Channel Management for Digital Products in the Two-sided Market with Network Externality Effects

,


Introduction
Te two-sided market in which the third-party online platforms connect suppliers and consumers provides more choices for digital product vendors on their distribution channels. With online platforms contributing increasingly to the economic growth of many nations, plenty of digital product frms choose to participate in a third-party online platform to supply their products through the platform. For example, mobile application developers publish their products in the App Store which is a typical online platform. Hence, third-party online platforms have become the signifcant distribution channels of digital products in such a market. However, it keeps several providers still stick to selling their products through traditional direct channels; for instance, Oracle communicates with its consumers through the ofcial website to provide database products and services. It follows that, in the two-sided market, digital products frms have to manage the issue of choosing their distribution channels from the emerging platform or the existing direct channel.
Both the direct and platform channels have their own benefts and drawbacks. Direct channels are often owned by sellers; therefore, digital product vendors can take the whole revenue generated from direct channels. However, vendors might lose the benefts of platforms' functions such as market coverage and information collection if they choose the direct channels and have to struggle to enlarge their market demands. By contrast, vendors supplying digital products in an online platform could enlarge their potential market through the market power of the platform but obtain only parts of the revenue; that is, the platform deprives vendors of proft. For instance, Apple Inc. would take 30% of the revenue generated by applications sold in the App Store, and only 70% of the revenue goes to publishers. Both the channel strategies have advantages and disadvantages; therefore, in reality, digital product frms have to face the dilemma to trade-of between the direct channel and the platform channel. Accordingly, the channel strategy of digital product vendors becomes more complex in the context of the two-sided market.
Te problem of channel selection for digital products has been widely explored in the existing literature. For example, researchers have been investigating the frms' trade-of between the direct channel and the retail channel, as well as the trade-of between the online channel and the ofine channel. However, despite a plethora of research on this problem, our knowledge is limited to the channel strategy in the context of the one-sided market in which providers sell products to consumers without intermediaries, and if we turn the situation to the two-sided market, little is known about digital products vendors' optimal channel decisions, especially the following two issues: frst, digital product frms trade-of on the channel selection when platforms become a signifcant distribution channel in the context of the twosided market and second, how the pricing of digital product and benefts of the frms are afected when both providers and consumers interact with the third-party online platform.
Taking these gaps in the extant research into account, the current work intends to investigate the optimality of trade-of between the direct channel and the platform channel. For digital products, the decisions of providers are supposed to be basing on the value of products rather than the cost, which is quite diferent from physical products [1]. Te reason is the special cost structure of digital products: providers commonly invest vast cost to produce the frst copy; however, after that, the marginal cost is extremely low. For example, the marginal production of mobile applications is to upload them to Apple Store or Google Play Store and let consumers download. Hence, the current work formulates the models of the customers' utility, which is related to the value of products, in the situations that digital product frms sell their products through the direct channel or the online platform. In these models, the customers' utility is impacted by network externality, which means the consumers' utility increases with the installed base of the products and is the signifcant economic characteristic of digital products [2,3]. Te current work presents the optimization models for these channel strategies. Te optimization models are derived from the utility models; in these optimization models, digital product frms determine the prices of products to maximize their proft, and optimality is afected by network externality and other factors. Te closed-form analysis shows that (1) the prices of digital products and the profts of frms increase with the network externality and products' features; (2) if the intensity of network externality in the online platform exceeds that in products (or not), then the platform channel strategy (or the direct channel strategy) is just the frms' optimal channel selection.
Te contribution of the current work is thus to extend the story of channel selection of digital product frms. In this work, we investigate the optimality on the channel decision issue of digital product frms in the context of the two-sided market, whereas the existing literature generally discusses this issue under the one-sided market; moreover, we explore the mathematical mechanism of the channel selection of digital product frms and that of the efect of network externality and other factors on frms' decisions. Terefore, the fndings of the current work are benefcial to digital product frms in making decision in the two-sided market.
Te rest of this paper is organized as follows: Section 2 reviews the existing literature about the channel selection problem and then discusses the merits of the current work compared with such literature. Section 3 presents the models of the consumers' utility and then develops the frm's optimization models in diferent channel strategies. Section 4 solves the optimization models in a closed-form solution, explores the optimality of channel selection in the presence of network externality, and investigates the impact of the characteristics of digital products on the benefts of frms. Section 5 concludes the current work with a discussion on its implications and limitations.

