Commercializing Open Source Software

Transcription

1 ommercializing Oen Source Software Byung ho Kim 1 bck@vt.edu Pamlin ollege of Business Virginia Tech Blacksburg, VA 4061 Tridas Mukhoadhyay tridas@cmu.edu Teer School of Business arnegie Mellon University Pittsburgh, PA 1513 Pei-yu hen 3 ychen@temle.edu Fox School of Business Temle University Philadelhia, PA Mailing Address: Byung ho Kim, 1007 Pamlin Hall (035), Deartment of Business Information Technology, Pamlin ollege of Business, Virginia Tech, Blacksburg, VA 4061; Phone: Mailing Address: Tridas Mukhoadhyay, Posner Hall 385B, Teer School of Business, arnegie Mellon University, Pittsburgh, PA 1513; Phone: Mailing Address: Pei-yu hen, 07E Seakman Hall, 1810 North 13th Street, Philadelhia, PA 191; Phone:

2 ommercializing Oen Source Software Abstract In this aer, we examine oen source software (OSS) business models with a focus on ricing strategies. We investigate the otimal ricing strategies of software vendors, both rorietary and oen source, under cometition. Our model considers motivations for, and barriers to OSS adotion, which have been exclusively discussed in ractice for the last decade. We characterize the conditions under which the commercial OSS model is viable when otential OSS customers incur cost to switch from an established rorietary software vendor to commercial OSS. Our findings give strategic insights and ricing guidelines to software vendors who consider commercializing their OSS roducts. Key words: Oen Source Software; Software Pricing; Dual-Licensing Model; Switching ost 1

3 1. Introduction Oen Source Software (OSS) is software for which the source code is available to the ublic, enabling anyone to coy, modify, and redistribute it (Varian and Shairo 003). Prorietary software, by contrast, is software that is distributed under a rorietary license agreement, usually for a fee. Oen source was a service mark of the Oen Source Initiative (OSI), a non-rofit organization that continues to rovide an official Oen Source Definition. According to the OSI definition, OSS is software whose source code can be freely modified and redistributed 4. The redistribution rights do not reclude a comany selling such software for rofit. Recently, OSS is gaining enormous momentum. According to a recent article in the New York Times, OSS is used heavily by big comanies such as IBM, Oracle, Google, Ale, and even Microsoft and thus, it becomes a weaon in cororate warfare (Lohr 010). A survey by Forrester Research shows that a significant ercentage of enterrises have adoted or will adot the OSS within the next 1 months in various business functions including database (66 ercent), web server and networking (63 ercent), and security tools (56 ercent) (Asay 009). An imortant question is then what motivates enterrises to emloy OSS? The Free/Libre and OSS (FLOSS) Survey found that firms are emloying OSS on the grounds of cost savings, flexibility and indeendence from giant software vendors (Wichmann 00). Firms consider the flexibility of OSS to be imortant since they believe that vendors of rorietary software routinely downlay the customizability of OSS, arguing customers are not interested in extending software functions themselves. A survey by Actuate confirms that the benefits from OSS adotion include cost savings (55%), vendor indeendence (49.3%) and flexibility (47.1%) while the main barriers are availability of long-term suort (58.%) and long-term maintenance (44.7%) (Mcarthy 006). Thus, firms that do not have a caable IT management team tend to be reluctant in adoting OSS. Lately, a new movement in the OSS industry becomes henomenal. As OSS gains oularity and the market share aroaches critical mass on account of its distribution under free license, vendors of such 4 The Oen Source Definition. htt://

4 OSS seek to caitalize on the ublicity and oularity of their OSS. Two models were roven to be viable for commercializing OSS: dual-licensing and suort model. Under the dual-licensing model, the OSS vendor offers the very same software under two different licenses. Oen source license allows the licensees to modify, distribute, and use the software for free, but it requires the release of any modifications under the same oen source license. The rorietary license ermits using the software under standard rorietary terms. Examles include MySQL AB s database, Oracle ororation s Bergeley DB, Qt Software s Qt develoment toolkit and Asterisk that is an OSS telecommunications software suite from Digium. Another aroach is the suort model, under which the vendor sells suort service for the OSS which is distributed at no charge. Red Hat and JBoss have been successfully commercializing OSS under the suort model. There is a lively debate going on among ractitioners about the viability of OSS business models (Moczar 005, Vaughan-Nichols 005). While the number of OSS vendors successfully adoting the aforementioned business models is growing, OSS commercialization is still at an early stage. The viability of OSS business models is still questionable and clear ricing guideline is not yet available to the OSS vendors who consider commercializing their roducts. For the last decade, a significant number of OSS vendors have successfully built a large installed base through free distribution, leading some of them, if not all, to consider making rofits from their OSS. Desite the great otential of OSS business models, little academic research has examined the issue of OSS commercialization. This aer examines the viability of the OSS business model focusing on the dual-licensing regime, under cometition with an established rorietary software vendor. Our focus is not the OSS vendors who launch their OSS under the duallicensing model outright, which is remote from reality, but the OSS vendors who have already reached a critical mass by building a sufficient installed based through distribution of its OSS under a free license and begin offering a commercial license. We identify the key success factors for the OSS business models and characterize the conditions under which OSS commercialization is viable. We only consider firmlevel customers since most OSS is distributed freely to individual customers. We model the motivations for and the barriers to OSS adotion and analyze their imact on the viability of the OSS business model. 3

