENSING IN OPEN SOURCE SOFTWARE MARKETS STEFANO COMINO Univesity of Udine FABIO M. MANENTI Univesity of Padova Januay 2010 MARCO FANNO WORKING PAPER N.112

2 Dual Licensing in Open Souce Softwae Makets Stefano Comino Fabio M. Manenti Januay 2010 Abstact In this pape we pesent a theoetical model to study the chaacteistics and the commecial sustainability of dual licensing, an open souce (OS) business stategy that has gained populaity among softwae vendos. With dual licensing, a fim eleases the same softwae poduct unde both a taditional popietay license and an open souce one. We show that the decision to employ a dual licensing stategy occus wheneve the feedbacks of the open souce community ae valuable enough compaed to the quality of the softwae that the fim is able to develop in-house. Ou analysis points to the cental ole of an appopiate managing of OS licenses in ode to balance the pos and cons of going open souce and to make this vesioning stategy viable fo softwae vendos; ou analysis also suggests a possible explanation fo the obseved polifeation of open souce licenses. J.E.L. codes: L11, L17, L86, D45. Keywods: open souce softwae, open souce business models, embedded softwae, dual licensing, vesioning, license polifeation. Much of this wok has been conducted while the authos wee visiting the School of Infomation of the Univesity of Califonia at Bekeley. We ae extemely gateful to Hal Vaian fo his hospitality. Financial suppot fom Pogetto di Ateneo - Padova, Pape pesented at the 2 nd FLOSS intenational wokshop on Fee/Libe open souce softwae - Rennes 2008, at the 3 d annual confeence of the EPIP association - Ben, 2008, and at the 36 th annual confeence of the EARIE - Ljubjana, The authos ae gateful to Mak Schankeman, Laua Vici and Macus Wagne fo helpful suggestions and comments on ealie vesions of the pape. Coesponding autho: Dipatimento di Scienze Economiche, Univesità di Udine, Via Tomadini 30/A, UDINE (Italy), Tel. (39) , Fax. (39) , stefano.comino@uniud.it Dipatimento di Scienze Economiche M. Fanno, Univesità di Padova, Via del Santo 33, PADOVA (Italy), fabio.manenti@unipd.it

3 1 Intoduction Until ecently, open souce (OS) has been seen unfamilia by the business community and, in many cases, it has been peceived as a eal theat by commecial vendos. In the vey last yeas, things have changed substantially and both lage established incumbents such as IBM, HP o NEC as well as stat-ups ae inceasingly embacing OS stategies. Commecial fims may enjoy seveal benefits by going open souce. A fim may take advantage of the contibutions of the community of OS developes eithe in the diect fom of code enhancements o in tems of educated feedbacks and eviews eceived fom expet uses. 1 Futhemoe, open souce epesents a poweful channel of softwae distibution: it may constitute a key stategic instument to impove the peceived quality of the poduct and to enlage the installed base of uses, thus helping fims in establishing an industy standad. The key issue fo a softwae vendo is how to design a sustainable business model based on open souce solutions, povided that vaious featues of OS softwae development and distibution seem to be unappopiate fo commecial exploitation. 2 In a ecent study based on 218 companies that wee collecting at least 25% of thei evenues, diectly o indiectly, fom open souce, Daffaa (2009) obseves that the most common OS business stategies fall into two main categoies. The sale of sevices that ae complementay to the open souce softwae, such as customization, consulting, taining and documentation, constitutes the fist, and pobably the most common, categoy of OS business stategies. 3 The sec- 1 It deseves to be noticed that non-code contibutions fom the OS community ae as impotant as code contibutions. Fo instance, Jullien (2006), in a study on the Open Cascade poject, epots that: bug-fixing, pepaation of documentation o tutoials and othe contibutions not diectly linked with code witing epesented the 20% of the value of the softwae. Simila findings, fo othe OS pojects, ae in Seigo (2006) and in Muelle (2007). 2 Fo instance, OS licenses equie the code of the softwae to be feely e-distibutable; when eleasing the softwae code, an individual, o the fim cannot pevent o estict (e.g. by equiing oyalties) its e-distibution (see aticle 1 of the Open Souce definition 3 Just to take a elevant example, in 2001, IBM stated the open souce poject Eclipse in ode to pomote the use of the pogamming language Java within seve poducts; IBM pofited fom selling elated poducts such as components of WebSphee and WebLogic (West and Gallaghe, 2004). Altenatively, softwae vendos often offe deployment suppot, customization and adds-on poducts fo OS solutions; see Rajala et al. (2007) fo a compehensive discussion of the well-known Red Hat case. 2

