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

Online platforms offer time-locked sales campaigns, whereby third-party vendors sell their products at a fixed price for a pre-specified length of time. To alleviate customers' uncertainty about a product's value, platforms often display to upcoming customers some information about previous customers' purchase decisions, which are the platform's proprietary observation. Using a dynamic Bayesian persuasion framework, we formulate and study how a platform should design its dynamic information provision strategy to maximize its expected revenue. We show that it suffices for the platform to use only three messages in disclosing information: a neutral recommendation that induces a customer to make her purchase decision according to her private assessment about the product; and a positive (resp., negative) recommendation that induces a customer to make the purchase (resp., not to make the purchase) by ignoring her private assessment. The platform's proprietary history can be represented by a single-dimensional summary statistic, which we term as the net purchase position. Subsequently, the platform's problem can be formulated and solved efficiently as a linear program. Further, we propose and optimize over a class of heuristic policies. The best heuristic policy provides only neutral recommendations to customers arriving up to a cut off customer and provides only positive or negative recommendations to customers arriving afterwards. The recommendation is positive if and only if the net purchase position achieved right after the cut-off customer exceeds a threshold. Finally, we demonstrate that our heuristic policy improves the platform's revenue over naïve policies commonly used in practice and is near-optimal