5 Our model catures two sources of customer heterogeneity in their valuation of software: taste and technology savviness. As a benchmark, we first examine a monooly case in which we comare rofits from two different software regimes: rorietary and oen source. We investigate how customers technology savviness and the OSS-generic benefits and drawbacks affect the monoolistic software vendor s incentive to choose an OSS regime over a rorietary one. We then extend our model to a realistic two-eriod setting under which an OSS vendor with a dual-licensing model enters the market which is already dominated by an established rorietary software vendor. Insired by a real-world software market (e.g., the database management software market where MySQL cometes with Microsoft SQL Server), we characterize the conditions under which the OSS dual-licensing model is viable. We examine the imact of switching cost that customers of rorietary software may incur when they switch to OSS on the viability of the commercial OSS licensing model. We also investigate how the otimal ricing strategies of both OSS and rorietary software vendors are affected by the OSS-secific factors, such as quality deficiency of OSS, suort costs to high- and low-tye customers in different scale, and the scoe of switching cost. Our aer contributes to the literature in the following ways. Firstly, while little academic research examines the issue of OSS commercialization, this study investigate the ricing issues of the commercial OSS licensing model through an economic lens, which has not yet been exlored much desite the growing interest in the economics of OSS. We identify the factors that affect the ricing decisions of OSS vendors. Secondly, our model catures the motivations for and the barriers to OSS adotion. We characterize the conditions under which the OSS business models are viable. By doing so, we rovide theoretical foundations of commercializing oen source software. Finally, our findings can give ricing guidelines for OSS vendors who consider commercializing OSS. The rest of this article is organized as follows. We discuss the related literature in Section. We resent our model in Section 3 and examine the benchmark monooly case in Section 4. In Section 5, we enrich our model and study the imact of switching cost on the viability of the OSS business model under cometition. Section 6 concludes the aer. 4

6 . Literature Review This aer is grounded on two streams of research: (1) information goods ricing, and () economics of OSS. Pricing strategies for information goods or IT-enabled ricing strategies have been widely examined by researchers in the domain of Information Systems. Dewan and Mendelson (1990) examine the otimal ricing olicy and caacity investment strategy in the context of ASP in the resence of nonlinear delay costs. Other oular toics include versioning (Bhargava and houdhary 001; Sundararajan 004), bundling (Bakos and Brynjolfsson 1999; Hitt and hen 005), rice discrimination (houdhary et al. 005; Dewan et al. 003), and rice disersion (lemons et al. 00). hen and Png (003) examine information goods ricing in the context of digital rights management. Prior literature on OSS focuses heavily on understanding the motivations of individual develoers to articiate in and contribute to OSS rojects (Shah 006). von Hiel and von Krogh (003) consider two models of innovation, rivate and collective, and argue that contributors to OSS rojects get intangible rivate benefits which are not resent for free riders, such as ersonal satisfaction and learning. Franke and von Hiel (003) examine the motivations of the Aache roject articiants and find that users desire to satisfy their own needs gives incentive for articiation. Raymond (1999) suggests that the reutation and the status motivate develoers articiation while Ghosh (1998) argues that enjoyment and creativity matter. Economists argue that existing economic theory can exlain OSS roject articiation (Learner and Tirole 001, 00). Hann et al. (006) argue that articiation in OSS rojects is driven by career concerns, learning, and reutation. Roberts et al. (006) develo a theoretical model to examine the system of interrelationshi between motivations, articiation, and erformance. Singh et al. (007) examines the relationshis among OSS develoers in their social network. Modeling cometition between rorietary software and OSS is an emerging issue among researchers who study OSS from an economic ersective. Raghunathan et al. (005) examine the quality debate in OSS by setting u an analytical model and show that OSS quality is not necessarily lower than rorietary software quality. asadesus-masanell and Ghemawat (006) analyze a dynamic mixed 5

