Product Strategy for Commercial Open Source Software Vineet Kumar Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213 [email protected]

Brett Gordon Graduate School of Business, Columbia University, Uris 511, 3022 Broadway, New York, NY 10027 [email protected]

Kannan Srinivasan Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213 [email protected]

Commercial open source software (COSS) products – privately developed software based on publicly available code – represent a rapidly growing multi-billion dollar market. A unique aspect of competition between COSS firms is that many use software licenses that require their enhancements to be made publicly available, creating an incentive for some firms to free-ride on others contributions. Despite its success, the COSS industry has received scant attention in the marketing literature. We develop a model of competition between COSS firms that incorporates the particular terms of the software licenses. Our model consists of (1) a vertically differentiated duopoly of software firms where product quality is composed of a mix of features and usability and (2) a developers market where firms hire developers to improve their product quality. Our analysis reveals several counterintuitive findings. First, when developers skills are unobservable to firms, all firms profits and consumer surplus can be higher than when skills are observable. Second, COSS products can be of higher quality than traditional closed source products. Third, when the market is large and signaling is costly, firms can benefit when they are mandated to make their software code public, even when one firm completely free-rides. Key words : Open Source, Product Strategy, Software Market, Signaling Models

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

1.

1

Introduction

Open source software has fundamentally altered the nature of competition in the software market and has gained widespread adoption among both consumers (e.g., the Firefox browser) and firms (e.g., the Apache web server). There is a growing business model of commercial open source software (COSS) firms that build commercial products based on open source software.1 Many software firms, such as Sun Microsystems, Oracle, and Computer Associates, have adopted the COSS business model for specific products.2 Despite its remarkable success in the marketplace, COSS has received surprisingly scant attention in the marketing literature. We aim to further our understanding of this growing market by studying the product strategy of COSS firms, developing a model that incorporates the unique aspects of this industry in a competitive setting. The open source movement gained prominence in the 1990s as a small community of expert developers who made the source code to their programs freely available for anyone to use and modify. In contrast, the source code for commercial software, such as Matlab or Microsoft Office, remains proprietary and not available to the public. The growth of open source software has been rapid: market researcher IDC estimates the value of this market will grow to $5.8 billion in 2011.3 Large technology firms such as IBM, Sun Microsystems, and Hewlett Packard have launched multibillion dollar open source initiatives, a trend that is likely to continue.4 Consumers often find that freely available open source software is not user-friendly and can require significant technical expertise. COSS firms add value to the base open source software by (a) improving user interfaces, offering technical assistance, product documentation and user manuals, 1

Open source software should be distinguished from two other forms of freely available software. Some firms make their software available for free (“freeware”) but do not make the source code available (e.g. Adobe’s Acrobat Reader). Another form is voluntary open source, where a firm releases the source code but with strong restrictions on its use and redistribution. We do not consider these cases because the strategic issues involved differ significantly from those faced by COSS firms. 2

Sun Microsystems produces StarOffice, a productivity suite that competes with Microsoft Office, based on the open source software OpenOffice. An exhaustive list of commercial applications based on open source can be found at Wikipedia, http://en.wikipedia.org/wiki/Commercial open source applications. 3

IDC, “Worldwide Open Source Software Business Models 2007-2011 Forecast: A Preliminary View,” May 2007.

4

Infoworld, “Open Source Platforms: IBM Invests $1 Billion in Linux,” December 18, 2000.

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and other support services (collectively termed “usability”) and (b) providing additional functionality that extend the basic operations performed by the software (collectively termed “features”). In essence, COSS firms provide the hand-holding many consumers require to effectively utilize open source software (Lakhani and von Hippel 2003), and have significantly aided the popularity of open source software among businesses and consumers. Red Hat Inc. is a prime example of a COSS firm that offers commercial products built upon the freely available Linux open source software, and are designed to simplify and extend the management and administration of the Linux operating system. Within the COSS industry, important distinctions exist between products, depending on the type of license used for the software. The GNU General Public License (GPL)—the most popular open source license—governs the terms under which software is released and dictates how modified versions may be sold or distributed, requiring any changes to be freely available in source code format.5 Thus, in COSS markets for software released under the GPL license, the “features” part of the product is a shared or public good and additional features developed by any firm must be made publicly available. We term settings with mandatory sharing as shared-features markets. In contrast, open source software licensed under the Berkeley Software Distribution (BSD) license allows firms to freely utilize features as part of their products without requiring them to release the source code. This aspect is similar to firms competing with traditional software products, and we term these settings as private-features markets. COSS firms are allowed to keep usability improvements private under either license.6 Thus, Red Hat must make publicly available any feature contributions it makes to Linux, but the firm can keep any usability enhancements private. These unique characteristics of the COSS market and the distinctions from traditional software products lie at the core of several puzzling aspects of the COSS industry. First, why would profitmaximizing COSS firms contribute to features, knowing their competitors can take advantage of these contributions? For example, Red Hat is known to be a large contributor to the features code 5

The full text is available from http://www.gnu.org/licenses/gpl.txt.

6

See Laurent (2004) for details on the exact terms of common licenses.

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of Linux even though it could confine its focus to usability improvements. What is the rationale for firms to develop features, and will all firms find it profitable to do so? Second, in the presence of free-riding behavior, how can COSS firms make positive profits? Third, industry observers note that some COSS products are of comparable or better quality than traditional software products. How can a market based on free-riding produce better quality products? We examine these issues by constructing a model of competition that captures the unique characteristics of the COSS market. We model two interacting markets: a product market consisting of consumers and COSS firms producing software products, and a developers market in which firms hire developers to create or improve software. We characterize firms’ optimal product design and pricing strategies as well as developers’ decisions under different competitive structures. In the product market, we formulate a vertically differentiated duopoly of ex-ante identical software firms. Product quality is a composite characteristic consisting of a mix of features and usability. Firms compete either in a private-features market or in a shared-features market. In both cases, firms make strategic product development decisions by simultaneously choosing the levels of features and usability to incorporate into their software products, and then setting prices after observing the quality level of the competitor’s product.7 The qualities and prices of all products are fully observable to consumers before they make a purchase decision. In the developers market, firms hire developers to create new features and improve usability of their software products. Developer skills in designing and improving functionality (features) and ease-of-use (usability) are the primary production inputs for software products, whether produced by commercial firms or independent open source developers (Boehm 1981, Lakhani and von Hippel 2003). We model a developers market with unobservable skills that explains how developers try to signal their skill-level by contributing features code to open source. Contributions are costly for the developers, with high-skilled developers incurring a lower cost than low-skilled ones. Firms observe these contributions and infer the skill-levels (or types) of developers and make them wage offers. 7

There are other dimensions of software quality such as reliability, portability, and efficiency that researchers have measured and quantified (Kan 2003). We do not explicitly model these alternative quality dimensions primarily to ensure tractability of the model in deriving useful insights in a competitive setting.

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Developers may choose to accept these offers or reject them, in which case they get a reservation wage level. We specifically evaluate the effects of signaling by developers on the product strategies of COSS firms. Our framework is consistent with empirical findings (Roberts et al. 2006) that developers signal their skill-level by contributing to open source features. We build upon the seminal job-market signaling model of Spence (1973), although we explicate several points of distinction in the model section. Our analysis helps explain the puzzles detailed above by obtaining these counterintuitive observations as equilibrium outcomes of our model of COSS markets. A high-quality firm may contribute to publicly-available features because having a larger base of features increases the value of differentiating on usability, which the firm can keep private. The low-quality firm has lesser incentive to contribute since it is able to free-ride. This behavior is consistent with empirical findings that the high-quality Red Hat contributes significant features code to Linux, but other vendors do not make similar contributions (Pal and Madanmohan 2002). Firms operating in markets with sharedfeatures make positive profits by differentiating more on usability than they would in privatefeatures markets. Product quality is higher in equilibrium in the shared-features case because reduced competition between firms in the developers market results in a lower cost of quality. To summarize, we consider two types of product markets and two types of developers markets, where each corresponds to a different set of institutional settings. Table 1 specifies these different markets or competitive structures and introduces our terminology. The quasi-public (QP) market Table 1

Model of Product and Developers Market

Product Market

Developers Market Perfect Imperfect (Observable Skills) (Unobservable Skills) Shared-features common-source quasi-public Private-features closed-source quasi-closed

denotes the case in which COSS firms compete with products created from open source software released under GPL (or similar) licenses, and is characterized by a shared-features product market and an imperfect developers market. The quasi-closed (QC) market corresponds to the case when

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firms develop software products based on BSD (or similar) licenses, with a private-features product market and an imperfect developers market. We compare the competitive product strategies of software firms and other measures, such as profits and consumer welfare under the three different markets highlighted in Table 1.8 The key insights from our analysis are the following. First, in shared-features markets, freeriding is the equilibrium strategy for the low-quality firm: only the high-quality firm develops both features and usability, whereas the low-quality firm only develops usability. This occurs due to the nature of competition in the product market: the high-quality firm contributes to features to enable a higher level of product differentiation, whereas the lower quality firm has less of an incentive to differentiate its product. The high-quality firm attains higher profits and contributes more features when the other firm free-rides compared to the case when both firms individually develop features. The intuition is that free-riding by the low-quality firm ensures that firms are not competing over developers. This reduced competition between firms lowers the equilibrium wage firms offer developers and thus reduces firms’ software development costs. These effects overcome the effect of reduced product differentiation and allow the high-quality firm to achieve higher profits. Second, asymmetric information causes COSS firms to distort their quality choices relative to closed-source firms. Firms in the shared-features market differentiate more on usability since they cannot differentiate on features, compared to firms competing in the private-features market. Both firms in the quasi-public market can develop less usability, though for different reasons. The highquality firm reduces features because of free-riding, and finds reducing usability to be optimal, since both dimensions of quality are complements. The low-quality firm has access to the same features as the high-quality firm but reduces usability to increase product differentiation to reduce the intensity of competition. 8

We do not detail the results for the common-source market since it is not commonly observed, and we can prove firms would not find voluntarily sharing features optimal when developer skills are observable. These results are available from the authors.

