Open source adoption strategy

Electronic Commerce Research and Applications 36 (2019) 100872

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Electronic Commerce Research and Applications journal homepage: www.elsevier.com/locate/elerap

Open source adoption strategy a,⁎

Evangelos Katsamakas , Mingdi Xin a b

T

b

Gabelli School of Business, Fordham University, New York, United States Merage School of Business, University of California Irvine, United States

A R T I C LE I N FO

A B S T R A C T

Keywords: Economic analysis Economic theory IT capabilities IT management Network effects Open innovation Open-source software Open-source strategy Platforms Technology adoption

Open innovation in the form of open-source software (OSS) has been a transformative force in the software industry and beyond. The growth of open source has created new ways to develop, distribute and adopt software in organizations. Despite the associated impressive growth of open source research, a rigorous analytical examination of open-source adoption in organizations constitutes a gap in the literature. This article fills this gap by providing insights toward a comprehensive open-source strategy. It develops a game-theoretic analytical model to explain when organizations adopt open source software applications and platforms, and what the implications are. The analysis characterizes conditions under which organizations adopt open source software, and examines whether these adoption patterns are socially beneficial. The article shows that open-source adoption depends crucially on organizational IT capabilities, network effects, and the fit of OSS with the organizations' application needs. The model predicts that firms may sometimes adopt a heterogeneous IT architecture that consists of open source and proprietary software. Moreover, the results suggest that open-source adoption is sometimes socially inefficient. Overall, this analysis contributes a nuanced understanding of the adoption of open innovation in the form of OSS that should be useful to managers and policy-makers involved in related decisions. The article concludes with practical managerial recommendations on formulating a comprehensive open-source strategy.

1. Introduction Open innovation in form of open-source software (OSS) has been a transformative force in the software industry and beyond. The growth of open source has created new ways to develop, distribute and adopt software in organizations. Despite the associated impressive growth of open source research, a rigorous analytical examination of open-source adoption strategy in organizations constitutes a gap in the existing literature. This paper fills this research gap. OSS is software created and maintained through open source development practices and distributed using an open source license. (see http://opensource.org/ for a directory. OSS offers several potential benefits that favor adoption, such as low cost by avoid licensing fees, flexibility to read, modify and customize the source code as needed, greater control and avoidance of vendor lock-in and restrictive licensing terms. The low cost makes useful applications accessible to small and medium enterprises that cannot afford expensive solutions by commercial enterprise software vendors. Examples of popular OSS are Linux (server operating system), MySQL (database server), Mozilla Firefox (web browser), Apache (web server), BIND (DNS server), Sendmail (e-mail server), Snort (intrusion ⁎

detection system), WordPress (content management system), Python and R (programming languages), Hadoop (big data infrastructure), Ethereum (blockchain platform), Android (operating system) and many others. (See http://sourceforge.net/directory/enterprise for a directory.) However, there are several barriers to open-source adoption. These barriers include lack of awareness, marketing, open source skills and training, legacy integration concerns, forking concerns, pre-existing investments in proprietary systems, and immaturity concerns (Nagy et al., 2010). This confluence of potential benefits and costs complicates the decisions of organizations considering open innovation adoption in form of open source (Golden, 2005; Ven et al., 2008). A motivation of this research is to help managers make well-informed decisions regarding open-source adoption. Moreover, policy-makers need guidelines to understand the social welfare implications from OSS promotion and adoption. Proprietary software firms and OSS distributors need to understand how they can optimize their product design and marketing strategies based on the factors that shape the organizational adoption of OSS. Then, the critical research question is which organizations adopt OSS, for what applications, what are the factors driving adoption, how these factors interact to determine adoption outcomes, and what are the

Corresponding author. E-mail addresses: [email protected] (E. Katsamakas), [email protected] (M. Xin).

https://doi.org/10.1016/j.elerap.2019.100872 Received 13 July 2018; Received in revised form 21 June 2019; Accepted 21 June 2019 Available online 24 June 2019 1567-4223/ © 2019 Elsevier B.V. All rights reserved.