7 duooly in which a for-rofit rorietary software vendor interacts with an OSS vendor in the resence of demand-side learning effects. Economides and Katsamakas (006) analyze the otimal two-sided ricing strategy of a latform firm and comare industry structures based on a rorietary latform such as Microsoft Windows with those based on an oen source latform such as Linux. Some research discusses the legal issues around commercial OSS (Gomulkiewicz 004, Välimäki 003). Our study aims to bridge the ga between information goods ricing and OSS literature by examining the ricing issues around OSS. 3. Model We analyze the otimal ricing decisions of software vendors and examine viability of the OSS business model in different scenarios. We consider the dual-licensing model for OSS in which the vendor rovides the same software under two different licenses: oen source license and rorietary license. Users who want to donate their source code to the oen source community can license software under an oen source license, namely the General Public License (GPL). Under this oen source license, the licensees can freely modify, distribute, and use the software at no charge. On the other hand, any users who want to use the OSS for rofit-seeking uroses must urchase a rorietary license. MySQL and Mozilla Firefox are the examles of OSS under the successful dual-licensing model. We analyze the otimal ricing of a rorietary license of OSS. 3.1 ustomers We only consider firm-level customers who are obligated to buy the rorietary license of OSS under the dual-licensing regime. We characterize customers by two dimensions constituting heterogeneity: software valuation and technical savviness. Different customers value the same software differently. For examle, a firm that heavily uses information technology values the same software more than others since a significant ortion of its core business deends on information systems owered by the software. v is a 6

8 taste arameter that catures customer heterogeneity in valuation of software. We assume that v is uniformly distributed on [0, 1], leading to a linear demand curve. Regarding technical savviness, customers divide into two segments. A roortion µ of customers are technologically savvy, and we call them high-tye customers. These customers have a caable in-house IT management team, which allows them to take advantage of the flexibility of OSS ( f ) by customizing the source code. The high-tye customers may adot OSS not only because OSS has cost advantage but also it gives them flexibility. ustomers in the remaining fraction (1 µ) are low-tye customers. ost advantage may be their only incentive for OSS adotion. High-tye customers are defined as customers to whom benefit exceeds cost from customization of OSS while low-tye customers are ones to whom cost exceeds benefit from customization. Thus, the net flexibility benefit is ositive for high-tye customers ( f > 0) while it is zero for low-tye customers ( f OL = 0) since without technical savvinness, no flexibility benefit can be exected. Prorietary software in our aer is closed-source rorietary software, thus, we do not consider the customization of it. Software maintenance and suort are costly to all customers. Denote suort cost with s j where j = H, L,, OL. We assume that low-tye customers suffer more from suort and maintenance of any software ( s < s, s < s ). To reflect reality, we also assume that H L OL suort is more costly for OSS than for rorietary software to the same-tye customer ( s < s, s < s ). We assume risk neutrality of customers. H L OL 3. Software Pricing Models We examine the otimal rices for the software under two different ricing schemes: (1) rorietary and () OSS dual-licensing. Deending on whether the source code is oen or closed, the very same software can lead to different levels of utility. We model such imact of the oenness of the source code on the customer utility. In this section, we derive customer utility and vendor rofit under each of the three software business models, based on which the equilibrium rices are obtained. 7

9 Prorietary Software We label the high-tye customers H and the low-tye customers L. The roortion of the high-tye customers is µ and the remaining roortion, 1 µ is the low-tye segment. Since rorietary software comes as a ackage with closed source code, the customizability of it is minimal regardless of customer tye. Low-tye customers suffer from suort and maintenance due to limited technical caability. in the subscrit means rorietary software. High-tye and low-tye customers enjoy utilities, uh = v t sh and ul = v t sl, resectively, where t reresents the value difference between rorietary software and OSS and is the rice of the rorietary software. Positive (negative) t imlies that rorietary software offers higher (lower) value than OSS. Let q H and q L be the demand for the software under a rorietary regime from the high-tye and the low-tye segments, resectively. The rofit for the OSS vendor then becomes π = ( μq (1 μ) q ). We assume zero marginal cost, which is reasonable for information goods such as software. OSS Dual-Licensing Model H L O in the subscrit reresents OSS dual-licensing model. When adoting OSS, only high-tye customers enjoy the flexibility. O denotes the rice of the rorietary license for OSS. The net benefits for hightye and low-tye customers become u = v O f s and uol = v O sol, resectively. We assume that for high-tye customers, net flexibility benefit always exceed suort cost ( f s > 0). Let q and q OL be the demand for the OSS under the dual-licensing model from the high-tye and the low-tye segments, resectively. The rofit for the OSS vendor then becomes π = ( μq (1 μ) q ). Table 1 summarizes the notations used in this aer. D OL O Notation v Descrition ustomer valuation of software 8