4 ond most significant categoy is elated to vesioning stategies. In many cases, fims offe diffeent vesions of the softwae and pofit fom selling upgaded packages poviding additional functionalities with espect to the open souce vesion of the softwae. Within this second categoy, a business stategy which is peculia to the softwae industy and that it is becoming inceasingly popula among commecial vendos is dual licensing. 4 With dual licensing fims mix taditional and OS-based stategies by offeing the same softwae poduct unde both a taditional popietay license and an open souce one; in the latte case, the softwae is typically povided fo fee o at a nominal fee. Thee ae vaious easons why customes, when offeed a fee OS vesion of a softwae, may still pefe to pay fo the popietay vesion; cetainly, one of the most impotant eason accues fom the ecipocal povision imposed by some OS licenses: open souce customes ae equied to edistibute thei deived woks unde the same licensing scheme as the oiginal softwae, including the equiement to make the souce code of the deived softwae publicly available. 5 To bette gasp this citical issue, it is useful to quote Oacle, the vendo of the embedded database BekeleyDB; in its web page, Oacle descibes its dual licensing stategy as follows: 6 Ou open souce license pemits you to use Bekeley DB [... ] at no chage unde the condition that if you use the softwae in an application you edistibute, the complete souce code fo you application must be available and feely edistibutable unde easonable conditions. If you do not want to elease the souce code fo you application, you may puchase a license fom Oacle. Commecial customes that use, modify and embed Bekeley DB into thei own appli- 4 Aound 10% of the companies in Daffaa s sample wee employing dual licensing. Some notable examples of softwae packages eleased accoding to this commecial stategy ae MySQL, Bekeley DB, Qt, and Asteisk. See Välimäki (2005) and Moody (2006) fo a discussion of these and of othe cases. 5 Oacle suggests that beyond elieving fom the ecipocal povision, thee ae additional benefits of adopting the popietay vesion: in the desciption of its dual licensing stategy, Oacle agues that the popietay vesion of the softwae includes legal assuances, waanties, and a wide aay technical and aftesale sevices povided by a full-time dedicated development team. Futhemoe, many OS softwae pojects ae distibuted unde licenses that allow the licenso to teminate the ageement conditional on the occuence of specific events, and this clealy puts the custome to a isk in case she/he needs to invest money and effot in using the softwae (see Rosen, 2004 fo a discussion of the so-called patent temination clauses ). 6 See 3

5 cations might be eluctant to use the OS vesion. These applications may be poducts pe se o, moe fequently, they ae pat of a moe complex system that customes poduce and sell. In both instances, it is clea that since customes want to keep popietay contol on thei deived poducts, they may be willing to pay in ode to be elieved fom the ecipocal povision imposed by the open souce vesion. The softwae vendo benefits fom eleasing fo fee the open souce vesion thanks to the contibutions of OS adoptes. These contibutions, eithe code o non-code, ae then incopoated into the popietay vesion and this helps to amelioate poduct s quality. 7 It deseves to be noticed that typically the softwae vendo keeps stong contol on the open souce poject and maintains the possibility of e-using code contibutions by equiing extenal pogammes to gant the pemission to incopoate the lines of code that they have witten into the popietay vesion. 8 As agued in the pape, the licensing tems of the open souce vesion of the softwae ae pivotal in the commecial sustainability of a dual licensing stategy. On the one side, a estictive license, e.g. a license that imposes the ecipocal povision, epesents an impotant safeguad against the possible cannibalization of the popietay vesion of the softwae since it discouages some potential customes fom adopting the open souce vesion. 9 7 Sun Micosystems, the poduce of MySQL descibes its dual licensing stategy as follows: We have ove 4 thousand paying customes who have chosen the commecially-licensed MySQL seve, and we have ove 4 million uses who use MySQL unde the GNU Geneal Public License (GPL). [...] Thanks to ou commecial customes, we can affod to develop and impove the poduct at a fast pace. [...] And thanks to the huge use community, MySQL undegoes igoous battle-testing ; see 8 Fo instance Digium, the poduce of the telecommunications softwae Asteisk, equies OS contibutos to sign the Digium open souce poject submission ageement ; accoding to this ageement, contibutos...gant Digium a pepetual, woldwide, oyalty-fee, ievocable, non-exclusive, and tansfeable license to use, epoduce, pepae deivative woks of, publicly display, publicly pefom, distibute the Submissions, and to sublicense such ights to othes. On The ights ganted may be execised in any fom o fomat, and Digium may distibute and sublicense to othes on any licensing tems... license ageement.php). In othe cases, the vendo ewites and eassembles the lines of code witten by OS pogammes and then includes them in the popietay vesion of the softwae. As obseved by Välimäki (2005), in MySQL AB poject All contibutions ae checked and ewitten by company developes... (p. 212). 9 Note that once the code has been eleased to the OS community, cannibalization may take the fom of the so called foking: OS pogammes might download the code and stat independent development on it. (see 4