Literature
Te current work aims to investigate the channel selection problem faced by digital product frms, and researchers have addressed this issue by exploring the dual-channel distribution of digital products.
One stream of the existing literature investigates the digital products frms' channel selection between the online and ofine channels. Consumers, in the past decades, have already been familiar with Internet-related merchandises and services, such as websites and smart devices [4], which have deeply afected the consumers' (and providers') behaviors about the adoption (and distribution) of digital products. For example, consumers have been used to adopting music copies (the typical digital product) by downloading them from the Internet; hence, many music frms choose to distribute their copies digitally through the Internet, and this impacts the operation strategies of the music industry [5]. Tus, there are plenty of literature studies investigating the online distribution of digital products and exploring the trade-of between online and ofine channels.
Comparing the online and ofine channel strategies, many factors would impact the channel selection of digital product providers, for instance, the network efect [6], the customization cost of products [7], security externality [8], the similarities between the channels [9], product availability [10], the market capacity [11], the impact of free riders [12], and the secondary marketplace [13], as well as the spillover efect [14]. In recent years, mobile Internet subscriptions have grown much more quickly than fxed line broadband subscriptions [15], which make mobile Internet a signifcant online channel to distribute digital products. Comparing with the fxed line channel, consumers in the mobile Internet channel tend to choose "head" products, which are the most popular products or the most sold products [16]; thus, digital product frms could launch the versions with the most demand through the mobile Internet. Tese literature studies intending to make trade-of between the online and ofine channel deem that online channels are useful to improve the transaction efectiveness of digital product suppliers; however, in some situations, they might still be suboptimal for suppliers.
Tere is another stream of the literature exploring the frms' selection between the direct and retail channels. Te channels discussed in the aforementioned literature studies, 2 Discrete Dynamics in Nature and Society including the online and ofine channels, are the direct channels in which providers directly sell products to end users. However, digital products are also able to be distributed through the retail channel in which retailers resell products to end users [17]. Such suppliers who sell products through the direct channel would become the competitor of their retail partners [18]. Researchers argue that network externality [19], retailers' attitude towards the risk [20], governments' policies [21][22][23], strategies of competitors [24], and market demands [25], as well as the similarity between the channels [26], would deeply impact digital products frms' selection between the direct and retail channels.
In reality, digital product suppliers often fnd that the retailer create an artifcially low price, which is harmful for the suppliers' benefts. Hence, suppliers would adopt a strategy that suppliers set ofcial price for retailers [27]. Zhu and Yao [28] compared this strategy with the traditional wholesale model of the e-book, a typical digital product, and demonstrated that the strategy that providers set price for retailers is often suboptimal to the traditional wholesale model.
Te prior literature abovementioned reveals the situations in which the certain channel strategy (online/ofine channel and direct/retail channel) would become the optimal decision for digital product frms. However, all of those literature studies explored the channel strategy in the context of the one-sided market. Recently, with the development of the two-sided market, online platforms have been playing an increasingly important role in the distribution of digital products. For example, airlines often distribute electronic tickets through online travel agency platforms [29], and in these years, data transactions are also conducted through trading platforms such as the Shanghai Data Exchange Corporation of China [30]. Terefore, astute managers would recognize the signifcance of third-party platforms as distribution channels in the two-sided market and make a trade-of between the emerging platform channel and other traditional channels [31]. However, little is known about the channel selection when digital product frms face the platform channel in the context of the two-sided market, and this would restrict the beneft of frms. Hence, the current work extends the story of channel selection by exploring digital products vendors' optimal decisions on distribution channels in the context of the two-sided market. Some researchers, for instance, Wei et al. [32], Zhao et al. [33], and Xu et al. [34], have explored the network externality in the two-sided platform, and inspired by these recent works, the current work examines how network externality and some other factors afect the optimal channel strategies and benefts of vendors.