Electronic Commerce Research and Applications 36 (2019) 100872

E. Katsamakas and M. Xin

Another stream addresses the competitive implications of OSS. Casadesus-Masanell and Ghemawat (2006) studied a dynamic setting of competition between Windows and Linux. Economides and Katsamakas (2006a) analyze strategic differences between a proprietary and an open-source technology platform. Economides and Katsamakas (2006b) studied innovation incentives of application and platform developers. Comino and Manenti (2005) analyzed the welfare implications of public policies supporting OSS, assuming informed and uninformed users. Katsamakas and Georgantzas (2010) discussed open source in the context of disruptive innovation strategy. Hann et al. (2013) showed that participation in open source projects is associated with increased wages, especially when roles in project and employment are aligned. A rigorous economic analysis of open-source adoption strategies in organizations is a gap in this research literature, and this article aims to address it. The analysis builds on empirical findings on open-source adoption.

implications for organizational value creation and social welfare? While the academic literature has extensively researched software development and other open source themes, there is a notable lack of modeling research on organizational open-source adoption strategies. This article analyzes organizational adoption of OSS to address that literature gap. The article characterizes the conditions under which organizations adopt OSS and implications for social efficiency. One innovation of this research is that the model captures significant technology management and adoption concerns. It formalizes important IT aspects, such as the heterogeneity of firms’ applications and capabilities, and concerns, such as the optimization of IT architecture and investment. The model focuses on open source platform adoption. Organizations with heterogeneous IT capabilities consider adopting an open source or a proprietary platform to optimize their IT architecture (based on the range of applications used). The article finds a variety of adoption patterns that depend on the strength of the network effect and the fit cost for the applications. Most often firms have a heterogeneous software infrastructure using both proprietary and OSS. The stronger the IT capabilities of a firm the more widespread is the adoption of OSS. Weak IT capability firms may adopt proprietary infrastructure for all their applications, and firms with strong IT capabilities may adopt only open source for all their applications. The adoption outcome is not socially optimal: it is socially excessive under certain conditions and socially insufficient under other conditions. This article discusses sources of inefficiencies.

2.2. Organizational adoption of open source Empirical studies on organizational adoption of open source provide a useful background and complement to this analytical research. Dedrick and West (2004) noted that the literature has paid little attention to organizational adoption of OSS. They interviewed IS managers to develop a grounded theory of open-source adoption informed by diffusion of innovation and economics of standards. This exploratory study identified three categories of factors influencing adoption: technology (e.g., cost and reliability), organization (e.g., approach to IT innovation), and environment. Similar factors were identified by Morgan and Finnegan (2007), who explored IT managers’ perceptions of OSS benefits and drawbacks in thirteen European companies. Goode (2005) surveyed more than 500 Australian firms to explore why they did not adopt OSS. They did this because they could not see its relevance. Moreover, managers were concerned about lack of support, substantial learning costs, and incompatibilities with existing applications. Ven and Verelst (2006) also conducted five case studies in Belgian organizations that use open source server software. The motivations for adoption were relatively low cost, high reliability and availability of external support. Access to the source code is relevant only for those organizations that perform development based on OSS. Li et al. (2013) surveyed more than 100 companies about open-source adoption. They found that OSS-adopting organizations have greater availability of internal OSS human capital, or access to external OSS human capital. Spinellis and Giannikas (2012) provided a novel empirical study. Instead of survey research, they analyzed data on Fortune-1000 companies’ web browsing and serving activities. Their dataset included 278 million web server logs and thousands of network probes. They found that open-source adoption was significant and increased over time. Adoption is advancing from applications to platforms, and is influenced by network effects. Adoption is more prevalent in larger organizations, and in IT-intensive and knowledge-intensive sectors of the economy. In summary, three categories of factors seem to influence adoption according to empirical studies. First, factors related to software products include cost, quality, network effects, and type (platform or application). Second, organization matters, such as the approach to IT innovation, the strategic importance of IT, IT capabilities (including OSS experience and skills/human-capital), and the value of customization. Third, environmental factors such as industry competition and ecosystem of support and services all create impacts. The model that follows builds on these empirical observations.