6 the othe side, the licensing tems affect also the size of the OS community, as well as the incentives that OS pogammes have in contibuting to the softwae poject. As documented in many empiical studies, the tems of distibution of an OS poject ae an impotant deteminant of its oveall pogess; Comino, Manenti and Paisi (2007) have shown that OS pojects eleased accoding to a moe estictive license ae less likely to succeed. Othes have shown that moe estictive licensing tems negatively affect the contibution (aveage lines of code witten) of the membes of the OS community (see and Feshtman and Gandal, 2007). Moe specifically, in this pape we conside a pofit maximizing fim that is developing a softwae poject tageted to commecial customes. The fim eithe develops the poject completely in-house o it employs a dual licensing stategy. In this latte case, it is cucial to manage appopiately the open souce license in ode to balance pos (the contibutions of the OS community) and cons (the isk of cannibalizing the popietay package) of going OS. Assuming that customes have heteogenous pefeences towads the estictions imposed by the OS license, we deive the conditions unde which dual licensing is pofitable. Moeove, we discuss how an appopiate definition of the licensing tems allows the fim to optimally segment its potential customes into two goups: those who adopt the OS vesion, and that contibute to enhance the softwae quality, and those that pay fo the popietay vesion. Ou pape is elated to vaious stands of economic liteatue. As this intoduction should have made evident, dual licensing epesents an example of vesioning; many authos have shown that vesioning may be a pofitable stategy when it allows the fim to enlage its maket shae and to sell also to customes with low quality evaluation (Shapio and Vaian, 1998; Belleflamme, 2005). Moeove, a bulk of papes has shown that, when the maket is affected by consumption extenalities, a fim may benefit fom ceating a competito in ode to expand the installed base of uses. Economides (1996) and Gaye and Shy (2003) ae two elevant examples of this liteatue; the fome shows that a monopolist may pofit fom inviting enty of a compatible ival, while the latte found that a softwae develope may benefit fom allowing piacy activity. In this pape, we show that vesioning, with the annexed ceation of a competito, might be pofitable also in the absence of any maket To pevent this isk, the fim must maintain a stong leadeship in the management of the poject. In the theoetical model, we do not account explicitly fo the isk of foking. 5

7 enlagement effect and without the possibility to exploit the benefit of geate consumption extenalities. In a context whee customes ae expet uses who ae also able to povide a significant contibution to the quality of the poduct, the benefits of eleasing an open souce vesion of the softwae accue to development extenalities. In this wold chaacteized by OS adoptes that become pat of the poduction pocess, the bette quality of the softwae achieved thanks to the effots of the OS community goes to the advantage of all customes, those who puchase the popietay vesion as well as those who adopt the open souce one. The theoetical liteatue on the economics of open souce has been focussed mainly on modeling competition between open souce and popietay softwae; little has been done to achieve a bette undestanding of the ationales fo commecial vendos to go open souce (see Lanzi, 2009 fo a ecent eview). An exception, close to ou pape, is epesented by Mustonen (2005); the autho models a fim s decision to suppot an existing open souce community that is developing a ival pogam. The autho shows that the fim may find it optimal to sustain OS when this pomotes compatibility between the OS and the popietay vesions of the softwae, and when the OS community povides a sufficiently valuable development extenality. Mustonens s development extenality diffes substantially fom ous. In Mustonen (2005) the stength of the extenality is exogenous, while in ou setting it is endogenously detemined and popotional to the size of the open souce community. Moe impotantly, in Mustonen (2005), the development extenality is elevant only in elation to the existence of the OS altenative, which exists independently of what the fim does; on the contay, if athe than suppoting an existing poject, it would be the fim that ceates the OS poject, as in ou model, then Mustonen s development extenality would not have any impact on fims behavio. The est of the pape is oganized as follows: in Section 2 we pesent the model and we deive the main esults, while in Section 3 we conclude. 2 The model Conside a commecial fim that has stated developing a new poject fo an embedded softwae. The softwae is diected to commecial customes who then need to spend some time and effot in ode to embed and tailo it to thei own poducts; in doing so, they impove the oiginal softwae by adding new functionalities o by simply fixing possible 6