10 s High-tye customer s suort cost for rorietary software H s Low-tye customer s suort cost for rorietary software L s High-tye customer s suort cost for OSS s Low-tye customer s suort cost for OSS OL f High-tye customer s net flexibility benefit from OSS (i.e., benefit from customization customization cost) t Value difference between rorietary software and OSS t > 0 means rorietary software gives higher value than OSS t < 0 means OSS gives higher value than rorietary software Table 1. Notations 4. Benchmark: Monooly ase In this section, we examine the otimal rice and the corresonding maximal rofit of a monoolistic software vendor under each of the two ricing regimes: rorietary and OSS. We investigate whether a monoolistic software vendor has an incentive to adot the OSS business model instead of the rorietary model. Monooly is worthwhile to examine as a benchmark because a natural monooly often occurs in software industry. Prorietary software ustomers who get ositive utility would buy the software, resulting in demands for the rorietary software from high-tye and low-tye customers to be q = 1 t s and q = 1 t s, 9 H H L L resectively. The rofit for the monoolistic software vendor under the rorietary regime becomes π = ( μq (1 μ) q ) = (1 t μs (1 μ) s ). Thus, the rofit-maximizing rice H L H L

11 becomes 1 = (1 t μsh (1 μ ) sl ), at which, the maximum rofit level becomes 1 (1 (1 ) ) π = t μsh μ sl. 4 OSS Dual-Licensing Model Under the dual-licensing regime, demands for the OSS from the high-tye and the low-tye segments are q = 1 f s and q = 1 s, resectively. The monoolistic software vendor gets O OL O OL rofit as π = ( μq (1 μ) q ) = (1 μ( f s ) (1 μ) s ). Thus, the otimal rice O OL O O OL O 1 under the dual-licensing model becomes O = (1 μ ( f s ) (1 μ ) sol ). The maximum rofit is 1 then πo = (1 μ ( f s ) (1 μ ) sol ). We comare the OSS ricing model with the rorietary 4 model and identify the conditions under which one regime is more rofitable for a monoolistic software vendor than the other. The following roosition summarizes the results from rice and rofit comarisons between an OSS ricing model and a rorietary model. Proosition 1: A monoolistic software vendor charges higher rice and makes higher rofit with a rorietary model than with an OSS model O O ( >, π > π ), when the aggregate value is higher under the rorietary regime than the OSS regime ( t μs (1 μ) s > μ( f s ) (1 μ) s ). H L OL Otherwise ( t μs (1 μ) s < μ( f s ) (1 μ) s ), the OSS regime leads to higher rice and H L OL rofit < O < O (, π π ). At the current stage of the software industry, rorietary business model is revalent. However, given the increasing oularity of commercial OSS, a software vendor may want to consider oening the source code and adoting OSS ricing models before introducing its software to the market. Proosition 1 indicates that the ortion of technically savvy customers and their flexibility benefit from the OSS are the key factor for the viability of the OSS dual-licensing model under monooly. When the aggregate benefit that high-tye customers enjoy from OSS outweighs aggregate suort cost for low-tye customers by 10

12 much, even the monoolistic software vendor may be better off with the oen source regime than with the rorietary one. In the current state, it is hard to find an examle for monoolistic commercial OSS. The findings imly that the current software market may not have sufficient high-tye customers and/or not much flexibility benefit from OSS is realized by them given the significant suort cost. It is also ossible that the suort cost from rorietary software is negligible comared to that from OSS, which makes the OSS dual-licensing model less attractive. The monoolistic software vendor may want to consider the OSS dual-licensing model only when it makes sure that many of the otential customers of its software are technologically savvy and that they will areciate flexibility due to the oenness of the source codes. Next, we examine a more realistic scenario under which an OSS vendor enters the market which is dominated by a rorietary software vendor. 5. Sequential Entry and Switching ost ommercializing OSS is an emerging but not yet oular concet to both academics and ractitioners. Although some OSS vendors have been successfully emloying the business models, the general alicability and viability of the OSS business models are still in question. Thus, it is worthwhile to identify the key success factors for the emerging OSS business models and characterize the conditions under which they are viable. In this section, we enrich our model to cature the key drivers for the success of the OSS business models, reflecting what is haening in reality. We model the cometition between an OSS vendor with the dual-licensing model and a rorietary software vendor in the alication software market, insired by the database management software cometition between MySQL and Microsoft SQL server. The success of MySQL has been exclusively discussed by software exerts. In the database management software market, MySQL has been successfully cometing with Microsoft for the segment of small businesses while Oracle and IBM comete for large businesses (Burgelman et al. 004). Motivated by the cometition between MySQL and Microsoft, we extend our model to two-eriod cometition setting in the resence of switching cost. In 11

