Engineering Social Learning: Information Design of Time-Locked Sales Campaigns for Online Platforms

Many online platforms offer time-locked sales campaigns, whereby products are sold at fixed prices for prespecified lengths of time. Platforms often display some information about previous customers' purchase decisions during campaigns. Using a dynamic Bayesian persuasion framework, we study how a revenue-maximizing platform should optimize its information policy for such a setting. We reformulate the platform's problem equivalently by reducing the dimensionality of its message space and proprietary history. Specifically, three messages suffice: a neutral recommendation that induces a customer to make her purchase decision according to her private signal about the product and a positive (respectively (resp.), negative) recommendation that induces her to purchase (resp., not purchase) by ignoring her signal. The platform's proprietary history can be represented by the net purchase position, a single-dimensional summary statistic that computes the cumulative difference between purchases and nonpurchases made by customers having received the neutral recommendation. Subsequently, we establish structural properties of the optimal policy and uncover the platform's fundamental trade-off: long-term information (and revenue) generation versus short-term revenue extraction. Further, we propose and optimize over a class of heuristic policies. The optimal heuristic policy provides only neutral recommendations up to a cutoff customer and provides only positive or negative recommendations afterward, with the recommendation being positive if and only if the net purchase position after the cutoff customer exceeds a threshold. This policy is easy to implement and numerically shown to perform well. Finally, we demonstrate the generality of our methodology and the robustness of our findings by relaxing some informational assumptions.