8 bugs. The fim faces an altenative in developing and distibuting the softwae. It can eithe complete the poject in-house, and then sell the softwae. Altenatively, it can endose a dual licensing stategy in ode to involve customes in the development of the poject, thus impoving the quality of the softwae. 10 In this case, the fim makes the open souce vesion of the softwae available at no fee by posting it on a public epositoy, and benefits fom the new functionalities and fom the bug-fixing activity of those customes who adopt it (i.e. it benefits fom the contibutions of the open souce community). At the same time, the fim pofits fom selling at a positive pice a second vesion of the softwae which is distibuted unde popietay licensing tems. In what follows, we will efe to these two vesions of the softwae as the open souce and the popietay vesion espectively. Fomally, the fim takes sequentially the following decisions: 1. it decides whethe to elease the souce code to the open souce community (i.e. whethe to employ a dual licensing stategy); if it eleases the code, the fim sets the degee of estictiveness of the OS licence: fomally, it chooses 0; 2. once the code has been developed, the fim chooses the pice p of the popietay vesion. In tun, customes obseve the fim s licensing and picing stategy and take thei adoption decision. 11 They may adopt the softwae, eithe the popietay o the OS vesion if 10 As discussed in the Intoduction, typically fims adopt vesioning stategies to incease sales o to enlage the installed base of uses; in ou setting, the benefit of dual licensing stategy (i.e. of eleasing the open souce vesion of the softwae) is not intended to enlage the maket in none of these ways, but at exploiting the so-called development extenality. In fact, we assume that customes have homogeneous pefeences with espect to the quality of the softwae (they ae heteogeneous only with espect to license estictiveness); this implies that, in equilibium, the maket is always fully coveed also when the fim does not elease the open souce vesion. The fact that dual licensing is not intended to incease sales is also suppoted by the pactical obsevation that fims distibute fo fee the open souce vesion. 11 Note that accoding to the timing of the model some uses may adopt the OS vesion at stage 1 and then contibute to the development of the code, while othes will postpone thei adoption decision afte the popietay vesion has been eleased. Assuming that customes i) do not deive additional benefits fom adopting the OS vesion at stage 1 and ii) they ationally foecast the size of the OS community, then the exact timing of adoption decision is not elevant. Allowing customes to deive additional benefits fom ealy 7

9 available, o they may choose not to adopt any softwae at all; in this last case they enjoy thei esevation utility u o. Customes evaluate not only the quality of the softwae pe-se, but also the tems of licensing. Since they embed it into thei own poducts, then, othe things equal, they pefe to obtain the softwae unde unestictive licensing tems. We assume that customes ae heteogeneous with espect to license estictiveness, and we paameteize thei pefeences with the tem t; in paticula, we assume that t is distibuted accoding to the c.d.f. F (t) ove the suppot [0, T ), whee T > 0 may be eithe finite o infinite. 12 Customes with a low t ae little affected by license estictiveness while customes chaacteized by a lage t eceive a stong disutility fom. Fomally, in case custome t chooses to adopt the OS vesion of the softwae, then she/he obtains a net benefit equal to: U OS (t, ) = V + θ()n t, whee V +θ()n is the oveall quality of the softwae, with V epesenting the quality developed by the fim and θ()n the development extenality accuing fom the OS community; θ()n is inceasing in N, the mass of open souce adoptes, and in the stength of the extenality, θ() 0. Finally, t epesents the disutility that the estictions imposed by the license cause to custome t. It is woth noting that, the paamete about license estictiveness, has a double effect on U OS. A moe estictive license esticts the possible uses of the softwae and, consequently, the evenues that the embedde can ean fom it; this is the diect effect of a moe estictive license on U OS, which we account fo with the tem t. In addition, thee is also an indiect negative effect that impacts all the OS adoptes though the tem θ(): as long as a lage places moe constaints on the possible uses of the code, OS adoptes ae less adoption would not significantly change ou esults. This way of modelling the timing of adoption decision widely accepted in the liteatue on technology adoption; among othes, see Katz and Shapio (1986). 12 The level of t depends both on the natue of the softwae and on the use that customes make of the softwae itself. Since customes use the code as an input to poduce othe, deived, softwae that they eithe sell diectly o that they embed into thei own poducts, then t is lage when the deived softwae epesents the coe of the customes poducts/technologies: the moe elevant the deived softwae in the embedded system, the lage the damage fo the embedde if foced by the license to elease the code unde ecipocal licensing tems. 8