2. Background The growth of OSS motivated a vibrant growth of practitioner writings (Raymond, 2001; DiBonna and Ockman, 1999; Fink, 2003; Rosenberg, 2000), and academic open source research (Weber, 2004; Fitzgerald, 2006). Several journal special issues and articles (Von Krogh and Von Hippel, 2006; Aksulu and Wade, 2010) provided comprehensive reviews of this extensive research literature. This section focuses on two open source research themes closest to the article’s research question: economics of open source and empirical studies on the organizational adoption of OSS. 2.1. Economics of open source The economics literature on open source consists of multiple streams (Lerner and Tirole, 2005; Rossi, 2004; Katsamakas and Xin, 2005). One stream focuses on the individual incentives to participate in open source projects. Johnson (2002) models the contribution to an open-source project as a problem of private provision of a public good and analyzes the effect of increasing the number of developers. Lerner and Tirole (2001, 2002) discuss the incentives of individual programmers and software firms to participate in open source projects. They argue that programmers are motivated by peer recognition and delayed career benefits, such as being hired by a software firm, or getting access to funding for future software ventures. A second stream analyzes the incentives of firms to contribute to open source development projects. Firms participate because they make money from complementary applications or services, they access development talent that they may hire in the future, they learn about competition and open-source technologies, and they promote open standards. Mustonen (2003) proposed a model in which the participation of programmers in open-source projects is endogenous and showed that a low implementation cost of an open-source application is crucial for its survival. Mustonen (2005) analyzed when a proprietary software firm may support the development of substitute OSS. Von Hippel and Von Krogh (2003) argued that OSS development combines elements of the private and the collective innovation models. Bitzer and Schröder (2005) modeled the incentive for private provision of OSS as a public good.

3. Model Our model considers multiple organizations that make software adoption decisions. Each organization needs to use a range of applications, for example core enterprise applications (server-side), collaboration applications, and personal productivity applications. Each 2

Electronic Commerce Research and Applications 36 (2019) 100872

E. Katsamakas and M. Xin

the cost of using it in more applications is almost zero (e.g., Google scaled its Linux infrastructure on thousands of servers avoiding an operating system licensing fee for each server). The cost of using W is mostly variable and depends on the number of applications, and the licensing fee p set by the vendor of W. An organization that deploys both L and W incurs an extra fixed cost CH, because it needs to manage a heterogeneous infrastructure. Deploying and managing a heterogeneous infrastructure is clearly costlier than managing a homogeneous infrastructure (only L or only W), including higher staffing costs, and dealing with potential incompatibilities. Another feature of the model is network effects (Economides, 1996; Parker and Van Alstyne, 2005; Bakos and Katsamakas, 2008). Organization θ benefits from network effects (hL (θ) , hW (θ) ) that depend on how many other organizations adopt the same platform (L or W) for the same range of applications. We assume linear network effect functions: θ hL (θ) = e [(1 − θ) (1 − tθ ) + ∫0 (1 − t (x )) dx ] hW (θ) = and 1

e [θtθ + ∫θ t (x ) dx ]. When the network effect e is strong, customers could be locked in either one of the competing platforms and sometimes the inferior one. Because this point is not the main focus of the current model, we restrict the magnitude of the network effect and assume that e < 1/4 .

Fig. 1. Organizations’ IT capabilities and IT architecture.

application runs on a software platform. Formally, there is a continuum of applications uniformly distributed in [0, 1]. There are two software platforms: a proprietary platform W and an open source platform L. Software platforms are differentiated based on which application each software fits best. We assume the proprietary software platform is located at 0, and the OSS platform is located at 1 on a line segment of length 1. If a firm adopts W or L for an application that does not locate at 0 or 1, then it incurs a product fit cost of c per unit distance. The whole range of applications used by each firm defines its IT architecture. Each firm adopts L or W for each one of its applications, in order to maximize the total value of its IT architecture. Hence, the model allows an organization to use L for some applications and W for others, if that is the IT architecture that creates the most value for the organization. Fig. 1 depicts salient aspects of model set-up. Organizations are heterogeneous with respect to their IT capabilities, indexed by θ , which is uniformly distributed in [0, 1]. There is a continuum of organizations of mass 1. A larger θ means stronger IT capabilities. The stronger the IT capabilities, the more value the organization can derive from open-source adoption, due to its ability to customize and extend the open source code. A firm with strong IT capabilities can take advantage of the openness of the code to customize its infrastructure, and are able to manage and support effectively the deployment of open source architecture. Firms with weak IT capabilities may find it difficult to get significant value out of open source, or they risk a failure, if there is no vendor to provide them with ready solutions and comprehensive support. Formally, the value that organization θ gains from adopting L for an application located at t is θ − c (1 − t ) , and the value from adopting W for an application located at t is VW − ct − p , where c is the fit cost. Thus, the value that the organization receives from its IT architecture by adopting W for t (θ) fraction of its applications that are close to W is U (θ) = uθ, L + uθ, W − CH , where uθ, L , uθ, W are the value derived from L and W, respectively:

u θ, L =

∫t

1

θ

4. Analysis and results An organization's IT adoption problem is discussed next. The IT architecture value maximization condition gives:

tθ =

c−e+V

∫0

e−1+c+V

−p

4.1. Profitability of the proprietary firm Given customers’ adoption decisions, we solve for the optimal pricing under each pattern listed in Table 1, and then compare the maximum profits for all cases to determine the profit-maximizing price and profit. The findings are summarized in the following proposition. All proofs not included in the body of the paper are in the Appendix. Proposition 1 ((Optimal Pricing Strategy).). The vendor’s optimal pricing strategy and profit in equilibrium depend on the range of parameter values:

• E1: •

(θ − c (1 − t )) dt − CL + hL (θ)

tθ

−p

W W Therefore, we have t (0) = , and t (1) = . 2c 2c There are six possible adoption patterns listed in Table 1. The maximal price that W can set and have positive sales is VW − e + c . This is decreasing in the network effect parameter e. This happens because an increase of the W price p benefits its competitor L more the stronger the network effect parameter e. In addition, the maximal price that W can charge and still have the whole market is VW − c − (1 − e ) , which is an increasing function of e. The reason is the increasing value of the product with increasing adoption base. Fig. 2 depicts all the possible patterns of open source platform adoption.

If e + c > 1/2 and 2e + c > 1, then p∗ = c/2 and π = c/8, (2e − 1) θ + c / 2 − e + 0.5 tθ = (Pattern 3) 2c E2: If e + c > 1/2 and 2e + c < 1, then p∗ = (c − e + 0.5)/3 and

π=

1 c (1 − 2e )

(

c − e + 0.5 3 , tθ 3

)

=

• E3: If e + c < 1/2 and 2c π= ( ) ,t =

and

u θ, W =

(2e − 1) θ + c − e + VW − p ≡ t (θ) 2c

1 c (1 − 2e )

c − e + 0.5 3 3

θ

(2e − 1) θ + 2(c − e + 0.5) / 3 (Pattern 2) 2c + e ≥ 1/2 , the p∗ = (c − e + 0.5)/3 (2e − 1) θ + 2(c − e + 0.5) / 3 2c

and

(Pattern 2)

(VW − ct − p) dt + hW (θ) The proprietary vendor’s profit is an increasing function of both the cost of product fit parameter c and the network externality parameter e, which is consistent with the results from literatures on network externalities and product differentiation. The equilibrium market

The cost structure of adopting L differs from the cost structure of adopting W. The open source platform L may require a substantial fixed cost CL to customize it and make sure it works for the organization, but 3

Electronic Commerce Research and Applications 36 (2019) 100872

adopt both W and L.

adopt c − e + VW − p 1 − 2e

c + e − VW + p 2e − 1

(θ − c (1 − t )) dt − CL + hL (θ ) +

∫0

tθ

(VW − ct ) dt

All firms adopt only W.

t (0) > 1 and t (1) > 1 B6

1 1 1 ⎛ + c − 2e⎞ (1 − 4e ) θ + 2c 2c ⎝ 2 ⎠

The social planner has to consider a tradeoff between social surplus from product fit and that from the network externality, which is related to the installed base of W or L for any application. The social surplus from the network effect is maximized when the market division line is flat, so that for each application all firms use W or all firms use L. On the other hand, the social surplus from product fit is maximized when the division line has a steep negative slope, so that high IT capability firms use L for more applications than low IT capability firms. To maximize the total social surplus, the social planner needs to balance these two effects. The result shows that the social optimal market share between W and L involves a division line that is flatter than the one in the market equilibrium. When c is relatively large compared to e, in particular c > 2e or c > 4e−0.5 when 0.25–0.5e < c < 1−2e, the difference in slope between the social optimal outcome and the market equilibrium is relatively small, which suggests a smaller surplus loss from network externality. The social optimal outcome leads to a market division line that is strictly above the one from market equilibrium. In other words, the social planner would like all firms to adopt more applications from W. This implies that when the product fit cost is high, the proprietary firm W charges too much for the software. Then, the social welfare loss is mostly from loss in product fit. As c decreases, the difference in slope between the two division lines increases, and the two division lines move toward each other. Hence, more and more social surplus loss comes from loss in network externality, and less and less comes from loss in product fit. The two division lines will finally cross. Fig. 4 shows areas of inefficient adoption for each possible equilibrium condition in Eqs. (1)–(3). As one can observe, the equilibrium division line is always steeper than the socially optimal market division line. In E1, all firms inefficiently adopt L for more applications than it is socially optimal. The inefficiency is larger, the stronger the IT capabilities of the firm. In E2, the pattern is similar, only now the high IT capability firms inefficiently adopt only open source. In E3 the socially optimal division is much steeper than in E1. We observe both excessive adoption of proprietary architecture by the low type firms and excessive adoption of open source architecture by the medium to high type firms.