13 reality, OSS vendors with monetary motivation are often late movers, that is, they are entrants to the market which is already dominated by a rorietary software vendor. Thus, investigating the imact of switching cost is imortant as in other studies of information goods. Researchers have exclusively studied the role of switching cost in the information goods market (e.g., hen and Hitt 00). We cature characteristics secific to the OSS such as quality deficiency of OSS, suort costs to high- and low-tye customers in different scale, and the scoe of switching cost as in the benchmark General Descrition of a Two-Period Model There are two decision eriods. In the first eriod, there exists only a rorietary software vendor who sets a rice 1 for a license which is good for eriod 1. There is a continuum of customers whose valuations of software, denoted by v, lie uniformly on [0, 1] in each eriod. Among those, the roortion of high-tye customers is μ while the rest 1 μ, are low-tye. We assume forward-looking behavior of customers. That is, given 1, each customer decides whether to buy rorietary software in eriod 1 or wait to see the available otions in eriod. In the second eriod, the OSS vendor enters the market and given eriod-1 rice of rorietary software and the market base, both the OSS vendor and the rorietary software vendor set their rices for the eriod- license in a simultaneous manner. In eriod, a new set of customers with the same rofile arrive. Thus, there are three different grous of customers: customers who live and buy in eriod 1 (grou 1), customers who live in eriod 1 and defer their urchase decision to eriod (grou ), and new customers in eriod (grou 3). In eriod, customers in grou 1 can stay with rorietary software by urchasing eriod- license or switch to OSS while incurring switching cost. ustomers in grous and 3 choose rorietary software or OSS or neither. We model the imact of the following arameters on the ricing decisions of software vendors. ustomers who switch from rorietary software to OSS in eriod incur switching cost denoted by wx1 where x1 is the number of customers who buy rorietary software in eriod 1 and w is a scale arameter which models the scoe of switching cost. This way of modeling switching cost is consistent 1

14 with the literature in that switching cost increases with the market size due to network externalities. Recall that we assume only high-tye customers enjoy flexibility benefit f from OSS while all customers suffer suort costs from any software in a different scale, denoted by s j where j = H, L,, OL. Our model also considers the value difference between rorietary software and OSS with a arameter t. Positive (negative) t means that rorietary software gives higher (lower) value that OSS. The structure of the game is illustrated in Figure 1. Period 1 Price 1 Prorietary Software Value vt High Tye Value v Flexibility f Suort cost s Switching cost wx 1 μ ustomer Period Price Prorietary Value vt Price O 1-μ Low Tye Value v Suort cost s OL Software OSS Switching cost wx 1 Figure 1. Sequential Entry and Market ometition 5.. Strategic hoice of Forward-Looking ustomers In this section, we analyze the strategic choice of different grous of customers. Grou 1 customers who urchase rorietary software in eriod 1 face two strategic choices in eriod : stay with rorietary software () or switch to OSS (O). The rest of eriod-1 customers who decide to wait and see the available otions in eriod (grou ) can buy rorietary software (X), OSS (XO), or neither (XX). The new customers who arrive in the second eriod (grou 3) have the same strategic choices as grou customers, that is, rorietary software (), OSS (O), or nothing (X). We have three different grous of 13

15 customers with two segments in terms of their technological savviness, and they have different sets of strategic choices. ertainly, customer utility from not buying any software (i.e., XX or X) is zero. Table resents customer utility from each of the different strategic choices. Strategic hoices High-Tye ( μ ) Low-Tye (1 μ) (Grou 1) v 1 t sh v t sh v 1 t s v t s L L O(Grou 1) v 1 t sh v O f s wx1 v 1 t sh v O sol wx1 X(Grou ) (Grou 3) XO(Grou ) O(Grou 3) H v t s v t s v O f s v O sol L Table. ustomer Utility Now we characterize the conditions under which a customer of each tye in each grou makes a articular software choice over the other. onsider a high-tye customer in grou 1. This customer will choose rorietary software in eriod if v t s > v f s wx 1. Note that high- H O and low-tye customers with ositive utility (i.e., v 1 t s > 0 and v 1 t s > 0, resectively) will buy the rorietary software in eriod 1 which leads to eriod-1 market base as x = μ(1 t s ) (1 μ)(1 t s ) = 1 t μs (1 μ) s. Thus, the condition 1 1 H 1 L 1 H L under which a high-tye customer in grou 1 chooses rorietary software can be rearranged as w1 < O t sh f s w(1 t μsh (1 μ) sl). OSS will be selected by the hightye customer if w 1 > t s f s w(1 t μs (1 μ) s ). Following the same O H H L logic, the condition under which a low-tye customer in grou 1 lays instead of O is w1 < O t sl sol w(1 t μsh (1 μ) sl). The low-tye customer will choose strategy O over when w 1 > t s s w(1 t μs (1 μ) s ). O L OL H L 14 H L

