Selling Advantages: Externality-Based Upgrades for Digital Goods under Income Effects

Many digital products, such as video games or social media, have a social component that allows firms to sell paid upgrades whose value derives from giving buyers an advantage over other users. While such externality-based upgrades are often inexpensive to design, they impose negative externalities on the remaining users and degrade their experience.  We analytically study the trade-off between externality-based and externality-free upgrade features in the design of digital goods when users are vertically differentiated by income effects. We show that the classical result that offering a single, externality-free version is optimal does not extend to settings with nonlinear income effects. Moreover, even when user costs are linear, it can be optimal to offer upgrades consisting of externality-based features. However, if such features are offered, optimal versioning also requires offering a version that includes all externality-free features and no externality-based features, as well as a low-quality free base version to mitigate negative externalities.  Our results provide guidance for the design of digital goods in markets where user interactions or income effects are present.