10 motivated in spending time and effot in impoving the code/fixing bugs. In othe tems, a lage affects negatively the extent of the development extenality; fomally we assume that θ() is a (weakly) deceasing function of : θ () The adoption of the popietay vesion delives a net benefit of: U P (p, ) = V + θ()n p, that is, the oveall quality of the softwae, V + θ()n, net of the pice p chaged by the fim. It deseves to be stessed that, in this case, the adopte does not eceive the disutility fom license estictiveness: by definition, the popietay vesion is licensed accoding to the embeddes pefeences; fomally, is set equal to zeo in this case. This fact implies that, iespectively of t, all customes eceive the same level of utility fom the popietay vesion of the softwae. Finally, notice that when the fim decides to develop the softwae completely in-house then only the popietay vesion of the softwae is available to customes. In this case, θ()n = 0 and the net utility fom adopting the softwae is simply V p. Fo the sake of simplicity, all though the pape we nomalize the fim s costs to zeo and we assume that customes have mass 1. Futhemoe, in ode to make the poblem of inteest, we assume that V > u o ; clealy, if V u o, then the stategy of completing the poject without eleasing the code to the OS community would neve be pofitable The optimal stategy Whethe going open souce is an optimal stategy can be veified by compaing the pofits that the fim achieves by distibuting only the popietay vesion with those obtained unde dual licensing. Howeve, the poblem can be educed to the analysis of dual licensing only, once noted that eleasing the code to the OS community at an extemely estictive license is equivalent to sell the popietay vesion only; in fact, when the fim sets the degee of 13 The assumption that θ() is a deceasing function is suppoted by the empiical liteatue on OS softwae, which finds evidence that the level of engagement of the OS community tends to decease with the estictions imposed by the license. See among othes, Comino, Manenti, and Paisi (2007) and Feshtman and Gandal (2007). 14 Absent the extenality, the utility fom adopting the popietay vesion is V p, and none would be willing to pay a positive pice fo the softwae when V u o. 9

11 license estictiveness to infinity, none would be willing to adopt the OS vesion and this makes, de facto, the fim distibuting only the popietay vesion of the softwae. Fomally, we intepet the choice as the case whee the fim chooses not to make the open souce vesion of the softwae available to customes. In ode to chaacteize the behavio of the fim, we fist need to detemine how many customes adopt the open souce vesion of the softwae (i.e. the size of the open souce community) and how many pay fo the popietay one. By compaing U P (p, ) and U OS (t, ), it follows that the custome who is indiffeent between the two vesions is located at t = p. In ode to sell to a positive amount of customes, the fim needs to set p and such that i) U P (p, ) U OS (t, ), fo at least some t, and ii) U P (p, ) u o. Condition i) implies that the fim sets the pice and the license estictiveness in a way such that such that p customes with t p < T. In tun, condition ii) implies that the maket is fully coveed; adopt the popietay vesion since, in this way, they obtain a net utility lage than both U OS and u o. Similaly, customes with t < p adopt the open souce vesion of the softwae since this guaantees a net benefit geate than both U P and u o. Accoding to these consideations, the mass of OS adoptes is simply given by N = F ( p ), while the mass of those who buy the popietay vesion is equal to 1 F ( p ). The following lemma chaacteizes a futhe condition that the pai (p, ) chosen by the fim must satisfy. Lemma 1. The fim sets (p, ) such that V + θ()f ( p ) p = uo. Poof. As obseved above, customes have homogeneous pefeences with espect to the popietay vesion of the softwae. This fact implies that the indiffeent custome and all those who adopt the popietay vesion of the softwae obtain the same level of utility. We pove the Lemma by contadiction; let us assume that, at the equilibium pai (p, ), this common level of utility is stictly lage than u o, namely U P (p, ) = V + θ()f ( ) p p = U OS (t = p, ) = V + θ()f ( ) p p > u o. It is easy to show that the fim can do bette by inceasing maginally, and in the same popotion, p and up, espectively, to p = p (1 + ε) and = (1 + ε), whee ε > 0 is a negligible numbe. At the new pai (p, ), the indiffeent custome is still located at p/; moeove, given that ε is negligible, then U P (p, ) and U OS (t = p, ) ae still geate o equal than u o. Theefoe, the masses of customes adopting the two vesions of the softwae do not change with espect to those at the oiginal pai. 10