16 Since the utility for the same-tye customers in grou and grou 3 is the same as shown in Table, the conditions under which rorietary software is referred to OSS are identical. A high-tye customer in grous or 3 will refer rorietary software if v t s > v f s, that is, O H. H O < t s f s Otherwise, OSS will be chosen. A low-tye customer in grous or 3 will choose rorietary software over OSS when < t s s, while OSS will be selected if > O L OL. t s s O L OL Recall that suort is assumed to be more costly for OSS than rorietary software regardless of customer tye (i.e., s > s H and sol sl > ). Thus, t sl sol is always ositive, meaning that the rorietary software vendor can attract low-tye customers in any grou by charging eriod rice lower than t s s. Thus, low-tye customers choice will always be rorietary software no matter to O L OL which grou they belong. The ricing strategies of the software vendors and the high-tye customers choices are not trivial. We consider the following three cases under each of which high-tye customers behave differently: ase I: Better Prorietary software ( t s f s > 0) H ase II: Better OSS, High Switching ost ( w(1 t μs (1 μ) s ) < t s f s < 0) H L H ase III: Better OSS, Low Switching ost ( t s f s < w(1 t μs (1 μ) s )) H H L We further analyze each of the aforementioned three cases and resent the outcome in the next section Software Prices and ustomer hoice at Equilibrium In this section, we analyze ricing strategies of rorietary and OSS vendors. Since boundary solutions are secial cases, we are interested in (1) whether there exists a unique interior solution in each of the three cases and if so, () what the otimal rices are and (3) what their characteristics are. We then seek managerial imlications of these. 15

17 ase I: Better Prorietary software ( t s f s > 0) H When the high-tye customers enjoy high value from OSS, the rorietary software vendor s otimal strategy is to set rices such that w 1 < t s f s w(1 t μs (1 μ) s ) and O H. O H H L < t s f s By doing so, the rorietary software vendor can serve all high-tye customers in all three grous. Since the OSS vendor knows the rorietary software vendor will set the rices which will revent the OSS vendor from making any ositive rofit, its best resonse is not entering the market. Then the customers otimal strategies can be summarized as follows: Grou 1: High () Low (), Grou : High (X) Low (X), Grou 3: High() Low () The rorietary software vendor s rofit function becomes asei = (1 1 t sh (1 ) sl ) 1 (1 t sh ) π μ μ μ (1 μ)(1 t s ) (1 t μs (1 μ) s ) L H L =(1 t μs (1 μ) s ) (1 t μs (1 μ) s ). 1 H L 1 H L In eriod, the rorietary software s roblem is Maxπ s.t. < t s f s. asei H Given the otimal eriod rice ( ), the rorietary software vendor solves the following roblem in eriod 1: 1 asei Maxπ ( ) s.t < H μ H μ L w 1 t s f s w(1 t s (1 ) s ). A further equilibrium analysis leads to the following Proosition. Proosition : When a high-tye customer enjoys higher value from rorietary software than from OSS ( t s > f s ), the rorietary software vendor lays a ricing strategy to revent the OSS H vendor from making ositive rofit. Proosition indicates that it would not be ossible for an OSS vendor to commercialize its roduct if it does not give any additional benefit to technically savvy customers. It turns out that a marketdominating rorietary software vendor will lay a ricing strategy to revent an OSS vendor from 16

18 entering the market, which may exlain what is haening in many of the real-world rorietary versus OSS cometition cases. This result imlies that roviding considerable benefits to a significant number of technically savvy customers in the market must recede commercializing OSS. We then investigate whether otimal ricing guidelines can be characterized. Proosition 3: There exists a unique interior solution in which the rorietary software vendor charges equal rice for both eriods, i.e., 1 t μsh (1 μ) sl 1 = =. Other ossible sets of otimal rices are characterized as below: t sh f s ω(1 t μsh (1 μ) sl ) 1 = (boundary), ω where 1 t μsh (1 μ) sl (interior) = or = H (boundary) t s f s. The results show that there exists a unique interior solution that is characterized as equal rices for both eriods. Under the conditions for the interior solution to exist, charging rice at the level of which, single eriod rofit is maximized is otimal. ase II: Better OSS, High Switching ost ( w(1 t μs (1 μ) s ) < t s f s < 0) H L H Given the moderate net value difference, the rorietary software vendor wants to offer rices such that w1 < O t sh f s w(1 t μsh (1 μ) sl) to ensure that high-tye customers who buy rorietary software will stay with it in eriod. Since t s f s < 0 < t s s, the low-tye customers in grou 1 will stay as well with such H SL OL rices. Also, the rorietary software vendor wants to serve low-tye customers in grous and 3 by charging eriod- rice such that < t s s. On the other hand, the OSS vendor knows that O L OL it can attract high-tye customers in grous and 3 by charging the rice such that O < ( t sh f s). Then the customers strategic choices can be summarized as follows: Grou 1: High () Low (), Grou : High (XO) Low (X), Grou 3: High (O) Low () 17

