Optimal Subscription Policies for Participation-Dependent Social-Learning Markets

In this work we study the economic interactions that arise between a service provider and a collection of users in a participation-dependent social-learning market. Specifically, we consider a two-stage model of a market where the objective of the service provider is to design attractive subscription policies (i.e., subscription price-period combo) so as to maximize its overall revenue. The users on the other hand make subscription decisions based on their individual preferences (private information) as well as the feedback given by the earlier subscribers (public information). For the proposed two-stage model, taking into account the statistical differences between the users who subscribed to stage-1 (i.e., promotional period) and those who did not, we derive the optimal price for stage-2 (i.e., operational period) for each possible history of the stage-1 process. Then, employing the technique of dynamic programming we derive the Bellman’s optimality equation, solving which yields the optimal subscription policy for stage-1. Using the structure of the optimal policy as a guideline, we propose a range of heuristic policies by relaxing some key aspect(s) of the optimal policy. Finally, we conduct an extensive numerical study to benchmark the efficacy of the optimal policy (in terms of the average revenue accrued by the provider) against the proposed heuristic policies.