Optimal Subscription Planning for Digital Goods

We consider a media service provider that gives users access to digital goods through subscription. In our model, different types of users with heterogeneous usage rates repeatedly use a platform over a period of time. There are multiple item types on the platform, and the value of an item to a user is random and depends on both the user type and the item type. The design of the platform's subscription planning comprises selecting a subscription fee for each set of item types. Before the beginning of the subscription period, given the subscription planning, users decide which set of item types to subscribe to (if any). During the subscription period, a user pays zero price to use an item if it has subscribed to a set that includes it and pays its rental price otherwise. For an exogenously given rental price, we establish the sufficient and necessary condition for the optimality of grand subscription-offering a single subscription set that includes all items. We then consider a setting in which the platform chooses both the subscription fee for each set of item types and the rental price of each item type and establish that there exist subscription fees proportional to the cardinality of each set of item types (with no rental offers) that achieve a logarithmic approximation (in the number of item types) of the optimal revenue. Finally, we demonstrate that our performance guarantee is tight for a class of problem instances.