12 Nonetheless, since the fim is selling at a highe pice it cetainly makes lage pofits, thus contadicting the initial assumption. The intuition fo the above lemma is simple. As in a standad monopoly model with unit demand, the fim optimally sets the pice and the estictiveness of the OS license in ode to extact all the suplus obtained by those who adopt the popietay vesion of the softwae. Lemma 1 is impotant since it implicitly defines the optimal pice fo the popietay vesion as a function of the degee of licence estictiveness chosen by the fim when posting the souce code on a public epositoy. We define as p () the pice which is implicitly detemined by the optimum condition V + θ()f ( p ) p = uo. Thanks to Lemma 1, the fims optimal stategy can be educed to the choice of, and the maximization poblem can be simplified as follows: ( ( )) p() max π() = p() 1 F. 0 Notice that if the fim would elease the OS vesion without estictions, then eveybody ) would adopt it: if = 0, then F = 1 and the fim makes zeo pofits since it sells ( p() nothing. In the opposite scenaio, when goes to infinity then no one would be willing ) to adopt the OS vesion of the softwae, and F = 0; fom Lemma 1, the fim sets ( p() p = V u o and it makes pofits equal to V u o. Fomally: lim π() = V u o. We ae now in the position to state the main esult of ou pape. Poposition 1. When the stength of the development extenality is sufficiently lage, then it is optimal to employ a dual licensing stategy. Fomally, when lim θ() > V u o, dual licensing is pofitable. Poof. Conside the deivative of the pofit function with espect to. Simple calculations ( ( )) ( ) show that π () = p () 1 F p() p()f p() p () p() df (t), whee, f(t) =. Using 2 dt the condition povided in Lemma 1, fom the implicit function theoem we have that: p () = θ()f ( ) p p 2 θ ()F ( ) p ( θ()f ( ) ) p. Using expession p () and Lemma 1, the deivative π () becomes: In ode to avoid cumbesome notation, in what follows we omit the aguments of functions θ(), θ (), F (t), and f(t). 11

13 π () = f V u o + θf θ + 2θF + V u o θf + } {{ } (A) + F ( (1 F ) f (V u o + θf )) θ θf + }{{} (B) (1) Conside lim π (); notice that since V u o epesents the hoizontal asymptote of π(), then lim π () = 0. In ode to pove the poposition, we need simply to show that π() conveges to V u o fom above, namely that lim π () = 0. Conside tem (B) of the above expession; note that as goes to infinity, then, since θ 0, this tem is negative. Tem (A) conveges to 0 povided that lim θ () > V u o. This is enough to pove that thee exist (at least) one finite value of such that π() > V u o. This esult is intuitive. The benefit of dual licensing accues fom the development extenality: the contibutions of the OS community impove the quality of the code and allow the fim to chage a lage pice fo the popietay vesion. On the othe hand, dual licensing entails the isk of cannibalizing the maket since the open souce vesion of the softwae competes with the popietay one. Dual licensing is a pofitable stategy fo the fim, wheneve the stength of the development extenality, θ(), is lage elative to the quality of the softwae that the fim is able to develop in-house, V. 16 In paticula, the poposition shows that when the stength of the extenality is sufficiently lage, the fim finds it optimal to set at a sufficiently low level so that thee exists a positive mass of open souce adoptes. Poposition 1 povides a geneal message; in ode to chaacteize moe closely the optimal dual licensing stategy, we need to make assumptions on the shape of the extenality; the next Poposition pesents the optimal stategy chosen by the fim when the stength of the extenality is constant, fomally when θ() = θ fo all. Poposition 2. Suppose that θ() = θ fo all, then the fim optimally employs a dual licensing stategy when θ > V u o. Unde dual licensing, the fim sets a pice p and a degee of license estictiveness such that, egadless of the c.d.f. F (t), the size of the OS community is equal to N( p, ) = 1 θ V +u o. 2 θ 16 Since θ () 0, the condition fo which the Poposition holds, lim θ() > V u o, implies that θ() > V u o fo any value of. 12