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Third, competition between the COSS firms in the quasi-closed market can induce developers to contribute more to open source features compared with the quasi-public market. This result is counterintuitive because feature contributions are made public under quasi-public competition. If the market is sufficiently large and signaling is not too costly, competition between the COSS firms in the quasi-closed market leads to a high equilibrium wage offered to developers. This high wage creates a strong incentive for high-skilled developers to make sufficiently large contributions to open source features to ensure separation from low-skilled developers, leading to an overall increase in the number of open source features developers produce. Fourth, the presence of asymmetric information resulting in signaling by developers contributing to open source features can result in higher profits for COSS firms and higher consumer surplus compared with the case of closed-source software firms. Signaling allows the firms to improve the quality of their products, and diminishes the intensity of competition between the firms. However, as signaling cost increases, firms can become less profitable because inducing developers to contribute to open source becomes more expensive, which in turn increases the intensity of competition between the firms. Our paper is related to two distinct streams of literature that have largely remained disparate. The first stream includes the broad literature on strategic product design, incorporating consumer preferences, firm decisions, and marketing mix variables. Krishnan and Ulrich (2001) provide a comprehensive and accessible survey of product design, including papers in both marketing and operations literatures, but the survey is focused more on tangible products distinct from the software products we study. In general, this area has focused on functionality, product line variety, and incorporating specific aspects of the consumer decision process (Kuksov 2004). From a methodological viewpoint, our paper is closely related to models of vertical differentiation with endogenous product quality decisions, beginning with the influential paper by Shaked and Sutton (1982), extended to include quality-dependent production costs by Moorthy (1988) and further by Desai (2001) to incorporate a horizontal taste component.

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Some recent papers studying firms’ strategies in the context of open source software evaluate product choices, pricing, and competition between open source and closed-source software. Leppamaki and Mustonen (2003) examine the strategy of a monopolist firm that hires developers to create a competing open source product. However, the model assumes a perfect market for product developers, ignores the multi-dimensional aspect of quality, and does not consider strategic interaction between the firms and developers. Economides and Katsamakas (2006) model two-sided pricing of software platforms (e.g., operating systems) and applications and evaluate the effects of competition between the platform providers. Casadesus-Masanell and Ghemawat (2006) focus on the dynamic pricing strategy of a profit-maximizing firm (Microsoft) facing a competitor (Linux) who prices at zero in the presence of network effects. However, the quality of the open source product in these papers is exogenous and neither paper explores the strategic interaction between firms or product design choices. Our work is complementary to these as we examine COSS products that do not compete with open source, but are based on open source. The second stream of literature examines the development process of developers who contribute to open source projects. The scope of topics in this stream is quite large; thus, we restrict our discussion to understanding the motivation of developers to contribute to open source. Contributing to open source projects primarily serves as a signal on the job market (Leppamaki and Mustonen 2003).9 Empirical evidence supports the notion that developers contribute due to economic incentives, such as higher wages or career concerns (Roberts et al. 2006, Hertel et al. 2003), and in a survey of the literature, Lerner and Tirole (2002) also conclude that a significant amount of “evidence is consistent with an economic perspective.” Thus, our paper integrates the above streams by jointly modeling the interaction between the open source developers market and the game of strategic interaction between COSS firms. The results in this paper have several managerial implications for firms involved in the open source industry. First, the type of license determines the structure of competition and has important effects in the product market as well as the developers market. These interactions must be 9

Other explanations include “ego gratification” due to peer recognition for technically challenging tasks (Hars 2002) and altruism or the “warm glow” effect (Andreoni 1990).

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Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

understood in order to accurately determine the optimal product strategy. Second, when faced with asymmetric information or an imperfect market for product developers, firms can leverage it to reduce the intensity of competition and increase profitability. Managers need not fear the quasi-public market since it can be more profitable than the quasi-closed one. The rest of the paper is organized as follows. §2 presents the formal model and analysis of the quasi-closed market. We develop the model of the product market with consumers and COSS firms, as well as the developers market which details the interaction between COSS firms and developers, in §2.1 and §2.2. We then evaluate the effects of different markets, explicitly characterizing the quasi-public and closed-source markets in §3. We demonstrate how the model and analysis differ from the quasi-closed case, and compare the three markets (QC, CLOSED, and QP) focusing on equilibrium quality levels, firm profits, and consumer surplus. In §4, we discuss the managerially relevant aspects of competitive strategy in COSS markets, and provide directions for further research in this area.

2.

The Quasi-Closed (QC) Market

We characterize two separate but interconnected markets: the first is a product market in which consumers purchase software produced by the firms, and the second is a developers market in which firms hire developers. The interaction between these markets generates the equilibrium outcomes of quality and its components, usability, and features, and the prices set by firms as well as developers’ wages. We consider the three different markets listed in Table 1, beginning with the quasi-closed as the baseline model in this section, and subsequently examining how the quasi-public and closed-source markets differ from this baseline. 2.1.

Model

Our product market model builds on earlier models of vertical differentiation (Shaked and Sutton 1982, Moorthy 1988) in which firms choose product quality, and incorporates the unique aspects of COSS products under either a shared-features or private-features market. We describe the sequence of events in the model in four stages common to all markets.

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Stage 1: Developers contribute to open source to signal their skill-level if it is not observable. Stage 2: Firms simultaneously make wage offers to developers, who decide whether to accept the offers. Firms determine product qualities. Stage 3: Firms simultaneously set prices in the product market. Stage 4: Consumers make their purchase decisions. The pricing subgame beginning in Stage 3 is characterized by the revenue functions because the cost of quality is fixed and sunk in Stage 2, and we assume marginal costs are zero since software is an information good. In Stage 2, firms observe developer signals and simultaneously make wage offers and product development decisions. In Stage 1, developers choose whether to contribute to open source features to signal their skill-level. Product Market: Consumers and Firms We formulate consumers’ utility for software products and the firms’ pricing and product design decisions. Consumers choose whether to purchase software from one of the COSS firms or not to purchase a product, in which case they receive a utility of zero.10 Consumers are heterogeneous in their preferences for quality, and a consumer indexed by θ has utility for a software product of quality q at price p given by: U (q; θ) = θq − p The marginal valuation for quality is distributed uniformly, θ ∼ U[0, M ]. Market coverage is derived endogenously.11 The quality q of a software product depends on its level of features F and its level of usability s and is defined by the function q = Q(F, s). A software product’s features or functionality define the set of tasks that can be accomplished with the product, whereas usability refers to the ease with which a consumer can make use of the product’s features. Consumers place more value on products 10 11

Since consumers have no utility for features alone, they do not derive positive utility from open source code.

Expert consumers may value features but not usability. These customers would not purchase the software product but have value for the amount of open source features developed in equilibrium. We do not model such customers in the product market analysis but examine the effect of the equilibrium choice on expert consumers’ surplus by determining the number of open source features.

