Successive release is a common strategy adopted by mobile app providers, and determining the launch timing of new app versions presents an important challenge to these providers. Network effect and consumers’ perceived value are significant factors that influence the decisions of providers. By focusing on a monopoly market, we develop an optimization model that incorporates the two factors to determine the optimal launch timing of new versions of mobile apps. The model is solved by Lagrangian method, and the closed-form results indicate that the monopoly provider launches new app versions as soon as possible if the consumers’ perceived value is not sufficiently high. Otherwise, the new version is launched after (or before) the sales of its former version reach maturity if the network effect is (or not) sufficiently high. Moreover, the monopoly app vendor delays the launch of a new version when the consumers enjoy a large network externality; however, the same vendor accelerates the release of upgrades if the consumers have a high perceived value of the app. This paper presents a novel mathematical formulation to analyze the launching policy of digital products.
Providers of mobile applications (commonly referred to as mobile “apps”) often adopt the successive release strategy to attract more users and keep their competitive advantage. Most of the apps being used today represent improved versions of their earlier generations, and such products will be substituted over time by even newer generations. When the firms launch their new products into markets, timing is one of the important factors for their profits [
Mobile apps are digital products, and the market decisions of such products should be based on their value to the consumers [
The primary goal of this work is to present a theoretical model for exploring how the two factors, namely, consumers’ perceived value and network effect, can influence the optimal market entry timing of an app. We develop an analytical model for deciding such timing and compare our findings with those reported in the literature. This model is based on the Bass model [
The rest of this paper is organized as follows. In Section
Our study is closely related to the market entry strategy for new products, which is a long-standing research topic that has been studied in various streams of literature in new product development, marketing, and economics.
The previous studies on this topic can be broadly classified into two categories. The first category incorporates product value to determine the optimal entry timing of the next product generation. Moorthy and Png [
Wang and Hui [
The second category considers the diffusion dynamics of existing products. Wilson and Norton [
We present an analytical model with a monopolistic app publisher denoted as
Given that
Consumers’ utility is also influenced by the network effect. According to [
The monopolist
Therefore, the instantaneous revenue of
The Notations section summarizes the notations used in this work.
We solve the optimization model using the Lagrangian method, which has been widely used in previous studies such as [
Given that the cumulative adopter at time
The Kuhn–Tucker conditions require
Therefore, we obtain
We then obtain the second-order condition of (
When the value of the parameter
The provider releases the new version as soon as possible if the consumers’ perceived value of the mobile app is not sufficiently high.
Equation (
When the value of the parameter
However, the transcendental nature of
Given that
The optimal launch timing of a new version of mobile app increases with the intensity of network effect. That is, the vendor delays introducing the upgrading versions if the intensity of network effect is strong.
When the intensity of network effect becomes stronger, it is optimal for the app publisher to prolong the sales timing of the old version. A longer sales timing could improve the adoption rate of the old version. Consequently, stronger intensity of network effect, together with the larger user-base, makes the consumers enjoy more utility. From (
Let us turn our analysis to parameter
The optimal launching time of a new mobile app version decreases along with the consumers’ perceived value. That is, the vendor accelerates the introducing of upgrading versions when the consumers enjoy a high perceived value.
A consumer with a higher perceived value can enjoy a better experience from the app. A better experience can also lead to a higher utility and a higher price that benefits the monopolist. In this condition, it is optimal for the vendor to launch new generations fast to generate profits within a relatively short time.
We then discuss the relationship between the optimal launch timing of
The first-order derivative of the monopolist’s profit
Given that
The new version of the mobile app should be launched after (before) the old version reaches its maturity when the intensity of the network effect is (not) sufficiently strong.
If the intensity of the network effect is not sufficiently strong, then the consumers will obtain a relative low utility, which in turn leads to low prices that can harm the profits of the monopolist. Therefore, the vendor should accelerate its app upgrades and grab the consumer surplus as fast as possible. However, if the intensity of the network effect is very strong, then it is optimal for the vendor to delay launching its new product. The reason is that to delay launching new product expands the installed base of the old products and then allows the consumers to enjoy much more externality from other users. Hence, the more externality eventually allows the vendor to charge high prices for the new version and earn more profits.
The successive release of mobile apps is a complex task, and the timing of launching a new version is one of the most difficult decisions that a manager must make. We build an analytical model that is driven solely by economic considerations to study this problem. We conduct a sensitivity analysis of two significant parameters, namely, the intensity of the network effect and the coefficient of consumers’ perceived value. The main implications of this analytical work are threefold. First, if the consumers’ perceived value is not sufficiently high, an astute manager should adopt the “now” launching strategy (defined by [
The summarization of the app vendor’s decision of when to launch new versions.
This work captures the impact of the network effect and the consumers’ perceived value on the optimal entry timing of new app versions. Nevertheless, this work also has its limitations.
First, this study assumes that the market consists of homogeneous customers in terms of their evaluation of product features. A challenging extension is to jointly consider customer heterogeneity.
Second, this work discusses the marketing policy of app vendors from the perspective of consumers’ value; hence, the revenue of vendors is limited to the fees from consumers. However, in the realistic market, many mobile app providers promise consumers with a free download and increase their profits from other avenues, such as ad revenues [
Third, this work presents a theoretical formulation to analyze the market entry strategy of mobile app vendors but does not provide concrete examples for lacking of numerical values of parameters. However, the value of parameters could be estimated through the realistic operating data. For instance, Jiang et al. [
Fourth, the proposed model can be further extended to examine a duopoly setting with two software providers. In a competitive market, firm decisions may be affected by new factors, such as consumer switching cost, as investigated by Mehra et al. [
Fifth, the findings from this study can be improved by incorporating development cost. Digital products often involve large up-front costs, which is an important economic consideration that the providers should consider.
Coefficient of consumers’ perceived value
Intensity of network effect
The inherent value of app
Launch timing of the initial version
Launch timing of the upgrade version
Market potential
Coefficient of innovation
Coefficient of imitation
The vendor’s cumulative profit
The vendor’s planning horizon.
The authors declare that they have no conflicts of interest.
The current paper is supported by Soft Science Research Program Project of Hebei Province (no. 16450124) and Research Foundation Program of Hebei University of Economics and Business (no. 2017KYY01).