14 Poof. When θ() = θ, expession (1) educes to: π () = f V u o + θf θ + 2θF + V u o. θf + ( ) p() The fist ode condition π () = 0 is uniquely solved when F = 1 2 θ V +u o. This θ implies that when θ V u o, the optimal size of the open souce community is zeo, while when θ > V u o, the mass of OS community is equal to 1 2 identifies a maximum povided that π(0) = 0 and lim π () = V u o. θ V +u o. This latte case necessaily θ We have aleady discussed when commenting Poposition 1 that the decision to employ a dual licensing stategy elies entiely on the compaison between the stength of the extenality and the in-house quality of the code. Poposition 2 highlights an additional inteesting featue of the equilibium stategy: when θ() is constant, the fim sets p and in a way such that the mass of OS adoptes is independent of the distibution of customes pefeences towads license estictiveness. In ode to intepet this latte esult, it is useful to conside the maximization poblem in tems of N athe than, povided that thee is a one-to-one mapping between and N: N = F (p/) o = p/f 1 (N). In this espect, Lemma 1 implicitly defines the optimal pice as a function of N, fomally p(n) = V + θ(p(n)/f 1 (N))N u o. The fim chooses N to maximize its pofits p(n)(1 N). When θ is constant, an incease in N has two effects: on the one side, fims pofits go up by θ(1 N); on the othe side, a lage N, educes sales and, theefoe, pofits of an amount equal to p(n) = V + θn u o. These two effects do not depend on the function F (t), thus explaining why at the equilibium the optimal size of the OS community is independent of the distibution of customes pefeences towads. Things become moe aticulated when the stength of the extenality deceases with the degee of license estictiveness. In this case an additional effect must be taken into account by the fim when deciding : a less estictive license is geneally moe desiable since it inceases the stength of the development extenality. We highlight these aguments in Poposition 3. Poposition 3. Suppose that θ () < 0; wheneve the fim finds it optimal to endose a dual licensing stategy, it does so by setting <, whee is defined in Poposition 2. Poof. When F = 1 2 θ() V +u o, π () calculated in the poof of Poposition 1 becomes: θ() (θ() V + u o ) (V + θ() u o ) θ (). 4θ() 2 13

15 It is immediate to see that this expession is negative. In fact, θ() V + u o > 0 when dual licensing is pofitable, i.e. when lim θ() > V u o. Similaly, given that V > u o by hypothesis, also V + θ() u o is positive. Finally, we ae discussing the scenaio with θ () < 0. This is enough to pove the Poposition. This poposition is inteesting and suggests that when θ () < 0, the fim tends to endose a moe po OS stategy by eleasing the code to the community unde a less estictive tems; this is a good thing fo the fim since it stimulates the contibutions fom the OS developes, which tanslates into highe quality of the popietay vesion and theefoe lage pofits. We conclude this section with a final obsevation elated to the welfae effects of dual licensing: Remak 1. When the fim employs a dual licensing stategy, it induces a Paeto impovement. Obviously, wheneve the fim chooses to dual licence its code, it does so because it obtains lage pofit. But also customes may be bette off: without dual licensing, all individuals end up with thei esevation utility u o. With dual licensing, those that puchase the popietay vesion still obtain u o ; howeve, customes adopting the OS vesion of the softwae obtain a utility which is stictly lage than the esevation level. The decision to povide the code to the OS community geneates some value though the development extenality; pat of this value goes to the fim and pat to individuals, thus explaining the Remak. 2.2 A specific example To bette gasp the intuition behind ou model, the following coollay chaacteizes the optimal stategy when θ() is constant and t is unifomly distibuted ove (0, b). Coollay 1. When t U (0, b) and θ() = θ > V u o, then the fim optimally employs a dual licensing stategy with p = V uo+θ 2, and = that V > 0, b θ ( ) (V u o ). θ(v uo+θ) b(θ V +u o. License estictiveness is such ) < 0, and θ < 0 when θ ( V u o, ( ) (V u o ) ), while θ > 0 when Poof. The equilibium pice and the level of license estictiveness ae obtained by solving the system of equations V + θf ( ) p p = uo and F ( ) p = 1 θ V +u o and by using the fact 2 θ 14

16 that, fo the case of uninfom distibution, F ( ) p = p. The compaative statics is obtained b by simply diffeentiating. The positive elationship between and V can be explained following the same aguments used to discuss Popositions 1, and 2: as V inceases, the fim benefits fom employing a moe popietay stategy, i.e. by selecting a moe estictive license. Conside now the ole of b that paameteizes the distibution of customes pefeences. Fom Poposition 2 we know that the fim sets the license estictiveness in ode to optimally segment customes into OS and popietay adoptes. When b gets lage the mass of customes that ae substantially affected by the license estictiveness inceases; theefoe, the fim needs to educe in ode to enlage the mass of OS adoptes up to the optimal size defined in Poposition 2. The impact of an incease in the stength of the development extenality on is moe aticulated and it entails to two opposite effects. A lage value of θ signals that the contibution of the OS community is highly valuable. Nonetheless, a lage θ makes the open souce vesion of the softwae also a stonge competito vis a vis the popietay one; moe specifically, as θ inceases a lage shae of customes is attacted by the OS vesion of the poduct. The fome effect dominates wheneve the size of the OS community is elatively small, that is when the stength of the extenality is not too lage, θ ( V u o, ( ) (V u o ) ). In this case, the fim benefits fom augmenting the size of the community though a eduction in the level of license estictiveness. On the opposite, the competition effect pevails when the OS community is aleady sufficiently lage; in this case, the fim eacts to a futhe incease in θ by selecting a lage. 3 Discussion and futue eseach In this pape we have poposed a theoetical model to study the chaacteistics and the commecial sustainability of a paticula open souce business stategy known as dual licensing. The focus is on the decision of a softwae vendo about whethe to develop a fully popietay vesion of a softwae o to employ a dual licensing stategy, in a context whee customes ae commecial fims that ae hamed by the estictions imposed by OS licenses. We have shown that dual licensing is pefeed when the feedbacks of the OS community 15