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that perform more functions and have higher usability, so that

∂Q ∂F

> 0 and

∂Q ∂s

> 0. However,

increasing the number of features may result in an overly complex product, and consumers may not be able to take advantage of many features if the product’s usability level is low. Conversely, a high level of usability is likely to be more beneficial when provided in conjunction with a large number of features.12 These two dimensions of quality are therefore complements, implying

∂2Q ∂s∂F

>

0. A simple functional form that captures this complementarity and is concave in both features and usability is Cobb-Douglas: Q(F, s) = F α sβ , where α > 0, β > 0 and 0 < α + β < 1 ensures concavity. We further choose α = β =

1 4

to obtain closed-form results that facilitate interpretation,

and verify the properties for other values of α and β through numerical analysis. 13 The assumption of complementarity of features and usability influences and drives some of the results. The formulation above for consumer utility and product quality is common to all markets. We focus first on the quasi-closed market where each firm builds upon publicly available open source features. Both firms have access to f0 features initially provided by the open source community. The level of f0 contributed is determined in equilibrium through developer signaling in the product developers market. Each firm determines its product quality by hiring f developers of skill-level η ∈ {ηL , ηH } to generate an additional ηf features, for a total of F = (f0 + ηf ) features, and by hiring s usability developers to develop usability. The corresponding wages for these feature and usability developers are w and ws , respectively, and the total cost of the resulting product is: C(f, s) = w · f + ws · s The quality of firm j’s product is 1

qj = Q(f0 + ηfj , sj ) = [(f0 + ηfj ) sj ] 4 12

For example, one reason the Apple iPhone has become hugely popular is that its intuitive user interface has made complex smart-phone applications more accessible, despite the fact that much of the same functionality was available on earlier smart-phones. In general, consumers do not benefit from products with a significant imbalance between their level of features and usability. Thompson et al. (2005) shows that consumers who purchase overly complex products face “feature fatigue” and that improving usability can significantly help consumers effectively utilize the features. 13

The results are available from the authors.

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Note that the quality depends on the freely available open source code f0 , additional features fj that the firm develops, and the usability level sj the firm chooses. Letting q1 > q2 , without loss of generality, we proceed to determine the consumer who is indifferent between the choices available. Consumer θˆ12 is indifferent between firm 1 and firm 2’s products, characterized by θˆ12 q1 − p1 = θˆ12 q2 − p2 , whereas consumer θˆ20 is indifferent between purchasing firm 2’s product and not purchasing any product, determined by θˆ12 =

p2 . q2

We compute the market

size mj for firm j to be:       p1 − p2 1 ˆ 1  1 1 p1 − p2 p2 ˆ ˆ M− and m2 = m1 = M − θ12 = θ12 − θ20 = − M M q1 − q2 M M q1 − q2 q2

(1)

Since software is an information good, we set variables costs to zero. The revenues are determined from the market size by Rj = pj mj (pj , p−j ), which yields the firms’ revenue maximization problem as a price-setting game: R1∗



p1 − p2 = max M − p1 q1 − q2



p1 and

R2∗



p1 − p2 p2 = max − p2 q1 − q2 q2



p2

(2)

These revenue functions are sufficient to allow us to derive the optimal prices set by the firms in Stage 3 given product quality choices from Stage 2. We next consider how the market for product developers influences the quality choices firms make in the product market. Market for Product Developers We explicitly model the market for developers, focusing on features developers, because creating new functionality is perceived to be more challenging and hence a more credible signal of skill-level (Roberts et al. 2006, Hars 2002). The market for usability developers is assumed to be a competitive market in which developers are available for hire at an exogenous wage ws .14 Developer skill-level is heterogeneously distributed with two types: highskilled (high-type) and low-skilled (low-type). Since our primary focus in not on the marginal effects of developer skills but rather on market level outcomes, we set the low-type developer’s skill-level low enough so that firms will never find it profitable to hire them if their type is observable. We 14

Our analysis is not qualitatively different if we endogenize ws , but it would complicate the exposition and analysis without adding much insight.

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ensure this condition is met by setting ηL = 0. As a consequence, only the skill-level of high-type developers directly influences equilibrium outcomes, and we drop the subscript on ηH for brevity and refer to it as simply η. The high-type developers have a reservation option r drawn from a distribution with density function ψ(·), cumulative distribution function Ψ(·), and support in the range [R, R] where 0 ≤ R < R.

15

This option can be interpreted as the utility a developer derives from her current job,

and she will accept a wage offer made by firms only if it exceeds the reservation option r. The low-type developers have a fixed reservation option RL = 0.16 Developers’ types are unobservable, and firms find it difficult to decide which developers to hire. Contributing to open source features provides a mechanism for developers to signal their skill-level to potential employers. These contributions are publicly observable and available to prospective employers to evaluate developers’ skills. Open source projects have “gatekeepers” who decide which submissions to include in the project. The gatekeepers are known to be effective in preventing lowquality code from being included in the project (Bagozzi and Dholakia 2006). These factors ensure that high-type developers contribute more to open source features than low-type developers. As is standard in signaling models, the cost to make a successful contribution differs according to the developer’s type. To contribute e features, high-types incur a cost of cH · e and low-types incur cL · e, with cH < cL indicating high-types face a lower signaling cost. The low-type developers will attempt to masquerade as high-type developers so that firms will hire them and pay higher wages based on their perceived skill-level. Thus high-type developers have an incentive to separate themselves from low-type developers, using contributions to open source features as a signaling device. If a developer chooses to signal and accepts an offer made by either of the COSS firms, she faces a wage schedule w(e). Her utility from accepting such an offer is represented by ut (w, e) = w(e) − ct e. Consequently, her maximum utility and optimal effort are 15

We do not require any further assumptions on the functional form of Ψ for our results. We use the general form in our description since it helps in presenting and interpreting different effects. 16

This assumption is made for simplicity and can be relaxed without qualitatively changing results in the paper.

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

u∗t = max w(e) − ct e e

and

13

e∗t = arg max w(e) − ct e. e

To ensure separation of the high- and low-types, the low-type developers must find it prohibitively expensive to imitate the high-type developers: this condition is represented below as ICL , the incentive compatibility for low-type developers.17 The high-type developers must be compensated such that they are at least indifferent between their reservation option r and working for COSS firms, represented below as individual rationality constraint IRH . (ICH )

w(eH ) − cH eH ≥ w(eL ) − cH eL

(IRH )

w(eH ) − cH eH ≥ r

(ICL )

(3)

w(eL ) − cL eL ≥ w(eH ) − cL eH

The above individual rationality and incentive compatibility constraints must hold for a developer with reservation utility r in all separating equilibria. Firms never find it optimal to hire low-type developers at any positive wage after their type is revealed, and w(eL ) = 0. Since low-type developers will never receive a wage higher than their reservation wage (RL = 0) in any separating equilibrium, they will not contribute to open source to signal in the developers market. Therefore, low-type developers do not have an individual rationality condition IRL that needs to be satisfied. The condition in ICL then reduces to 0 ≥ w(eH ) − cL eH . Developers with reservations wage r ≤ rˆ = w(eH ) − cH e∗H will choose to signal and developers with r > rˆ choose their reservation option and will not signal. Thus the number of developers who signal is NH = Ψ(ˆ r) = Ψ(w(eH ) − cH eH ). The above IR and IC conditions are necessary but not sufficient to determine the equilibrium wage, which further requires modeling the competition between firms for developers. The initial level of open source features available in Stage 1, f0 (w), is a function of the wage and is determined in equilibrium by the number of high-type developers and their contributions: f0 (w) = Ψ(w(eH ) − cH eH )eH 17

We focus only on separating equilibria and not on pooling equilibria in order to convey the main insights in the simplest manner.

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Observe that the wage influences contributions of the developers, which in turn induce different levels of open source features. That is, a higher equilibrium wage leads to higher initial feature contributions through developers signaling their skill-levels, which in turn raises the initial quality of the products available to the COSS firms. In the canonical job-market signaling model (Spence 1973), workers capture the entire surplus less the signaling loss, and perfect competition between hiring firms ensures zero firm profits. Our model uses the essential signaling insight from Spence, but several features distinguish our context from his. The first distinction is that in Spence’s setting, multiple workers do not make a difference because a firm’s profits are a linear function of worker productivity. However, in our verticallydifferentiated setting, firms hire developers until the increase in marginal profit from hiring an additional developer is equal to the market wage for that type. This setting allows the ex-ante identical firms to make positive profits because they earn a surplus for each developer who is not at the margin. The second distinction is that higher levels of signaling in Stage 1 reduce firms’ demand for developers in Stage 2. Developers would therefore like to signal a minimal amount both because of signaling cost and because of reduced demand. Firms on the other hand prefer developers to signal more because it later decreases the intensity of competition in the market for developers. These two distinctions are essential to accurately model the COSS market and ensure signaling by developers and profitability of firms in equilibrium. Overall, in our model the product market and the developers market are therefore intricately connected due to the unique nature of COSS products. We proceed to characterize the resulting equilibrium interaction between these markets, and evaluate the equilibrium strategies and outcomes beginning with the last stage of the product market competition. 2.2.

