Designing Subscription Services with Imperfect Information and Dynamic Learning

Abstract

This dissertation studies how a subscription service provider offers contracts to customers without full information on their preferences. The first essay studies a mechanism design problem for business interruption (BI) insurance. More specifically, we study how an insurer deals with adverse selection and moral hazard when offering BI insurance to a firm. The firm makes demand forecasts and can make a recovery effort if a disruption occurs; both are unobservable to the insurer. We first find that because of the joint effect of limited production capacity and self-impelled recovery effort, the firm with a lower demand forecast benefits more from the BI insurance than that with a higher demand forecast. Anticipating a higher premium, the low-demand firm has an incentive to pretend to have the higher demand forecast to obtain more profit. We then characterize the optimal insurance contracts to deal with information asymmetry and show how the firm's operational and informational characteristics affect the optimal insurance contracts. We also analyze the case where the firm can choose its initial capacity and find that from the firm's perspective, capacity and BI insurance could be either substitutes or complements.The second essay focuses on the learning-and-earning trade-off in subscription service offerings. We consider a service provider offering a subscription service to customers over a multi-period planning horizon. The customers decide whether to subscribe according to a utility model representing their preferences for the subscription service. The provider has a prior belief about the customer utility model. Adjusting the price and subscription period over time, the provider updates its belief based on the transaction data of new customers and the usage data of existing subscribers. The provider aims to minimize its regret, namely the expected profit loss relative to a clairvoyant with full information on the customer utility model. To analyze regret, we first study the clairvoyant's full-information problem. The resulting dynamic program, however, suffers from the curse of dimensionality. We develop a customer-centric approach to resolve this issue and obtain the optimal policy for the full-information problem. This approach strikes an optimal balance between immediate and future profits from an individual customer. When the provider does not have full information, we find that a simple and commonly used certainty-equivalence policy, which learns only passively, exhibits poor performance. We illustrate that this can be due to incomplete or slow learning, but it can also occur because of offering a suboptimal contract with a long subscription period in the beginning. We propose a two-phase learning policy that first focuses on information accumulation and then profit maximization. We show that our policy achieves asymptotically optimal performance with its regret growing logarithmically in the planning horizon. Our results indicate that the provider should be cautious about offering a long subscription period when it is uncertain about customer preferences.