p < VW − c − (1 − e )

adopt only L.

adopt only W; firms with θ > Firms with θ ≤

c + e − VW + p (2e − 1)

t S (θ) = −

t (0) > 1 and 0 ≤ t (1) < 1

both W and L; clients with θ >

c − e + VW − p 1 − 2e

1

θ

Solving the optimization problem, the social optimal adoption outcome is:

B5

p < VW − e − cVW − c − (1 − e ) < p p < VW + c − (1 − e )

c + e − VW + p (2e − 1)

Clients with θ ≤

p < VW − e − cVW + c − (1 − e ) < p B4

B3

1

∫0 ⎡⎣∫t

+ hW (θ) − CH ⎤ dθ ⎦

t (0) ≤ 0 and t (1) < 0 0 < t (0) ≤ 1 and t (1) ≤ 0 0 < t (0) ≤ 1 and t (1) > 0 t (0) > 1 and t (1) < 0

p < VW − e + cVW − e − c ≤ p p < VW + c − (1 − e )

All firms adopt both L and W

only adopt W; clients with

c + e − VW + p (2e − 1)

≤θ≤

c − e + VW − p 1 − 2e

adopt both W and L; firms with θ > c − e + VW − p 1 − 2e

Firms with θ ≤

All firms adopt only L.

t (θ )

B1 B2

p ≥ VW − e + c p < VW − e + cVW − e − c ≤ pVW + c − (1 − e ) < p

Adoption pattern

max

Constraint

Condition

4.2. Social welfare We determine the socially-optimal adoption pattern and compare it with the market equilibrium. A social planner maximizes the total surplus:

Pattern

Table 1 Adoption patterns conditions and W's profits.

condition depends on the magnitude of these two parameters. When the sum of c and e is relatively small, the vendor has less market power. The low IT capability firms adopt both products and the high IT capability firms adopt only L. Increases in c and e make it more and more costly for the high IT capability firms to adopt L for applications that W fits better (located closer to W), and hence gives the vendor more market power. Accordingly, the line that divides the market between L and W will get flatter with increasing c and e, as shown in Fig. 3. When both c and e are relatively large, all firms adopt both W and L for some applications under equilibrium.

⎡ c + e − VW + p ⎤ + ∫c1+ e − VW + p t (θ) dθ⎥ π = p⎢ (2e − 1) ⎢ ⎥ (2 e − 1) ⎣ ⎦ π=p

c−e+V

t (θ) dθ 1

π = p ∫0 t (θ) dθ

c − e + VW − p 1 − 2e

π = p ∫0

π=0

adopt only L.

W’s Profit function

−p

W ⎤ ⎡ c + e − VW + p 2e + ∫c + e −1V−W π = p⎢ + p t (θ ) dθ⎥ (2e − 1) ⎥ ⎢ e − (2 1) ⎦ ⎣

E. Katsamakas and M. Xin

4

Electronic Commerce Research and Applications 36 (2019) 100872

E. Katsamakas and M. Xin

Fig. 2. Patterns of open source platform (L) adoption (as in Fig. 1, (x, y) = (IT capabilities, IT architecture)).

scenario in which only W is available in the market (organizations do not have any open source option). Then the proprietary vendor of W is a monopolist and the value that organizations derive from adopting W is t U (θ) = ∫0 θ (VW − ct − p) dt + etθ . Each organization maximizes the value of its IT architecture as follows:

max U (θ) s. t . 0 ≤ tθ ≤ 1 tθ

Solving the optimization problem, we have tθM = constraints

VW + e − p c

are

VW + e − p c

VW + e − p . c

≤ 1 ⇔ VW + e − c ≤ p

The and

≥ 0 ⇔ p ≤ VW + e . Thus, if p < VW + e − c , then all firms adopt W for all applications; if VW + e − c ≤ p ≤ VW + e then all firms adopt W for VW + e − p of their applications; if p > VW + e then no one c adopt W for any application. The monopolist's profit function is:

π = ptθ = p

VW + e − p c

The monopolist's problem is:

max π

Fig. 3. Equilibrium adoption with increasing c and e.

s. t .

p

VW + e − c ≤ p ≤ VW + e

The FOC gives p =

4.3. Benchmark Case: Proprietary monopoly

If

VW + e 2

VW + e . 2

Then tθ =

VW + e 2c

and π =

≥ VW + e − c ⇔ c ≥ (VW + e )/2, then V

p∗

1 (V 4c W

+ e )2 > 0 .