17 (the development extenality) ae valuable enough compaed to the quality of the softwae that the fim is able to develop on its own. Ou analysis points to the cucial ole of OS licensing schemes fo fims embacing open souce stategies. Though an appopiate definition of the licensing tems of distibution of the OS vesion of the softwae, the fim balances the opposing effects of going open souce. A moe estictive license potects the popietay vesion of the softwae against the isk of cannibalization at the cost of educing the size of the OS community that contibutes to softwae development; moeove, licensing tems also affect OS pogammes incentives to contibute to the development of a bette softwae. Even though the theoetical model focuses on the ole of ecipocal povisions in making vesioning viable, ou esults have a boade intepetation. As discussed in the Intoduction, thee ae additional dimensions of OS licenses that might distub potential customes; 17 in these cases, a softwae house may pofitably go OS and sell an upgaded vesion of the softwae to those customes who ae willing to pay to be feed fom the specific povisions/limitations of the OS vesion The impotance of an appopiate management of OS licenses fo softwae vendos, contibutes explaining one of the most debated phenomenon in the OS wold, known as license polifeation. 18 At the time of witing this pape, moe than 70 diffeent licensing schemes have been egisteed as OS licenses; these licenses diffe along seveal dimensions. 19 Inteestingly, vaious commecial vendos have ceated thei own open souce license, thus confiming a possible stategic ole in the design of the license See footnote License polifeation epesents one of the majo challenges to OS; indeed, the pesence of diffeent schemes may pose seious poblems given that some licenses ae potentially incompatible with each othe; fo a discussion see Rosen (2004), chapte 10, and the epot of the License Polifeation Committee, available at the Open Souce Initiative web-site, 19 Take, fo instance, the ecipocal povision; not all the OS licenses impose such povision (this is the case of the BSD and the othe so-called academic licenses ) while, at the same time, an exteme heteogeneity in tems of the degee of ecipocity imposed on deivative woks can be obseved between those licenses that do have ecipocal povisions. 20 The case of Nokia is emblematic. At the ul opensouce.nokia.com/ seveal diffeent softwae pojects ae available fo download and often pojects ae licensed unde diffeent tems. Some pojects ae distibuted unde the Nokia Open Souce License, othes ae available unde diffeent OS licensing templates such as: GPL, BSD, Mozilla Public License, LGPL, and othes. Similaly, also IBM, Intel and Micosoft have ceated 16

18 One simplifying assumption that we have implicitly made in the pape and that deseves futhe discussion is that the only way fo the fim to benefit fom the contibution of the community is by making the OS vesion of the code feely available on a public epositoy. This assumption is made on pactical gounds; the fact that a vast majoity of OS pojects hosted on public epositoies such as SouceFoge.net and sponsoed by commecial vendos ae feely available, goes exactly in this diection. Moe specifically, this assumption is suppoted by the obsevation of the stategies adopted by those fims, such as Oacle and Sun Micosystems, whose expeiences have been inspiing ou pape. This assumption, howeve, is not innocuous since it implies that the fim cannot do bette by following othe stategies, moe aticulated than those descibed in the pape. Fo example, the fim cannot benefit fom selling at a positive pice an open souce vesion of the softwae (i.e. a vesion with > 0). Indeed, in ou famewok, adoptes of this vesion of the softwae ae assumed not to contibute to the development of the poject; moeove, since they bea the disutility due to the estictions imposed by the OS license, they ae willing to pay a pice which is smalle than what they would pay fo the popietay vesion. Consequently, the fim is cetainly bette-off inducing these customes to adopt eithe the feely available OS vesion (to let them contibute to the poject), o the popietay vesion (to chage them a lage pice). Simila aguments apply to the feasibility of multiple licensing stategies, i.e. the elease of moe than one OS vesion of the softwae at a zeo pice; in this case, OS adoptes will cetainly select the vesion eleased unde the less estictive license. Finally, in the pape we focus on the behavio of a monopolist poducing a cetain softwae. An impotant extension that we leave fo futue eseach elates to the ole of open souce stategies in competitive famewoks. thei OS license. 17

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