Equilibrium Analysis

In this section, we analyze the subgame-perfect equilibria of the above model. The pricing subgame beginning in Stage 3 applies to all cases for the product and developers markets, and we begin

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at the last stage and solve the model by backward induction. We examine the firms’ product design decisions, explicitly characterizing the production of open source features in equilibrium. The saliency of modeling the market for product developers becomes apparent from the interaction between contributions made by the developers to open source features, f0 and the subsequent product quality offered by the COSS firms. Pricing Equilibrium The optimal price for each firm in stage 3 is derived as a best response function of the quality levels of both firms and the price set by the other firm. Firms’ revenues, prices, and the consumer surplus are represented as functions of product quality levels in Lemma A1 (detailed in the Appendix). This establishes the equilibrium outcomes of the pricing sub-game conditional on quality decisions made in Stage 2. Note that factors such as wages, costs, and market characteristics determine revenue and prices only in the sense that they affect the quality levels chosen by the firms in the previous stage, and the pricing subgame does not directly depend on these factors. We proceed to characterize the equilibrium of Stage 2 of the game, how firms make product design choices of features and usability, and evaluate the degree of product differentiation in equilibrium. Product Quality Equilibrium The solution of the sub-game beginning in Stage 2 requires the firms to strategically determine the optimal product design, i.e. the mix of features and usability depending on the market characteristics, with both firms making simultaneous moves. The profit functions are derived by substituting the features and usability levels into the revenue functions in Lemma A1and accounting for the costs of development:   1 1 1 4M [(f0 +f1 )s1 ] 2 [(f0 +f1 )s1 ] 4 −[(f0 +f2 )s2 ] 4   − wf1 − ws s1 π1 (f0 , f1 , s1 , f2 , s2 ) = 1 1 2 [(f0 +f2 )s2 ] 4 −4[(f0 +f1 )s1 ] 4   1 1 1 M [(f0 +f1 )(f0 +f2 )s1 s2 ] 4 [(f0 +f1 )s1 ] 4 −[(f0 +f2 )s2 ] 4   π2 (f0 , f1 , s1 , f2 , s2 ) = − wf2 − ws s2 1 1 2 4[(f0 +f1 )s1 ] 4 −[(f0 +f2 )s2 ] 4

We attempt to collapse the Stage 2 sub-game involving two strategic quality components to one overall quality level for each firm. If the competitive best response quality chosen by a firm only depends only on the overall quality of its competitor, how the competitor chooses to develop

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usability and features to attain a specific quality level should not matter. If best responses only depend on quality, firms will minimize the cost of attaining a given quality level by optimally combining a mix of usability and features. However, it is unclear whether the best response depends only on the quality or whether it depends on either features or usability levels as well as quality. The following result provides a resolution and explicitly characterizes the optimal decomposition of quality.18 Proposition 1. [Quality Decomposition]The optimal level of features and usability to contribute to a quality target qj for firm j when the first stage produces f0 features due to developers’ signaling actions is as follows: (i) Low-quality region: When qj2 < f0

q

w , ηws

fj∗ = 0, (ii) High-quality region: When qj2 ≥ f0 fj∗

r

=

ws 2 f0 q − , wη j η

q

∗

the optimal quality decomposition is

s∗j =

qj4 , f0

w , ηws

the optimal quality decomposition is

s =

r

w 2 q , ws η j

and C(qj ) = ws

qj4 f0

r

and C(qj ) = 2

(4)

wws 2 q − wf0 η j

(5)

where fj∗ and s∗j are the optimal levels of features and usability, and C(q) is the minimum cost of obtaining quality q. In the low-quality region, the firm does not add to the available open source features f0 , but adds qj4 f0

to the usability level. The firm does not add features beyond f0 because consumers do not value

them highly or because the market size is small. We focus further analysis on the high-quality region, where the existing level of open source features f0 is inadequate for product market competition. We focus on this region primarily because the analysis of the low-quality region obviates the need for analyzing the market for product developers and does not explain why developers contribute to open source features.19 18

We will subsequently find that such a decomposition does not apply to the quasi-public market.

19

The full set of results for the low-quality case is available from the authors upon request.

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To choose a quality level in a private-features market, the above result tells us cost of quality is quadratic (whereas consumers’ utility is linear in quality). Using the optimal decomposition and the cost of quality, we can solve for the equilibrium levels of features and usability from Stage 2. Proposition 2. In the quasi-closed market with firms vertically differentiated in equilibrium, each firm develops both usability and features. Specifically, given f0 open source features initially available for use, quality and its components are M φj qj = 2

r

η , ws w

M 2 φ2j fj = 4

r

η f0 − , 3 ws w η

M 2 φ2j sj = 4

r

η ws3 w

for j ∈ {1, 2}, where the constants φ1 and φ2 are defined in the appendix. No symmetric equilibrium exists in which firms choose the same quality q1 = q2 = q. Both firms develop features incrementally more than the freely available open source code f0 since we focus on the high-quality region in Proposition 1. Firms optimally reduce the number of features they develop when there are more open source features, since these are additive and perfect substitutes. We find firms differentiate their products more on the less expensive dimension of quality, implying that if features are less expensive to produce, the firms will differentiate more on features (f1 − f2 > s1 − s2 ). The intuitive explanation is that firms differentiate their products more on the dimension that yields a greater return to differentiation. Equilibrium in Market for Product Developers We previously derived product market equilibria assuming the firms were able to hire high-type developers at wage w. We now determine the equilibrium wage by evaluating the firms’ demand for developers and the supply dictated by wage as well as signaling considerations. We solve the developers’ signaling game by focusing on separating equilibria in which the high-type and low-type developers choose different contributions to open source software. We investigate what equilibrium wage results under asymmetric information in a signaling equilibrium. A critical issue to examine is the effect of the wage on the product market equilibrium and we study its dual effects. First, an increase in the wage level w makes high-type developers contribute more

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to open source, which increases the signaling contribution f0 . Second is the substitution effect between the available open source features f0 and those developed by the firms (f1 or f2 ), implying that firms develop fewer features as more open source features become available in Stage 1. We evaluate the conditions required for separation of the high-type and low-type developers, and how much they contribute to open source features. The signaling equilibrium is characterized by assuming a fixed wage w for the high type developers, and identifies the level of open source feature contributions developers make to signal their type, and the number of developers who will choose to signal. The following result provides a characterization of separating equilibria in terms of wage and contributions to open source features, beginning with necessary conditions, and providing a unique equilibrium after refining incredible equilibria.

Lemma 1 [Separating Equilibrium] For the case of unobservable developer skills in any product market, the separating equilibria for the signaling game between the developers and firms can be characterized by the following conditions where r is the reservation utility of a developer and w is the market wage: (i) The necessary conditions for contributions for each developer type are:    {0}, r > w 1 − ccHL i   eL (r, w) = 0, eH (r, w) ∈ h  w , w−r , r ≤ w 1 − cH cL cH cL (ii) The least-cost separating equilibrium is characterized by high-type developers making contributions e∗H (r, w) and common out-of-equilibrium beliefs µ(H |e, w) for firms specified by    ( cH 0, r > w 1 − 0, e < eLCS (w) c L  e∗H (r, w) = and µ(H | e, w) =  w , r ≤ w 1 − cH 1, e ≥ eLCS (w) cL cL This least-cost equilibrium is the only separating equilibrium that satisfies the Intuitive Criterion, and the unique least-cost contribution by high-type developers is eLCS (w) =

w . cL

(iii) In the least-cost separating equilibrium, the number of high-type developers who contribute to open source features is NH∗ (w) = Ψ(w − cH eLCS (w)) and the number of features developed in Stage 1 is f0 (w) = Ψ(w − cH eLCS (w)) · eLCS (w).

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19

Part (i) of Lemma 1 identifies necessary conditions that any separating equilibrium must satisfy. These conditions arise from the individual rationality and incentive compatibility constraints specified in (3). In the full-information case, low-type developers were never hired because their skill-level was too low. With unobservable types, a separating equilibrium allows firms to perfectly distinguish low-type from high-type developers. In any separating equilibrium, low-types do not contribute to open source features since they will not be offered a positive wage, so a necessary condition is eL = 0. The high-type developers must signal by contributing a sufficient number of features to ensure low-types will not find imitation profitable: this condition is captured by (ICL ) in equation (3), using which we obtain e∗H (w) ≥

w . cL

However, the high-type developer must also

find signaling to be better than her reservation utility r: w − cH eH > r, so a developer r will signal a w−r cH

to obtain wage w. An infinite number of such separating equilibria exists in which   a high-type developer with reservation utility r ≤ w 1 − ccHL may make any contribution in the h i continuum cwL , w−r . Each such equilibrium is equally valid without imposing further restrictions cH maximum of

on out-of-equilibrium beliefs. This multiplicity of equilibria requiring refinement is a well-known feature of similar signaling models, and the Intuitive Criterion (Cho and Kreps 1987) is commonly used to refine ‘unreasonable’ equilibria. Part (ii) of the lemma establishes the out-of-equilibrium beliefs corresponding to the Intuitive Criterion to determine a unique separating equilibrium that is least-cost. In our context, least-cost also refers to the minimum separation required at each prevailing wage. This purification of out-of-equilibrium beliefs requires that any observed deviation from the equilibrium path will more likely be from the type that could profit the most from the deviation. This refinement gives us the minimum contribution to open source the high-type developers must make to sustain a separating equilibrium, and the corresponding minimum wage firms must pay to ensure separation. For part (iii), focusing on the minimum amount of separation given by eLCS (w), we know developers with r < r∗ = w − cH eLCS (w) will choose to signal, so the number of developers who signal is Ψ(r∗ ) = Ψ(w − cH eLCS (w)). The number of open source features produced in Stage 1 is simply the product of the number of developers choosing to signal and the contribution of each developer.