= (VW + e )/2 and

+e

W < VW + e − c ⇔ c π = (VW + e )2 /4c, tθ = (VW + e )/2. If 2 ∗ < (VW + e )/2 , then p =VW + e − c , π = VW + e − c and tθ = 1. The monopolist’s profit is an increasing function of the intensity of

In order to provide a deeper understanding on the value of open source platform adoption, in this subsection, we examine a benchmark

Fig. 4. Areas of inefficient adoption are between the red and green line. (As in framework of Fig. 1, (x,y) = (IT capabilities, IT architecture)). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 5

Electronic Commerce Research and Applications 36 (2019) 100872

E. Katsamakas and M. Xin

Overall, the analysis shows that open source may co-exist with proprietary software, either within a firm that adopts a mixed opensource/proprietary architecture, or within a market for applications or platforms, when some firms adopt open source, and other adopt some proprietary solutions. From a policy perspective, open-source adoption is not always the most desirable outcome. This is an important lesson for managers of organizations, or government policy-makers, who may either ignore open source or see open source as a panacea. Many technology adoption decisions (e.g., adoption of large enterprise systems) are centralized in the hands of the CIO or a committee, as assumed in this article. However, this assumption may not always be true. Future research should focus more on related governance issues and their implications.

Fig. 5. Adoption of proprietary platform W when vendor of W is a monopoly (no open source option) (As in framework of Fig. 1, (x,y) = (IT capabilities, IT architecture)).

network externality, and a decreasing function of the product fit cost c. When the fit cost c is high, the organizations’ valuation for applications decreases rapidly with the distance of the application from the location of W. Hence, it is too costly for the monopolist to lower the price so that firms adopt W for all applications. Therefore, the profit maximization price is set such that all organizations adopt W for the applications that are relatively close to the location of W only. (See Fig. 5) This creates a loss of social welfare similar to the classical deadweight loss. Here, the welfare loss is not from some organizations being priced out of the market, but because all organizations are priced out of the applications that do not have a good fit with the platform of the monopolist. On the other hand, when the fit cost c is low, the vendor of W sets a price so that all firms adopt W for all their applications. A stronger e benefits the monopolist, since the firms’ valuation for the product increases with the adoption base. As expected, the W vendor’s profit under the monopoly case is higher than the W vendor’s profit under competition from OSS. The introduction of an open source platform in a market where only a proprietary platform is offered creates interesting new patterns of adoption, as one can see by comparing Figs. 2 and 5.

6. Concluding remarks: Towards an open-source strategy Building on our analytical modeling work and extrapolating our insights, we recommend a comprehensive open-source strategy, outlined in terms of three elements. First, an organization needs to assess what open source applications and what open source platforms to incorporate into its IT architecture, based on its IT capabilities, the value of openness, network effects and the quality of alternatives. The choice of applications is distinct from the choice of platforms, as our analysis has shown. A crucial parameter here is the value of openness for the organization. As a financial industry tech executive noted “open source has changed the traditional buy-versus-build scenario to one of buy, build or extend. Open source allows you to add features that are very specific to your business. Our organization makes extensive use of open source, and it will be an integral part of what we do for many years to come.” (2006 Linux on Wall Street Conference, New York). Open source is a software artifact derived from open innovation processes. In turn, the artifact becomes an enabler of further customization, open innovation and learning within the adopting organization. Second, an organization needs to think what open source components to incorporate into its own product architecture. The goal is to lower the cost structure, and maybe enable further customization. For example, a vendor of smartphones may incorporate an open source operating system into its products, after careful evaluation of benefits and costs. In this context, the utility function is the profit function from selling the end-product which incorporates open source components. Software customization of end-products may be a source of competitive advantage, if it used to achieve product differentiation. Third, an organization needs to contemplate what open source and open innovation practices to leverage across the organizational boundaries or internally. There are a number of questions to consider. (1) What development projects to “open-source” to facilitate development cost-sharing, collaboration, access to external knowledge and expertise, community feedback and ideas, and standardization and gain a leadership position in industry? (2) What existing open source projects initiated by third-parties to get involved with, in order to learn, influence and again establish technical leadership reputation? This involvement could also be a precursor of internal adoption of the output software. And (3) what open source development processes and tools to use internally. These choices can provide business value, but the transition to open innovation practices is not trivial, because the organization would need to adapt the processes through which they assimilate and produce knowledge (Chesbrough, 2003). For example, engagement in OSS development practices, involves technical change and organizational change affecting the roles of employees (Alexy et al., 2013), and some employees may not be supportive of such change. Overall, adoption of open source, seen as a process and output of open innovation practices, can provide significant value to organizations. This article provided rigorous insights into the adoption of OSS. Open source developers, while aiming at writing high quality code, set