Model Settings
It is assumed that a frm with a monopoly position develops and releases digital products to consumers whose type is denoted as v i uniformly distributed between 0 and 1 (i.e., v i ∼U[0, 1], and the subscript i means that consumers are heterogeneous). Te features of digital products are denoted as s, and the monopolist has two choices on distributing the products: frst, the provider adopts the direct channel strategy; that is, digital products are distributed through the direct channel in price p 1 . Second, the provider adopts the platform channel strategy; that is, digital products are distributed through the platform channel in price p 2 . Te notations and their defnitions in the situations of the two channel strategies are shown in Table 1, and the current work intends to investigate the optimality of the monopolist's pricing decision and channel selection facing the two available channel strategies in the context of the two-sided market.

Direct Channel Strategy.
Tis section presents the consumers' utility model and the monopolist's optimization model when digital products are distributed through the direct channel.

Consumers' Utility.
When consumers adopt digital products, the values that they enjoy are twofold: the frst is the inherent value of products deriving from the features of digital products; hence, this part of the value is defned as s · v i . Te second is the value deriving from network externality, and because of the network externality efect, consumers would obtain more utility from the increasing installed base of the digital product [35]; hence, network externality is defned as λ · Q 1 , where λ represents the intensity of network externality in the direct channel and Q 1 represents the installed base of digital products. Consumers also need to pay the cost for obtaining the products' value. Tis cost contains economic cost (i.e. the price of digital products) and the learning cost c (s > c). Te consumers' utility U 1 is shown in equation (1). In reality, the aim of consumers adopting digital products is to enjoy the features of products; therefore, it is assumed that the value deriving from the products' features actually dominate that deriving from the network externality efect, that is, s ≫ λ: (1)

Firm's Proft.
When digital products are launched through the direct channel, consumers whose utility is nonnegative would purchase digital products. Tere exists a consumer v 1 whose utility equals 0; that is, v 1 is indiferent in purchasing s or not, and the consumer v i ≥ v 1 would pay for products. Te market segmentation in the direct channel is shown in Figure 1.
Inspired by Cheng and Liu [2], the demand of products is just the products' installed base; hence, D 1 � Q 1 � s − (p 1 + c)/s − λ, and then, the optimization model for the direct channel strategy is obtained in equations (2) and (3), where the price p 1 is the decision variable, the frm's proft π 1 is the objective function, and the intensity of network externality λ is an important parameter that might impact the optimality of the price p 1 and proft π 1 : Discrete Dynamics in Nature and Society

Platform Channel Strategy.
Tis section presents the utility model for consumers and the optimization model for the monopolist in the situation that digital products are launched through the online platform channel.

Consumers' Utility.
If the monopolist launches digital products through the platform channel, then consumers must adopt the online platform service before they purchase products. Te features of the online platform are defned as s T , and the inherent value obtained by the consumer v i from the online platform is s T · v i . In reality, online platforms are often more complex and contain more features than digital products distributed through them (compare Apple's App Store and the mobile applications sold in the App Store). Hence, it is assumed that the features of digital products and online platforms satisfy s T > s. Online platforms have also characteristics of network externality [36], this makes the network externality also have efects in platform channels, and platforms with most users be most valuable to other users [37]. Te intensity of the network externality in the platform is denoted as λ T , and the installed base of the platform service is denoted as Q T ; therefore, consumers would enjoy the value λ T · Q T generated by the network externality of the platform service. Adopting the online platform service is often for free (e.g., Amazon and Netfix) but incurs the learning cost c T (s T >c T ); therefore, the consumers' utility from adopting the online platform is shown in equation (4). Consumers who have adopted the online platform would determine whether to purchase digital products from the platform. Te utility of consumers who purchase products through the online platform is shown in equation (5), in which Q 2 represents the installed base of the digital products sold in the online platform: In reality, the products' value derived from their functionalities and the learning cost needed to pay for enjoying the value are explicit to consumers; however, the network efect is somewhat implicit to consumers. Terefore, the current work assumes that s, s T ≥ λ, λ T and c ≥ λ, λ T . Moreover, consumers often need to pay more learning cost to conquer the online platform service. For example, the users of the App Store need to learn how to search and pay for applications and how to distinguish the best products from the applications with similar functionalities. Terefore, this work assumes that the quality-cost ratio in the direct channel dominates that in the platform channel, that is,

