Consignment contract for mobile apps between a single retailer and competitive developers with different risk attitudes

Highlights

• A consignment contract with revenue sharing, vertical and horizontal competition.

• Demand is stochastic and affected by both price and quality investment.

• Equilibrium strategies are obtained under risk-aversion, -neutrality and -seeking.

• Due to stochastic dominance, price is independent of quality and revenue shares.

• Closed-form solutions are obtained under exponential utility function.

Abstract

Consider n mobile application (app) developers selling their software through a common platform provider (retailer), who offers a consignment contract with revenue sharing. Each app developer simultaneously determines the selling price of his app and the extent to which he invests in its quality. The demand for the app, which depends on both price and quality investment, is uncertain, so the risk attitudes of the supply chain members have to be considered. The members' equilibrium strategies are analyzed under different attitudes toward risk: risk-aversion, risk-neutrality and risk-seeking. We show that the retailer's utility function has no effect on the equilibrium strategies, and suggest schemes to identify these strategies for any utility function of the developers. Closed-form solutions are obtained under the exponential utility function.

Introduction

Mobile applications (apps) are software programs designed to run on smartphones and tablets. They are commonly downloaded through application distribution platforms, such as the Apple (iTunes) App Store, Google Play, the Windows Phone Store and BlackBerry App World. As suggested by Apple's central marketing message—“there's an app for that”—the market for apps is crowded and diverse (BBC Trust, 2010). At the same time, there is intense competition among companies marketing similar apps. For example, the iTunes App Store offers at least 12 device finder apps, similar to “Find My iPhone”; these apps compete with one another in terms of both price and quality (Myers, 2012). Clearly, the question of how to manage brand competition and channel competition is important both for app developers (the suppliers) and the platform distributor (i.e., the app retailer).

This study considers a supply chain of a single platform distributor and n competitive app developers, where the vertical business relationships are delineated by a contract. Many platform distributers propose consignment contracts to app developers, based on a revenue sharing policy (Gans, 2012, Jiang, 2012, Wang, Jiang and Shen, 2004, Zhang, De Matta and Lowe, 2010). In this type of contract, the developer continues to own the app and typically bears sole responsibility for determining its selling price. For every sold app, the platform distributor charges the developer an agreed percentage of the selling price (Hsieh & Hsieh, 2013).

Most research on consignment contracts has focused on a channel structure consisting of a single supplier and a single retailer (Jiang, 2012, Li, Zhu and Huang, 2009, Ru and Wang, 2010, Wang, Jiang and Shen, 2004). Only a few papers have studied the effect of competition among suppliers (Adida and Ratisoontorn, 2011, Wang, 2006), as we do here. Furthermore, whereas most work thus far has assumed that supply chain members are risk-neutral, we study the influence of different risk attitudes on the supply chain performance. In addition, while the papers above study the competition effect only via prices, we extend it to consider investment in the quality of the app as well (El Ouardighi and Kim, 2010, Hasan et al., 2012, Spriestersbach and Springer, 2004, Xie, Yue, Wang and Lai, 2011).

In what follows we formulate the objectives of the supply chain members and provide a procedure to obtain the equilibrium solution. We analyze the effects of vertical and horizontal competition in the supply chain, and show that, owing to the property of first order stochastic dominance, the retailer's utility function has no effect on the equilibrium solution. Moreover, we show that the equilibrium selling prices can be set in advance of the other decision variables regardless of the developers' utility functions. On the other hand, the quality investments of the developers and their revenue shares are affected by their risk attitudes. Notably, we find that, under the exponential utility function, the equilibrium revenue share of each developer is dependent on the developer's risk sensitivity level but is not affected by the horizontal competition. We provide closed-form solutions and sensitivity analysis regarding the risk aversion levels of the developers. We show that risk-seeking behavior of the developer can produce higher expected profit than risk-neutral behavior, and that the retailer benefits from developers who are risk-seeking.