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The equilibrium wage is determined by matching demand and supply for high-type developers: f1∗ (f0 (w∗ ), w∗ ) + f2∗ (f0 (w), w∗ ) = NH∗ (w). Using the demand from Proposition 2, we can implicitly characterize the equilibrium wage in the quasi-closed market: M 2 (φ21 + φ22 ) 4

r


η 3 = (wQC ) 2 Ψ(wQC − cH eLCS (wQC )) 1 + 2eLCS (wQC ) ws

(6)

What are the properties of the wage and how does it depend on the model primitives? These issues are detailed in the following result. Proposition 3. The least-cost separating equilibrium wage for high type developers in the imperfect developers market satisfies the following properties: It is increasing in market size QC

QC

QC

> 0), signaling cost ( ∂w > 0), and skill-level ( ∂w∂η > 0), and decreasing in wage paid to ( ∂w ∂M ∂cH QC

usability developers, ( ∂w < 0). ∂ws Both firms compete for high-type developers, and developers anticipate this competition. The wage increases with the market size M since a larger market will cause the firms to invest more in developing a higher quality, and competition between firms drives wages higher. The wage is higher when the complementary dimension of usability is less expensive, because a low ws permits firms to invest more in usability, which raises the value of features for consumers and firms. When signaling is difficult (more expensive) for the high-type developers, fewer will signal and more will choose their reservation option, thereby resulting in fewer open source features. The marginal value of features is then higher for the firms since the substitution effect of open source features is weaker, thereby raising the developers wage.

3.

Effects of Market Structure

The previous section evaluated the case of firms producing COSS products under the quasi-closed market. We now focus on the other two markets in Table 1, namely the quasi-public and the closed-source cases. The quasi-public market results in COSS software products, and has a different product market, but the same imperfect developers market in which firms cannot observe the skills of the developers. The closed-source market, on the other hand, has a product market that is

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

21

identical to the quasi-closed case, but a perfect developers market where the skills of the developers are known to the firms. We then compare the three markets by examining the equilibrium outcomes in both the product markets as well as the developers markets. 3.1.

Quasi-Public (QP) Market

The quasi-public case is characterized by a shared-features product market and an imperfect developers market. As in the quasi-closed case, we begin with the product market model, and examine how these markets differ. The developers market description requires additional structure, which we explore below. Model In the quasi-public market, firms must share any features they develop based on open source. The GPL license, used by Linux and many other open source software products, incorporate this condition on any person or firm modifying or adding code to the software. The quality of firm j is therefore: 1

qj = Q(Fj , sj ) = [(f0 + ηfj + ηf−j ) sj )] 4 where firm j hires fj features developers and sj usability developers. The difference between the quality here and in the quasi-closed market is the extra ηf−j term due to the shared features. The rest of the product market model in the quasi-public case is identical to the quasi-closed market. However, this extra term substantially changes the strategic interaction and equilibrium outcomes as we demonstrate below. Equilibrium Analysis Since the features each firm develops are available to competitors, it is insufficient to examine a firm’s overall quality for competitive responses. Each firm’s feature contribution directly affects the quality of the other firm, so Proposition 1 does not apply to the quasi-public market. The minimum cost to attain a given quality for a firm depends on both firms’ contributions to features as well as the quality levels of both firms, so it is impossible to uniquely characterize the best response in terms of the firm’s qualities. The threat of free-riding by one firm—leading to decreased product differentiation and increased price competition (as in Shaked and Sutton (1982) and Moorthy (1988)) —makes it unclear whether

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firms developing features can be sustained in equilibrium. Observe that features are required to ensure the software product has value to the consumers, and product sales are positive only when consumers can purchase a product with features. Since firms free-ride off each other’s feature contributions and cannot appropriate the benefits of developing more features, the equilibrium level of feature contributions is not obvious. It is also interesting to examine the development choices made by the (ex-post) high-quality firm compared to those made by the low-quality firm. Do both firms contribute to features and usability, and, if so, to what degree? The following result provides the outcomes for markets with shared-features behavior where consumers value highquality products sufficiently, so firms find it optimal to develop features in addition to the open source features f0 . We evaluate the equilibrium quality levels for the firms in the shared-features market and examine how they differ from the private-features market. In the quasi-public market, both firms can use the initial open source features f0 as well as each other’s feature contributions in their software products. Features cannot contribute directly to product quality differentiation, but can only magnify the effect of usability differences between the firms, implying that ex-post, the low-quality firm invests less in usability than the high-quality firm. We find that under this competitive structure, only the high-quality firm develops further features beyond f0 in equilibrium. The low-quality firm fully free-rides on the features provided by the high-quality firm. Why does the high-quality firm choose to provide features? The intuition arises from the fact that quality dimensions are complements, implying that the marginal utility of usability is increasing in the level of features. The high-quality firm develops features because doing so enables it to increase the level of product differentiation investing more in the usability dimension, thus reducing the level of competition. Proposition 4. In the quasi-public duopoly market with firms producing different quality COSS products in equilibrium, the ex-post high-quality COSS firm will develop features but the low-quality COSS firm will not do so. The features, usability, and overall quality levels in this equilibrium are detailed below:

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

f1∗

=

s∗1 = q1∗ =

r

η(σ1 −σ2 )3 w 3 ws (4σ1 −σ2 )3

M 2 σ13

M 2 σ15

r

η(σ1 −σ2 ) 3 wws

4σ1 −σ2 M σ12

23

r

η(σ1 −σ2 ) wws

4σ1 −σ2

− fη0

,

f2∗ = 0 s∗2 =

M 2 σ1

r

η(σ1 −σ2 ) 4 σ2 3 wws

4σ1 −σ2 r

,

q2∗ =

M σ 1 σ2

η(σ1 −σ2 ) wws

4σ1 −σ2

where σ1 and σ2 are defined in the Appendix. The product market outcome above has a critical implication for the developers market. Both firms will not compete over developer talent because the low-quality firm will not hire developers (f2∗ = 0). Note that since the high-quality firm is a monopsonist in the developers market, it will only pay the minimum wage to the high-type developers. However, firms not directly competing with the two COSS firms often value high-type developers. For example, a company in the embedded Linux business may value a developer who has contributed features to the Linux kernel but does not directly compete with Red Hat. We formalize this notion by modeling the presence of an alternative market in which a high-type developer receives a fixed wage of w ˆ when her type is known to this market. The alternative market provides a minimum value to signaling by developers, who may otherwise choose not to signal when faced with a monopsonist COSS firm. The high-quality firm cannot commit to offer a higher wage than w ˆ before developers signal, since such a commitment would be incredible after the developers have signaled. The wage offer cannot be lower than w ˆ or the firm will not be able to hire any high-type developers. The highquality firm cannot induce the high-type developers to contribute more to open source than the minimum amount eLCS (w) ˆ that is required to separate them from the low-type developers. This is because the firm makes wage offers after the signaling stage, and even if the developers made more contributions than required for signaling, the firm will not offer a wage higher than w ˆ is Stage 2. Therefore, the wage offered by the high-quality firm is exactly w. ˆ The developers expect the firm to pay exactly w ˆ and choose to contribute only the minimal level required for separation. Note that this happens even though it may be Pareto–improving for firms to pay a higher wage and for

24

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developers to contribute a higher level to open source features.20 By Lemma 1, we then know the contributions made by the developers to open source features in Stage 1 is eLCS (w) ˆ = 3.2.

w ˆ . cL

Closed-Source Market

The product market model and analysis for the closed-source market is identical to the quasi-closed case, but the developers market is significantly different. In the closed-source market, the firms face no information asymmetry, and they can observe the skill-levels (types) of developers. This obviates the need for signaling by the high-type developers. Since the rationale for high-type developers contributing to open source features was to reveal their superior skill-level, there is no open source software produced in this case. This market can be interpreted as traditional software firms like Microsoft or Oracle competing in both the product market and in the developers market. Model We can model the closed-source market as a special case of the imperfect developers market in which the high-type developers face zero signaling cost (cH = 0), and the low-type developers face an infinite signaling cost (cL → ∞). These signaling costs are consistent with the requirement that there are no initial open source features created in Stage 1, i.e. f0 = 0 since w cL →∞ cL

lim eLCS (w) = lim

cL →∞

= 0. Developers retain their reservation option and have the option of

accepting offers from firms, as in the quasi-closed case. Equilibrium Analysis The number of developers willing to give up their reservation utility at a wage w is simply Ψ(w). The implicit expression for the equilibrium wage in the closed-source market 2 q M 2 (φ2 3 1 +φ2 ) η can be derived from (6) as = (wCLOSED ) 2 Ψ(wCLOSED ). How do the properties of 4 ws the wage here differ from the quasi-closed market? We find the comparative statics effects derived for the quasi-closed wage in Proposition 3 apply to the closed-source case, except for the effect of 20

The following assumption that the wage level of the alternative market w ˆ is neither too low nor too high is required to ensure the wage in the quasi-closed market is not changed due to the presence of the alternative market.         r ˆ 3 3 M 2 (φ21 + φ22 ) cH w ˆ η cH 2w (w) ˆ 2 w ˆ 1− 1+ < < (w) ˆ 2 w ˆ 1− 1+ cL cL 4 ws cL cL The first condition ensures that demand from the high-quality firm for developers at wage w ˆ in the quasi-public market does not exceed the number of high type developers signaling, whereas the second ensures that when both firms hire developers in the quasi-closed market, a higher wage induces developers to signal beyond eLCS (w) ˆ = cwˆL .