Firm's Proft.
If the monopolist releases digital products through the platform channel, then consumers would determine whether to adopt the platform service frst. Tere exists the consumer v T satisfying U T (v T ) � 0; that is, v T is indiferent between adopting and not adopting the platform, and the consumer v i ≥ v T would participate in the online platform. Hence, it could be obtained from (4) that v T � c T − λ T · Q T /s T . In addition, within those who have adopted the platform service, the consumer whose utility obtained from digital products is nonnegative would purchase products. Te products' indiferent consumer among platform users is denoted as v 2 satisfying U 2 (v 2 ) � 0, and the consumer v i ≥ v 2 would purchase the digital product. It could be obtained from equation (5) that v 2 � p 2 + c − λ T · Q 2 /s. Te market segmentation for the platform channel strategy is shown in Figure 2.

Notations
Defnition v i Heterogeneous consumers v 1 /v 2 Te consumer who is indiferent between buying and not buying products the from direct/platform channel v T Te consumer who is indiferent between adopting and not adopting platform services s/s T Features of the digital product/platform service p 1 /p 2 Price in the direct/platform channel (decision variable) π 1 /π 2 Proft in the direct/platform channel (objective function) λ/λ T Intensity of network externality in the direct/platform channel Q 1 /Q 2 Installed base of the digital products in the direct/platform channel Q T Installed base of platform services Terefore, the demand of the online platform is Hence, the optimization model of the provider in the situation of the platform channel strategy is shown in equations (6) and (7), in which the price p 2 is the decision variable, the proft π 2 is the objective function, and the optimality might be impacted by the parameter λ T : s.t. p 2 ≥ 0.

Results and Analysis
Tis section solves the optimization model of each channel strategy, explores the optimal pricing in the two channel strategies, investigates how the intensity of the network efect impacts the optimal price and proft in each channel strategy, and compares the optimal profts of the two possible channel strategies to fnd the equilibrium of the channel strategy. In this section, the closed-form formulations of optimality are presented and illustrated by the numerical analysis. In reality, the parameter s represents the number of digital products' functionalities, c represents the efort of consumers to learn how to use products, and λ and λ T represent the value created by the individual user in the direct and platform channels, respectively; it follows that the units of parameters are various. Terefore, in order to avoid the problem of units, these parameters are normalized into [0, 1] in the numerical examples.

Te Solutions of the Optimization Models.
Te current work investigates the optimality of the direct channel strategy frst. In this situation, the optimization model on the provider's decision is shown in equations (2) and (3); thus, the Lagrangian function and the corresponding Kuhn-Tucker conditions of the optimization model are as follows: According to equation (9), it could be known that the second-order condition of z 2 L/zp 2 1 � − 2/s − λ <0; therefore, L(p 1 ) is a concave function, the optimization model has the inner-point solution, and then, optimality is obtained that p * 1 � s − c/2, D * 1 � s − c/2(s − λ), and π * 1 � (s − c) 2

/4(s − λ).
Let us turn to the optimality of the platform channel strategy. When digital products are distributed through the platform channel, the optimization model of the provider's decision is shown in equations (6) and (7); hence, the Lagrangian function and the Kuhn-Tucker conditions are as follows: Terefore, the second-order condition of z 2 L/zp 2 2 � − 2/s − λ T < 0, and L(p 2 ) is a concave function; then, it could be calculated that p * . Te optimality of the optimization models for the direct and platform channel strategies is listed in Table 2.
Te optimality shown in Table 2 reveals that the optimal price in the direct channel (p * 1 ) is the same as that in the platform channel (p * 2 ), and technically, p * j (j = 1,2) is positively impacted by the products' features (s) and negatively impacted by the consumers' learning cost (c), see equations (11) and (12). Hence, it could be obtained the following proposition, and the impact of parameter s and c are illustrated in Figure 3depicted depending on the formulations ofp * j shown in Table 2.
Proposition 1. Te direct and platform channels share the same optimal price which is positively and negatively impacted by the features of digital products and the learning cost of consumers, respectively.
Let us explain the fnding of Proposition 1. Actually, digital product providers need to make pricing decision before they launch products to the market; thus, even though network externality might afect the pricing of digital products, providers could not precisely evaluate this efect before products are distributed in the market because Terefore, what is more realistic for providers is pricing digital products, depending mainly on their characteristics such as the products' features and consumers' learning cost. It could be known from (1) that consumers would obtain more utility from products with more features and less learning cost. If consumers are able to obtain more utility from products, they would have more willingness to pay for products; hence, digital products' prices increase (decrease) with products' features (learning cost). In addition, it might be optimal for providers to make digital products in direct and platform channels share the same price, for this would be benefcial to avoid the possible cannibalization between the two channels.