19 The rorietary software vendor s rofit function can be written as aseii = (1 1 t sh (1 ) sl ) 1 (1 1 t sh )(1 t sh ) π μ μ μ (1 μ)(1 t s )(1 t s ) (1 μ)( t s )(1 t s ) 1 L L 1 L L (1 μ)(1 t s ) L 1 t μsh μ sl 1 μ 1 t sh t sh μ t sl = (1 (1 ) ) (1 )(1 ) (1 )(1 ). In eriod, the rorietary software s roblem is aseii Maxπ s.t. < t s s. L OL Given the otimal eriod rice ( ), the rorietary software vendor solves the following roblem: 1 aseii Maxπ ( ) s.t < H μ H μ L w 1 t s f s w(1 t s (1 ) s ). Now, the OSS vendor s rofit function can be written as aseii O = ( 1 t sh)(1 O f s) O (1 O f s) O π μ μ = μ(1 t s )(1 f s ). 1 H O O The OSS vendor solves the following roblem: Maxπ s.t < ( t s f s ). O aseii O O H Further equilibrium analysis leads to the following Proosition. Proosition 4: When a high-tye customer enjoys higher value from OSS than from rorietary software but switching cost is high, eriod 1 customers of rorietary software will not switch to OSS. Among all other customers in eriod, high-tye customers will choose OSS while low-tye customers will buy rorietary software. When technically savvy customers derive higher utility from OSS than from rorietary software, the OSS dual-licensing model is viable. With high switching cost, i.e., customers of rorietary software would incur high cost to switch to OSS in the second eriod, they will stay with the rorietary software. However, the new high-tye customers who arrive in the second eriod will choose OSS over rorietary software. 18

20 Proosition 5: Prorietary software s eriod 1 rice always has a boundary solution while eriod- rice can be either. The detailed exressions are as follows: t(1 ω) ω f (1 μω) sh (1 μ) ωsl s 1 = (boundary), ω = L OL (boundary) t s s. The otimal rice for OSS is indeendent of rorietary software rices as follows: 1 O(interior) = (1 f s), (boundary) ( t s f s ). O = H It is interesting that the unique solution for eriod-1 rice is boundary. Given the high comlexity due to customers forward-looking behavior, it turns out that interior solution does not exist. Since no existing customer of rorietary software will not switch to OSS given high level of cost, OSS software vendor s otimal rice level is not affected by the scoe of switching cost. We further investigate the imact of switching cost on rorietary software vendor s rices. Figure illustrates how the scoe of switching cost influences rorietary software vendor s rices. It is reasonable that the rorietary software vendor charges more in eriod 1 as switching to OSS becomes more costly to the customers. 1.0 Imact of Switching ost on Prices Price Switching ost HwL Figure. Imact of Switching ost on Prorietary software Prices 19

21 ase III: Better OSS, Low Switching ost ( t s f s < w(1 t μs (1 μ) s )) H H L Grou 1: High (O) Low (), Grou : High (XO) Low (X), Grou 3: High (O) Low () The rorietary software vendor s rofit function can be written as aseiii = (1 1 t sh (1 ) sl ) 1 (1 )(1 1 t sl )(1 t sl ) π μ μ μ (1 μ)( t s )(1 t s ) (1 μ)(1 t s ) 1 L L L = (1 t μs (1 μ) s ) (1 μ)(1 t s ). 1 H L 1 L In eriod, the rorietary software s roblem is aseiii Maxπ s.t. < t s s. L OL Given the otimal eriod rice ( ), the rorietary software vendor solves the following roblem: 1 aseiii Maxπ ( ) s.t < L OL μ H μ L w 1 t s s w(1 t s (1 ) s ). Note that 1 1 t μsh (1 μ) sl is eriod 1 demand for the rorietary software which is always ositive. Thus, < t s s is a sufficient condition for L OL < L OL μ H μ L w 1 t s s w(1 t s (1 ) s ). Now, the OSS vendor s rofit function can be written as aseiii O = (1 1 t sh )(1 O f s (1 1 t sh )) O π μ ω μ( t s )(1 f s ) μ(1 f s ) 1 H O O O O = μ(1 t s )(1 f s ω(1 t s )) 1 H O 1 H O μ(1 t s )(1 f s ). 1 H O O Note that < ( t s s w(1 t μs (1 μ) s )) is sufficient to O L OL H L < ( t s s w(1 t μs (1 μ) s )). The OSS vendor solves the following roblem: O H OL H L O aseiii O Maxπ s.t < ( t s s w(1 t μs (1 μ) s )). O L OL H L Further equilibrium analysis leads to the following Proosition. 0