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

25

signaling cost, cH .21 Observe that Proposition 2, which applies to the product market will continue to hold for the closed-source market since the developers market determines the wage, and the effects of signaling directly apply there. However, the wage level affects the quality components, usability, and features, so the product design outcomes in the closed-source market will be different than in the quasi-closed market. 3.3.

Comparison of Markets

We have derived equilibria under three markets: quasi-closed, quasi-public and closed-source. In each case, ex-ante identical firms compete in the product as well the developers market and are differentiated ex-post. We now focus our attention on how firms’ profits, product qualities, and price levels compare across markets. These results will allow us to highlight some potential insights for managers in industries with open source software. Additionally, critical policy issues that have been unexplored in these emerging competitive structures deserve further examination. In order to ensure sufficient conditions for the results, we assume that the signaling cost for high-type developers is not excessive:    h i CLOSED Assumption 1. (A1) cH < c˜H where Ψ wCLOSED 1 − c˜cHL 1 + 2w cL = Ψ(wCLOSED )

Our first result below compares the equilibrium wage across the different markets. We demonstrate that the closed-source market provides the highest wages, followed by the quasi-closed market and then the quasi-public market. Competition between firms drives higher wages for developers so we intuitively expect wQP < wQC , which turns out to hold. The intuition for why wQC is less than wCLOSED is this: The number of developers is reduced because they incur a cost to signal in the quasi-closed market, compared to the closed-source market, and this ought to lead to higher wages. However, this effect is dominated by the substitutability effect, which refers to the fact that that the marginal value of features development to firms is lower due to the presence of open source features. Therefore, developer wages are lower in the quasi-closed market under asymmetric information compared with the closed-source market with complete information. 21

We do not list this finding as a formal result. It is clear from the proof of proposition 3 that the effects after taking the limits as cH → 0 and cL → ∞ will not be altered.

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Result 1 The equilibrium wage for high type developers in the developers market is ordered as follows when the cost of signaling is not excessive: wQP < wQC < wCLOSED We examine the equilibrium provision of open source features since, which is a critical variable of interest to policy makers as well as to the initial creators of open source software who can choose the license terms. Firms seeking to enter the market are interested in the total number of open source features available because it provides a base they can use to build upon. Institutions concerned with the appropriate policies to facilitate open source innovation have a similar stake in the level of open source features. Result 2 (Contribution to Open Source) The equilibrium contribution to open source features is higher under the quasi-closed market compared with the quasi-public market when the market size is large and the signaling costs for high-type developers to separate are low. In the quasi-public market, both firms have access not only to the contributions to open source made as a signal by high-type developers, but also to the features developed by the ex-post highquality firm. In contrast, the quasi-closed market allows firms to keep their features private leaving only the signaling contributions to features as open source. Thus, we expect more open source features in the quasi-public market. However, when the consumer market is large, firms compete for developers more intensely in the quasi-closed market because there is a greater price premium for a higher quality product. This creates a greater incentive for the high-type developers to separate themselves from the low-type developers. When separation is relatively easy (cH is small compared with cL ), more high-type developers enter the market, which results in more open source features. The above result would not have been apparent without modeling the effect of the market for product developers, which points to the importance of examining both markets in conjunction. We proceed to evaluate how the characteristics of the product and developers markets determine the equilibrium levels of usability and features and the overall level of quality.

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

Result 3 (Product Quality)

27

(i) The low-quality product always has a lower quality level in

the quasi-closed market compared to the quasi-public market. (ii) For small (large) market size and low (high) signaling costs, the high-quality software product in the quasi-closed market is characterized by higher (lower) quality levels compared to the quasi-public market. (iii) When separation is easy, both firms in the quasi-closed market produce a higher quality product compared to the closed-source market. (iv) The usability ratio

s1 s2

is always larger for the quasi-public market compared to the quasi-closed

market, and the features ratio

f1 f2

ferentiation captured by the ratio

is larger under the quasi-closed market. The quality difq1 q2

is higher for the quasi-closed market compared to the

quasi-public market. The low-quality firm’s quality is always higher in the quasi-public market since the firm is able to free-ride on the features of the high-quality firm, even though the low-quality firm may develop a lower level of usability. This effect holds independently of the model parameters, such as market size or signaling costs. In fact, as the market size increases, the quality difference of the low-quality firm compared across the quasi-closed and quasi-public markets increases further. The effect of market on the high-quality firm’s quality level is more nuanced: it depends on the market size, signaling cost, and cost (or wage) to develop usability. When the market size is large and usability wages are low, there is higher demand for developers and lower cost of developing a higher quality product, which increases the equilibrium wage high-type developers receive. These effects are collectively stronger for the quasi-public market than in the quasi-closed market; therefore, the quality level chosen by the high-quality firm is higher in the quasi-public market. This effect is stronger when the signaling cost is higher for the high-type developers, which leads to increased competition between the firms in the quasi-closed market. In contrast, when the market size is small, signaling is relatively easy and usability wages are high. Then the effects discussed above are weak and the high-quality product is better under the quasi-closed market.

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Next, we compare the quality levels between the quasi-closed and the closed-source markets. We find that when firms do not have complete information on developer types (quasi-closed) product qualities are higher because competition between the firms for developers is diminished due to the presence of open source features, resulting in lower wages. This result requires assumption (A1), i.e. the signaling cost for the high-type developers should not be excessive. If developers of different types have similar signaling costs, the excessive distortion of open source contributions required for the separating equilibrium leads to diminished participation by high-type developers, leading to lower quality levels in the quasi-closed market. In both the quasi-public and quasi-closed markets, the marginal benefit of usability increases with the level of public contribution of features. This finding implies that more signaling by programmers increases the firms’ incentives to develop usability. In the quasi-public market, the firms differentiate more on usability, but this differentiation is not sufficient to overcome the fact that the features levels are the same for both products since they are publicly available. The quality differentiation in the quasi-public market is therefore lower than in the quasi-closed case. We do not separately study the price levels since they are determined in Lemma A1to be proportional to the equilibrium quality levels that we have discussed above. We focus next on the components of quality, features, and usability. The equilibrium usability and features outcomes determine the revenues and profits of the firms under each market, and we examine these below. Result 4 (Profits) The low-quality firm makes a higher profit under the quasi-public market. When the market size is small (large) or signaling is easy (difficult), the high-quality firm makes a higher profit under the quasi-closed (quasi-public) market. The market structures result from the choice of license governing the distribution of open source software, and in our model this choice is exogenously imposed on the firms. We observe that the gains to the low-quality firm from free-riding in the quasi-public market are too significant to be affected by market parameters, and the low-quality firm would always prefer the quasi-public market. However, the case of the high-quality firm is somewhat subtle. When the market is not

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

29

too large and signaling costs are low, the high-quality firm prefers the quasi-closed market because the competition for developers is less intense and the firm does not have to share features with the low-quality firm. However, when competition becomes too intense, the high-quality firm would prefer to let the low-quality firm free-ride in order to decrease the competition in the market for developers. In a situation where the high-quality firm controls the copyright of the source code, the firm may choose to release its source code freely just to mitigate the intensity of competition. Indeed, we observe in practice several software firms that are voluntarily releasing the source code to their software products, and the reasoning above helps us to understand a possible driver for this behavior. Next, we examine the effect of market on consumers, detailed in the following result. Result 5 (Consumer Surplus) The consumer surplus is higher in the quasi-public market compared with the quasi-closed or closed-source markets under all market conditions. The above result is general and does not depend on the parameters. It summarizes that from the viewpoint of consumers, the quasi-public market is the best, and points out that socially-conscious contributors should consider licensing their software under a GPL-like framework, making features publicly available. This result is not what we might intuitively expect: the lack of information by firms regarding the true types of developers increases the surplus to consumers. The reason is that both the utility of the signal (open source features) used in the products developed by the firms and decreased competition in the developers market due to free-riding on features by the low-quality firm. However, the consumer surplus must be balanced against potentially lower profits made by firms and lower wages received by high-type developers under the quasi-public market.

4.