Impacts of the Parameters on the Benefts of Suppliers.
Let us turn to the comparative statics analysis on parameters λ, λ T , s, and c to investigate how the network externality, products' features, and consumers' learning cost impact the monopolist's benefts. It could be known that the impact of comparative statics analysis on those parameters is studied to explore their efect on the monopolist's optimal demand and proft. According to the closedform solution listed in Table 2, equations (13)-(18) could be obtained, and then, the following proposition which is illustrated in Figures 4-6 could also be obtained. Figures 4-6 are depicted depending on the formulations of D * j and π * j (j �1, 2) in Table 2:  6 Discrete Dynamics in Nature and Society

Proposition . When digital products are distributed through the direct and platform channels, the frm's demand/ proft increases with the network externality efect and product's features but decreases with the consumers' learning cost. Moreover, the installed base is benefcial to the frm.
We frst analyze the impact of the network efect on optimality. In the situation where digital products are distributed through the direct channel, the consumer's utility is afected by the network externality efect of products. It could be known from equation (1) that consumers would obtain more utility if the parameter λ increases, and then, more consumers would obtain nonnegative utility from products. Terefore, the demand of products D * 1 and the frm's proft π * 1 increase with λ, as shown in Figure 4(a). Similarly, when digital products are distributed through the online platform, the consumers' utility would be impacted by network externality in the platform and increase with the parameter λ T (see equation (5)). Terefore, the products' demand D * 2 and the monopolist's proft π * 2 would in turn increase with the parameter λ T , as depicted in Figure 4(b).
We next explore the impact of product features and consumers' learning cost. It could also be known from equation (1) that the consumers' utility increases (decrease) with product features s (learning cost c). Terefore, if products have more features, or are easier to use, there would be more consumers obtaining enough utility and choosing to purchase products, and this means that the demand in the two channels increases (decrease) with product features (learning cost), see Figure 5. Te increasing demand is also benefcial to the proft of the provider; hence, digital products with more features and lower learning cost would lead to higher proft, see Figure 6. Moreover, it is found from equations (13)- (18) and Figures 4-6 that network externality, product features, and learning cost have the same efect to the products' demand and the provider's proft; that is, the products' demand would change synchronously with the provider's proft. Tus, it could be deduced that the market demand (i.e., the installed base of the products) positively impacts the proft of digital product frms.

Equilibrium of Channel Selections.
Te equilibrium of the monopolist's channel strategies is supposed to be explored to determine the optimal channel structure in different situations. Comparing the optimal proft in direct and platform channel strategies, π * 1 and π * 2 , then It has been known from the settings in Section 3 that s > c, λ, λ T , and s − c, s − λ, s − λ T >0; therefore, if λ > λ T , π * 1 > π * 2 , the frm is supposed to choose the direct channel strategy, and if λ ≤ λ T , π * 1 ≤ π * 2 , the frm is supposed to adopt the platform channel strategy. Tus, equation (19) could be obtained and is illustrated in Figure 7, and then, the channel equilibrium is characterized in Proposition 3.
Proposition 3. Digital products are supposed to be distributed through the platform channels if the intensity of the network externality in the platform channel dominates that in the direct channel; otherwise, digital products should be distributed through the direct channel.
When the intensity of network externality in the online platform is stronger than that in the direct channel, that is, λ T > λ, consumers obtain more utility from the platform service (see equation (4)), and the online platform becomes more attractive. In this situation, the monopolist releasing its products through the platform channel could enlarge its demand with the help of the installed base of the online platform; hence, π * 2 may exceed π * 1 . However, when the intensity of network externality in the direct channel is stronger than that in the platform channel (i.e., λ T ≤ λ), the platform service becomes less attractive, and participating in the online platform would not help the frm enlarge its Discrete Dynamics in Nature and Society 7 market coverage, which may lead to π * 1 > π * 2 . In this case, it is optimal for the frm to distribute its products through the direct channel to squeeze more proft, and the beneft of the frm would increase with higher willingness to pay and utility derived from the stronger intensity of the network efect in the direct channel.