5. Discussion The growth of OSS has had a significant impact on the software industry and the organizations adopting software. Despite the associated growth of open source research, a rigorous analytical examination of open-source adoption strategy constitutes a gap in existing literature that this we address. The model examined platform adoption in organizations adding to a nuanced understanding of when open source is adopted in organizations and what are the implications for managers and policy-makers. Organizations with heterogeneous IT capabilities seek to optimize their IT architecture (range of applications) deploying either an OSS platform, or a proprietary one, or both. In the model, network effects depend on the installed base of each application and a fit cost which captures the fact that a given software platform is ideal for some applications but less fit for other applications. We found that there are a number of adoption patterns that depend on the strength of the network effect and the fit cost for the applications. Most often firms adopt a mix of proprietary and OSS. Our results about the co-existence of open source and proprietary software in an organization are consistent with evidence from the IT press. For example, a survey of IT managers by Information Week as early as 2004 showed that 60% of the firms have mixed IT architecture, 2% exclusively open source and 38% exclusively commercial. The stronger the IT capabilities of a firm the more it adopts OSS. Weak IT capability firms may adopt proprietary infrastructure for all their applications, and firms with strong IT capabilities may adopt only open source. The adoption outcome is not socially optimal. The market does not internalize the network externalities, as much as a social planner does. Adoption of open source or proprietary software might be socially excessive at equilibrium, depending on the conditions identified. 6

Electronic Commerce Research and Applications 36 (2019) 100872

E. Katsamakas and M. Xin

Declaration of Competing Interest

the seeds of an open innovation revolution in business.

Authors have no conflict of interest. Appendix:. Adoption, prices and profits Table 1 presented earlier shows six cases, named patterns B1-B6. First, we solve each case and then we compare the maximum profits to determine price and profit in equilibrium. Pattern B1. When the price is too high, all firms adopt L or stay out of the market. No one adopts W. The proprietary vendor’s profit is equal to zero. Pattern B2. We solve the optimization problem by first using the first-order condition (FOC), and then checking the inequality constraints:

max p ∫0

c − e + VW − p 1 − 2e

t (θ) dθ

p

s. t . c − e + VW − p ≤1 0 < t (θ = 0) = 2c t (θ = 1) =

e − 1 + c + VW − p 2c

≤0

The FOCs give:

(c − e + VW − p) (c − e + VW − 3p) = 0 ⇒ p = c − e + VW or 3p = c − e + VW Here, p = c − e + VW is the minimum, and 3p = c − e + VW is the maximum. The constraints can be simplified as: c − e + VW − p > 0 ⇔ p < c − e + VW 2c c − e + VW − p ≤ 1 ⇔ −c − e + VW ≤ p 2c e − 1 + c + VW − p ≤ 0 ⇔ e − 1 + c + VW ≤ 2c

p

If e + c ≥ 1/2 , then the constraints are reduced to e − 1 + c + VW ≤ p < c − e + VW ; If e + c < 1/2 , then the constraints are reduced to − c − e + VW ≤ p < c − e + VW . Now check with p = (c − e + VW )/3: (c − e + VW ) < c − e + VW ⇔ c − e + VW > 0 3 (c − e + VW ) ≥ e − 1 + c + VW ⇔ 2e + c ≤ 1 3 (c − e + VW ) ≥ VW − c − e ⇔ 2c + e ≥ 1/2 3

Therefore, if e + c ≥ 1/2 and 2e + c ≤ 1, then p∗ = (c − e + VW )/3 and π = and π = (e − 0.5 + c ) (1 − 2e )