Discussion and Conclusion

Several firms are building commercial software products based on freely available open source software, and it is critical for managers in the software industry to understand the strategic imperatives that drive product design decisions in these markets. We have constructed a model to determine product strategies under competition between firms, evaluating competition in two markets. We

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formulate a product market where consumers and firms transact, and a market for developers who contribute to open source projects to signal their skill-level and are hired by firms to create and enhance their software products. We specify two types of product markets (shared-features and private-features) and different informational conditions under which the developers market operates (observable or unobservable skill-levels) to capture the details of the COSS market. The value of having an integrated model of both markets is apparent from our findings, and incorrectly treating one of the markets to be exogenously specified would lead to erroneous results. We find several counterintuitive and novel results. First, competing software producers can both make a higher profit under a quasi-public (or GPL-like) market in the presence of free-riding, when developer types are unobservable. Second, contribution to open source projects can be higher under a quasi-closed market under reasonable conditions. Third, consumers benefit more under a quasi-public market, independent of conditions in the developers market. Several of our results are empirically testable, and further empirical research is warranted to inform both managers and policy makers. Our work lends itself to extension along several dimensions. First, when firms consider making their software open source, we could examine their choice of license and how this is determined in equilibrium. We have provided a rationale for why firms can release their proprietary software as open-source. Second, several researchers have focused on intrinsic benefits to highly skilled developers in contributing to open source software, and this additional effect can easily be incorporated in our model. Since this fast-growing and important market has not been adequately examined by marketing academics, we expect several issues involving product design, pricing, so forth to be explored further.

Appendix. Mathematical Appendix We denote the uniform pdf and cdf of θ ∼ U [0, M ] by g(θ) =

1 M

and G(θ) =

θ M

for notational clarity.

Lemma A1 is similar, but not identical, to the corresponding case in Shaked and Sutton (1982). The firm with higher ex-post quality sets a higher price, and the ratio of prices increases with the quality ratio. The

31

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pricing power of both firms diminishes when the quality levels are closer than when they are dissimilar due to the reduced intensity of competition. Lemma A1 In a vertically differentiated duopoly with quality levels q1 and q2 , with q1 > q2 The optimal prices are set at: p∗1 (q1 , q2 ) =

2M q1 (q1 −q2 ) 4q1 −q2

4M q12 (q1 −q2 ) (4q1 −q2 )2

M q1 (q1 −q2 )q2 (4q1 −q2 )2

and R2∗ (q1 , q2 ) =

and p∗2 (q1 , q2 ) =

M q2 (q1 −q2 ) 4q1 −q2

. The revenues of the firms are R1∗ (q1 , q2 ) =

. The consumer surplus is CS(q1 , q2 ) =

2 M q1 (4q1 +5q2 ) 2(4q1 −q2 )2

.

Proof of Lemma A1 For setting prices, firms only focus on the revenues since the quality choices have been made in the prior stage. The FOCs of revenue with respect to price are:   ∂R1 p∗1 p∗1 − p∗2 p∗1 − p∗2 ∂R2 1 1 p∗2 ∗ = M − = − = 0 and + p − − − =0 2 ∂p1 p∗ ,p∗ q1 − q2 q1 − q2 ∂p2 p∗ ,p∗ q1 − q2 q2 q1 − q2 q2 1

2

1

2

Solving these FOCs simultaneously, we obtain   q1 − q2 M q2 (q1 − q2 ) p∗1 (q1 , q2 ) = 2M q1 and p∗2 (q1 , q2 ) = 4q1 − q2 4q1 − q2 Substituting these prices in (2), we obtain the expression in the Lemma. The consumer surplus with these quality levels given g(θ) =

1 M

is:

Z

θ1

CS(q1 , q2 ) =

(θq2 − p∗2 ) g(θ)dθ +

θ2

Z

M

(θq1 − p∗1 ) g(θ)dθ =

θ1

M q12 (4q1 + 5q2 ) 2 (4q1 − q2 )2

Proof of Proposition 1 When the product contains no open-source features, the firm’s problem, (f ∗ , s∗ ) = 1

ws w minf,s wf + ws s subject to the constraint (ηf s) 4 = q yields f ∗ (q) = q 2 ηw and s∗ (q) = q 2 ηw . The overall cost s q s 2 of providing quality q is then C(q) = wf ∗ (q) + ws s∗ (q) , so C(q) = 2 ww q . η p When COSS firms compete in the product market, firm j’s quality is qj = 4 (f0 + ηf1 + ηf2 ) sj and depends

on the feature levels contributed by both firms. Solving for an optimal value of f1 requires knowing f2 , which determines q1 . Therefore, we cannot decompose the quality uniquely.



Proof of Proposition 2 The quality decomposition result from Proposition 1 implies we can reduce the duopoly market competition in the private-features market as represented by the following profits: Π1 (q1 , q2 ) = R1 (q1 , q2 ) − C(q1 ), Π2 (q1 , q2 ) = R2 (q1 , q2 ) − C(q2 ) where the revenue expressions are given in Lemma A1, and the expression for minimum cost of achieving a quality level is obtained from Proposition 1. The quality best responses for each firm is given by the solution to these FOCs: ∂Π2 M q12 (4q1 − 7q2 ) ∂Π1 2M q1 (8q12 − 6q2 q1 + 4q22 ) = − 2cq = 0 and = − 2cq2 = 0 1 ∂q1 (4q1 − q2 ) 3 ∂q2 (4q1 − q2 ) 3

32

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

where c = 2

q

wws η

. Solving these FOCs, we obtain q1 =

M φ1

q

2

η wws

and q2 =

M φ2

q

2

η wws

, where φ1 and φ2 are

constants that are the positive real solutions of the polynomial equations below: (φ1 ) −128 + 1168x − 31111x2 + 235824x3 = 0 and (φ2 ) −16 + 944x − 13057x2 + 58956x3 = 0 Using these and the optimal quality decomposition results from Proposition 1, we obtain the results stated. Consider any potential symmetric equilibrium characterized by the equilibrium features and usability outcomes f1 = f2 = f ∗ and s1 = s2 = s∗ . With equal quality levels, the firms will charge equal prices (Lemma A1), and obtain half the market. If the firms charge different prices (say p1 > p2 ), all consumers will prefer firm 2’s product since the qualities are equal. Further, we demonstrate that both firms charge zero prices. If either firm charges p0 > 0, its competitor can obtain the entire market by offering a price of p00 = p0 − , where  > 0 is a small deviation. The rationale is that costs that are sunk in Stage 2 and do not affect pricing in Stage 3. Therefore, firms earn zero revenue and have positive costs in any symmetric equilibrium. Consider a profitable deviation by firm 2, setting s2 = s0 = s∗ − δ, where δ > 0 is a small deviation. Firm 2 can obtain higher revenues by part (i), and has lower development costs, thereby increasing profits beyond the symmetric equilibrium outcome. Thus, there is no equilibrium with symmetric strategies.



Proof of Proposition 3 For the quasi-public market, the FOCs for the firm profits with respect to both features fj and usability sj for j = 1, 2 are: p √ √
√ √ √
√
√ 4 f0 + η (f1 + f2 )M 2 4 s2 − 3 4 s1 4 s2 + 4 s1 M η s1 4 s1 − 4 s2 ∂Π1 ∂Π1
− w , = = √ √ √
−w √ √ s ∂s1 ∂f1 s1 4 4 s1 − 4 s2 3 (f0 + η (f1 + f2 )) 3/4 4 s2 − 4 4 s1 2 ∂Π2 M = ∂s2

p 4

√ √
√ √
√ √ √ f0 + η (f1 + f2 ) s1 4 4 s1 − 7 4 s2 M η 4 s1 4 s1 − 4 s2 4 s2 ∂Π2 − ws , = √ √
−w √ √
∂f2 4 (f0 + η (f1 + f2 )) 3/4 4 s2 − 4 4 s1 2 4 4 4 s1 − 4 s2 3 s23/4

We check whether an interior solution is possible in which both COSS firms can hire developers to develop features. To check, we take the difference between the FOCs with respect to feature level: √ √
√ M η 4 s1 4 s1 − 4 s2 ∂Π1 ∂Π2 − = √ √
∂f1 ∂f2 4 (f0 + η (f1 + f2 )) 3/4 4 4 s1 − 4 s2 We find that and

∂ Π2 ∂f2

∂ Π1 ∂f1

−

∂ Π2 ∂f2

> 0 at any wage level since s1 > s2 always holds. Therefore, both FOCs

∂ Π1 ∂f1

=0

= 0 cannot be simultaneously satisfied, which implies we cannot have an interior solution for both

firms. Thus, either

∂ Π1 ∂f1

> 0 or

∂ Π2 ∂f2

< 0 or both must hold. If

∂ Π1 ∂f1

> 0, firm 1 will find it optimal to hire more

developers and add features. Since firm 1 can improve upon a situation that has equilibrium with this condition. Therefore,