Managerial Insights.
Te fndings of the current work provide the following insights that are helpful for digital product frms when they make channel decision in the context of the two-sided market.
First, the network efect in the direct and platform channels is extraordinarily signifcant and supposed to be taken into account seriously by digital product suppliers when they determine the distribution channel. For digital product frms, they need to choose the channel that contributes more to the network efect. If frms provide small digital products, for instance, the mobile application, they could launch their products in third-party platforms (e.g., Google Play Store), for the platforms often have a vast number of users and might provide a huge potential installed base that positively impacts the network efect. However, if frms provide large digital products, they need to choose the direct channel (e.g., Oracle, the enterprise database frm, provides its product through its ofcial website), and the reason is that the target markets of large digital products are smaller. Hence, the network efect of these products mainly depends on transaction communications between those enterprises, rather than the number of the users, and obviously, the direct channel would provide more information and technology support that are conducive to transaction communications which would generate network efect.
Second, some other factors, such as the features of products and the learning cost of consumers, would also impact the proft of digital products frms; therefore, digital product frms need to take into account these factors when they develop products. Firms could make their digital products contain more functionalities; for instance, the  Discrete Dynamics in Nature and Society instant message software (such as Facebook, Messenger, and WeChat) is often able to turn the voice into text; in addition, frms also need to make their products easy to use. For example, digital product suppliers always devote to reinforcing user-friendly interfaces. Tird, digital products are supposed to price the same price in the direct or platform channels. When digital product frms intend to change distribution channels, for instance, some frms decide to participate into the platforms to sell their digital products and not to distribute products through former direct channels any more, frms need to make the prices in the new channels same as those in former channels: if the prices are higher than before, the demand would decrease; however, if prices become lower, consumers who have purchased products might feel unfair, and this feeling of consumers is also not benefcial to digital product frms [39].

Conclusion
In the context of the two-sided market, online platforms have brought about opportunities for the distribution of digital products, and digital product frms also face challenges on channel selection. To investigate the feasibility of diferent channel strategies and explore their range of applications, the current work develops optimization models in the situations that digital products are distributed through the direct and platform channels, compares the optimality of the two channels, and then analyzes the channel selections of digital product vendors. Te results show that there is no single best channel strategy that exists in diferent scenarios; that is, digital product vendors are supposed to launch their products through direct channels if the network efect in direct channels dominates that in platform channels. Otherwise, platforms are the optimal channels of those vendors. In addition, the profts and demand of digital product frms would be positively afected by the network efect, and the two channels would share the same prices impacted by some other factors such as product features and the consumers' learning cost.
Tere are several possible directions for the future research following this paper. First, the future work could investigate the channel strategy when digital product frms adopt some other pricing schema. Although the current work has considered a relevant pricing decision, there are still some interesting pricing strategies, such as freemium and pay-per-use, which might impact the channel strategy of digital product frms. Terefore, future work may take into account the efect of diferent pricing schemes on the channel preferences of digital product frms. Second, the future work could explore the impact of some other market structures. Te current work focuses on the monopoly setting and the optimal channel strategies of digital product frms in the monopoly market. However, the other market structures may lead to another strategy in channel selection. For example, in the duopoly market, digital product frms would choose the distribution channel that depends not only on the characteristics of products but also on channel strategies adopted by their counterparty. Tird, future research could also consider the roles of the cooperation within those distribution channels. Te main concern in the current work is the competition between diferent channels; however, these channels could also cooperate with each other to grab profts. For instance, in reality, Microsoft adopts the hybrid channel strategy to sell Mac Ofce; that is, Microsoft distributes Mac Ofce through both the direct channel (i.e., the ofcial website of Microsoft) and the platform channel (i.e., the App Store of Apple Inc.). Tus, how to cooperate these diverse channels via pricing or the other strategies would defnitely be a challenge.

Data Availability
All the data used in the numerical analysis are listed in detail and available in the manuscript.

Conflicts of Interest
Te authors declare that they have no conficts of interest.