Revenue Management; Analysis of Algorithms; Dynamic Programming
Motivated by online advertising, the authors model and analyze a revenue management problem where a platform interacts with a set of customers over a number of periods. Unlike traditional network revenue management, which treats the interaction between platform and customers as one-shot, the authors consider stateful customers who can dynamically change their goodwill toward the platform depending on the quality of their past interactions. Customer goodwill further determines the amount of budget that they allocate to the platform in the future. These dynamics create a trade-off between the platform myopically maximizing short-term revenues, versus maximizing the long-term goodwill of its customers to collect higher future revenues.The authors identify a set of natural conditions under which myopic policies that ignore the budget dynamics are either optimal or admit parametric guarantees; such simple policies are particularly desirable since they do not require the platform to learn the parameters of each customer dynamic and only rely on data that is readily available to the platform.The authors also show that, if these conditions do not hold, myopic and finite look-ahead policies can perform arbitrarily poorly in this repeated setting. From an optimization perspective, this is one of a few instances where myopic policies are optimal or have parametric performance guarantees for a dynamic program with nonconvex dynamics.The authors extend their model to the cases where supply varies over time and where customers may not interact with the platform in every period.