∂ Π1 ∂f1

∂ Π1 ∂f1

> 0, we cannot have an

= 0 in equilibrium and f1∗ > 0. On the other hand,

∂ Π2 ∂f2

eLCS from the least-cost contribution to e0H = eLCS (w) +  where  > 0. The best possible belief for any type at this level e0H is µ(H|e0H , w) = 1. For the high type, this deviation to e0H is not profitable since w − cH e0H < w − cH eLCS (w). Therefore, no such deviation contributing beyond eLCS (w) is profitable, and any deviation below eLCS (w) will result in the firm believing the developer is low-type, implying eLCS (w) is an equilibrium strategy for the high-types. For the low-type developer, for any e > eLCS , we have w − cL e < 0 so the low-type will not deviate from e∗L = 0. Hence, eLCS (w) is an equilibrium. We apply the intuitive criterion for part (ii) to eliminate non-LCS equilibria: Suppose another equilibrium exists where the high type contributes e0 . This equilibrium requires that firms’ beliefs on the equilibrium ( 0, e < e0 path are: µ(e, w) = . Consider a deviation e˜ from the equilibrium path where cwL < e˜ < e0 . The 1, e ≥ e0 best possible belief, µ(˜ e, w) = 1 is still not sufficient to induce the low-type developers to contribute e˜ since w − cL e˜ < 0. Therefore, only the high-type developer could have deviated to e˜, and the intuitive criterion requires the firms to assign beliefs µ(H|e0 , w) = 1 after observing e˜. This reasoning leads to an inconsistent



34

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

off-equilibrium-path belief and we can therefore eliminates this equilibrium. We can apply this criterion to filter any equilibrium with high type contributing e0 > eLCS (w), and the only remaining equilibrium is the least-cost separating equilibrium. In a least-cost equilibrium, the high-type developers who signal are those with reservation utilities r < rLCS = w − cH eLCS (w) so the number of entering developers is Ψ(rLCS ) = Ψ(w − cH eLCS (w)), which proves part (iii).



Proof of Proposition 4 The comparative statics are determined by applying the implicit function theorem to (6):    h i 3 w 2 −w ψ w 1 − ccHL cL dwQC >0 = −  h i    h i 3  5  1 3 cH cH cH dcH 5w 2 2w 2 3 w=wQC 2 + 2 + w Ψ w 1 − + w 1 − ψ w 1 − 2 cL cL cL cL cL We find the comparative statics of the wage with respect to ws , η and M in a similar manner.



 h i   3 3 Proof of Result 1 Denote ξ QC (w) = (w) 2 ψ w 1 − ccHL 1 + 2 cwL and ξ CLOSED (w) = (w) 2 Ψ(w). We h i QC 3 observe that as cH → 0,we get lim ξ QC (wQC ) = (wQC ) 2 Ψ(wQC ) 1 + 2 wcL and since ξ CLOSED (wCLOSED ) = cH →0 h i QC 3 3 3 CLOSED 2 CLOSED (w ) Ψ(w ) we get (wQC ) 2 Ψ(wQC ) 1 + 2 wcL = (wCLOSED ) 2 Ψ(wCLOSED ), implying wQC < h i QC wCLOSED . For high values of cH approaching cL , we have lim ξ QC (wQC ) = Ψ(wQC × 0) 1 + 2 wcL = cH →cL ∂ξCLOSED 2 q M 2 (φ2 + φ ) ∂cH 1 2 η dwQC QC QC ⇒ w → ∞. First, we establish w is increasing in c : = − > 0 since H ∂ξCLOSED 4 ws dcH ∂w  h i   CLOSED 5 ∂ξCLOSED > 0. = − c1L (w) 2 ψ w 1 − ccHL 1 + 2 cwL < 0 and ∂ξ ∂w ∂cH Since wQC is continuous and increasing in cH , we know ∃˜ cH so that when cH < c˜H we get wQC < wCLOSED and when cH > c˜H we have wQC > wCLOSED ceteris paribus. The threshold value c˜H is defined as solving 2 q M 2 ( φ2 1 +φ2 ) η ξ QC (wCLOSED ; c˜H ) = , which is the condition specified in Assumption (A1).  4 ws Proof of Result 2 The contribution to open source in the quasi-closed market is F QC =  h i QC w Ψ wQC 1 − ccHL whereas in the quasi-public market, contributions made by the firms and due to cL 3 q M 2 σ 3 σ1 −σ2 ) 2 η developers signaling is F QP = (41σ(1 −σ . Substituting from the implicit wage equation (6), we 3 w ˆ3 ws 2) 3

obtain F QC > F QP ⇐⇒

1 cL 2+ w

>

4σ13 (σ1 −σ2 ) 2 1 3 3 φ2 1 (4σ1 −σ2 ) w ˆ2

which holds when w ˆ is large, cL is low, or when wQC is high,

which in turn occurs when M is large or ws is low.

 q

QC

(wQC )

Proof of Result 3 For part (i), we obtain the quality levels from Propositions 2 and 4 to find: q2QP (wQP ) = 2 q q φ2 (4σ1 −σ2 ) w ˆ w ˆ √ < wQC . We know the final fraction is less than 1 from Proposition 1. Comparing 2σ1 σ2 σ1 −σ2 wQC

35

Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

the quality levels for the high-quality product in both the quasi-public and quasi-closed markets, we find q  2 QC q1 (wQC ) φ1 (4σ1 −σ2 ) φ1 (4σ1 −σ2 ) QP QC w ˆ QC QP √ √ . This condition can , we must have w < w > q = . For q 2 2 QP 1 1 2σ σ1 −σ2 wQC 2σ σ1 −σ2 q (wQP ) 1

1

1

only hold for small market sizes and low signaling costs and proves part (ii). Comparing the quasi-closed and closed-source markets, we obtain from 1 and assumption (A1) that wQC < wCLOSED . The other parameters are identical across these two markets, which gives us part (iii) since quality depends inversely on wage levels. QC

Part (iv) requires

q1

QC q2

=

φ1 φ2

QP

>

q1

QP

q2

=

σ1 σ2

which we can numerically verify.



Proof of Result 4 For the low-quality firms, the profits under different markets can be derived from the equilibrium quality levels as: QP

QP

Π2 = γ 2 M where γ2QP =

2

r

η and ΠQC = γ2QC M 2 2 ww ˆ s

5 σ1 σ2 (σ2 −σ1 ) σ2 +σ12 16σ23 −1 +σ1 σ2 −8σ24 √ σ1 −σ2 (4σ1 −σ2 )3

(

(

)

(

))

r



η wQC ws

and γ2QC =

+Ψ w

QC

  QC 2 cH (w ) 1− cL ηcL

2 φ2 φ1 (8φ2 −1)φ2 −φ3 2 −φ1 (16φ2 −1)

)

(

2(φ2 −4φ1 )2

. The low-quality

firm has a higher profit under the quasi-public market than the quasi-closed market with the same wage since γ2QP > γ2QC . Since wQC > wQP from Proposition 1, the firm always has a higher profit in the quasi-public market. The profits of the high-quality firms under different market conditions are similarly derived to be:  h  h i 2 i QC 2 q q (w ˆ) (w ) QC QP QC cH η η QC 2 2 and Π = Ψ w 1 − where ΠQP =Ψ w ˆ 1 − ccHL + γ M + γ M 1 1 1 1 ηcL ww ˆ s cL ηcL wQC ws √ 3 2 2 2 σ φ (4(2φ2 φ1 +φ1 )−16φ1 −φ2 (φ2 +4)) (σ1 −σ2 )(σ1 (3−σ1 (σ2 −4σ1 ) )−3σ2 ) γ1QP = 1 and γ1QC = 1 . When w ˆ = wQC , then we 2(φ2 −4φ1 )2 (4σ1 −σ2 )3 find that ΠQC > ΠQP since γ1QP < γ1QC . Observe that ΠQC decreases with wQC , which is higher when the 1 1 1 market size M is large, or when signaling becomes difficult (cH is high). These conditions therefore result in lower profits for the high-quality firm in the quasi-closed setting.



Proof of Result 5 From Lemma A1, we can rewrite the consumer surplus expression as: CS(q1 , q2 ) =    q1 4 q +5 q1 2   q1 q2 2 . Observe that the term in square brackets only depends on the quality ratio, which is q1 4 q −1 2

independent of the wage and other model primitives but depends on the market. We know that when the wages are identical CS QP (w) > CS QC (w) and the surplus is increasing in the quality level, which in turn decreases with the equilibrium wage. Since wQP < wQC , the surplus inequality will continue to hold at the equilibrium wage. Comparing CS CLOSED and CS QC , we observe that the quality ratios and therefore the term within square brackets is identical for these two markets. Since the consumer surplus is directly proportional to the quality level of the high-quality product and wCLOSED > wQC , we know q1CLOSED < q1QC since q1 decreases with wage level. This reasoning then implies CS QP > CS QC > CS CLOSED .



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Kumar, Gordon and Srinivasan: Product Strategy for Commercial Open Source Software

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