22 Proosition 6: When a high-tye customer enjoys higher value from OSS than from rorietary software and switching cost is low, all high-tye customers will choose OSS while all low-tye customers will buy rorietary software in eriod. Proosition 6 shows that commercial OSS is viable enough to attract existing customers of rorietary software as long as it gives considerable value to the technically savvy customers while switching cost is not significant. This result may encourage OSS vendors who consider commercializing its OSS which might reach a critical mass after years of free distribution. The key success factors include customizability of the OSS, easiness of it, and the number of customers who are technically caable. Next, we examine how otimal rices change with the scoe of switching cost. Proosition 7: There exists a unique solution for eriod-1 rice as 1 1 = (1 t μsh (1 μ ) sl ) while otimal eriod- rice can be The OSS vendor s otimal rice is as follows: 1 (interior) = (1 t ssl) (boundary) ( t s s w(1 t s (1 ) s )). = L OL μ H μ L t t w w1 f t 1 sh sh t w wsh O (interior) = (3 t 1 sh) O L OL 3 (1 ) (3 ) (1 (1 ) ) H 1 H (3 t 1 sh) 3 s ( t s ) s (1 (1 t) w ws s ), (boundary) = t s s w(1 t μs (1 μ) s ). As summarized in Proosition 6, when OSS allows a high-tye customer to enjoy sufficient benefit and switching is not much costly, all high-tye customers of rorietary software in eriod 1 will switch to OSS. Since the condition for eriod- ricing suffices the condition for eriod-1 ricing, the solution for eriod-1 rice is always interior. Interestingly, otimal OSS rice is influenced by switching cost arameter since in this high benefit/low switching cost region, all high-tye customers of rorietary software will switch to OSS. Figure 3 illustrates such imact. It shows that OSS rice decreases with H L 1

23 switching cost and can be set even higher than rorietary software s eriod- rice. The results imly that the commercial OSS model is convincing in this region. 1.0 Imact of Switching ost on Prices O Price Switching ost HwL Figure 3. Imact of Switching ost on OSS Price 6. onclusion ommercializing OSS is becoming an imortant and attractive issue among software vendors as the critical mass has been reached for certain OSS such as Linux. In reality, some OSS vendors (e.g., Red Hat and MySQL) have already emloyed either of the two available business models for OSS: the duallicensing model and the suort model. The generalizability of such successful commercialization of OSS has been widely discussed among ractitioners. Nevertheless, the viability of the OSS business models is still in question and the key success factors have not been clearly identified by academic researchers. In this aer, we examine the OSS business models under various scenarios and characterize the conditions under which the OSS business models are viable. As a benchmark, we examine the otimal ricing strategy under monooly. Our result indicates that the total net benefit from OSS is a key driver of a successful dual-licensing model under monooly.

24 Insired by a real-world software markets, we enrich our model to examine the imact of switching cost on the viability of the OSS business models. We set u a two-eriod game and analyze the customers incentive to switch from the market-dominating rorietary software to the newly introduced OSS. We find that the dual-licensing model is rofitable in the resence of large switching cost. When the switching cost is low, software vendors slit the market in the second eriod in a way that the rorietary software serves low-tye customers and the OSS vendor covers the high-tye customer segment. Interestingly, we find that the OSS may dominate the market in the second eriod when the customers enjoy considerable benefit while not suffering much from switching from rorietary software to OSS. Our aer contributes to the literature in the following ways. First, this aer examines the issue of ricing OSS through an economic lens. In site of the growing interest in rorietary OSS among industry exerts and jurists, little academic study has studied the ricing strategies under the OSS business models. We identify the factors that affect the viability of the ricing models for OSS and find the conditions under which each model can be successful. Second, our result can give ricing guidelines to OSS vendors, which is not clear in the current state. Finally, we model the motivations for and the barriers to oen source adotion, which rovides a better icture of the OSS market. onsidering such factors based on survey statistics may allow us to better understand the issue of OSS. Although our findings are significant, this study can be imroved in several ways. Firstly, modeling other strategic motivations of OSS vendors than ricing may bring insights to the results. For examle, oen source has been viewed as a marketing strategy by which the software vendor is able to build a customer base for its new software in a short amount of time. While this aer only considers firm-level customers and focuses on ricing strategies of OSS vendors, it would be an interesting direction to examine the marketing asects of OSS with individual customers, for examle, market exansion due to free distribution of OSS. Secondly, our model catures network externality in the switching cost function which increases with the network size. Isolating network externality and examining its imact may hel to understand the interlay between the network size of users of a free version of the OSS and the rofitability of a commercial version. 3

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