1 ; 4c

1 c (1 − 2e )

(

c − e + 0.5 3 ; 3

)

if e + c ≥ 1/2 and 2e + c > 1, then p∗ = e − 0.5 + c

if e + c < 1/2 and 2c + e ≥ 1/2 , then p∗ = (c − e + VW )/3 and π =

1 c (1 − 2e )

(

c − e + 0.5 3 ; 3

)

if e + c < 1/2 and

1 e ) c (1 − 2e) .

p∗

= −c − e + 0.5 and π = (0.5 − c − 2c + e < 1/2 , then Pattern B3. We next solve the optimization problem by using the FOC, and then check the inequality constraints: 1

max p ∫0 t (θ) dθ p

c − e + VW − p ≤ 2c e − 1 + c + VW − p >0 2c

s. t . 0 < t (θ = 0) = t (θ = 1) =

The FOC gives: πp′ = 1 , 2

1 (2c 4c

1

+ 2VW − 4p − 1) = 0 ⇒ p =

2c + 2VW − 1 4

Since e < the constraints are simplified asVW − c − e ≤ p < e − 1 + c + VW . If − c − e > e − 1 + c ⇔ e + c > 1/2 , then since VW − c − e = 0.5 − c − e < 0 , the constraint becomes 0 ≤ p < e + c − 0.5. Now we check if the constraints are satisfied: 2c + 2VW − 1 ≥0⇔c≥ 4 2c + 2VW − 1 < e + c − 0.5 ⇔ 1 4

1 2

> e + c , then this case is impossible. If

0 < 2e + c (e + c − 0.5) (1 − 2e )

Hence if 1 < 2e + c , then p∗ = c/2 and π = c/8; otherwise p∗ = e + c − 0.5 and π = . 4c Pattern B4. It's easy to verify that the constraints are only valid when e + c < 1/2 , and the constraints can be reduced to 0 ≤ p < VW − c − e . c−e+V

−p

W ⎡c + e − V + p ⎤ 2e max p ⎢ (2e −W1) + ∫c + e −1 −VW + p t (θ ) dθ⎥ p (2e − 1) ⎣ ⎦ s. t . c − e + VW − p t (θ = 0) = >1 2c

t (θ = 1) =

e − 1 + c + VW − p 2c

<0 −e + VW − p 1 − 2e

−

). Given the properties of the quadratic function, we have

p∗

The first-order derivative of the profit function is: πp′ =

(

c = (1 − 2e)

p 1 − 2e

(

c − VW + e + p c

). When p = V

= VW − c − e and π = 7

W

− c − e , the first order derivative is positive

c (VW − c − e ) . 1 − 2e

Electronic Commerce Research and Applications 36 (2019) 100872

E. Katsamakas and M. Xin

Pattern B5. We solve te following optimization problem:

max p ⎡ ⎢ p ⎣

1

+ ∫c + e − VW + p t (θ) dθ⎤ ⎥ (2e − 1) ⎦ s. t . c − e + VW − p > 1 ⇔ p < VW − e − c t (θ = 0) = 2c 0 ≤ t (θ = 1) =

c + e − VW + p (2e − 1)

e − 1 + c + VW − p 2c

< 1 ⇔ 0 ≤ e − 1 + c + VW − p < 2c

⇔ p ≤ e − 1 + c + VW and e − 1 + VW − c < p The constraints are reduced to e − 1 + VW − c < p < VW − e − c if e + c > 1/2 . Since VW − e − c < 0 , this case is never optimal. And the the constraints are reduced to e − 1 + VW − c < p < e − 1 + c + VW = e − 0.5 + c if e + c < 1/2 . Since e − 0.5 + c < 0 , this case is never optimal either. Pattern B6. We next solve:

max p p c − e + VW − p >1 2c e − 1 + c + VW − p >1 2c

s. t . t (θ = 0) = t (θ = 1) =

The constraints can be simplified as: current case is

c − e + VW − p 2c e − 1 + c + VW − p 2c

> 1 ⇔ −e + VW − c > p

. Since e < 1/2 , we have the optimal pricing and profit under the

> 1 ⇔ e − 1 + VW − c > p

p∗ = e − 1 + VW − c . When VW = 0.5, the optimal pricing p∗ = e − 0.5 − c < 0 and π = e − 0.5 − c < 0. Therefore, this case cannot π = e − 1 + VW − c

be optimal.

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