Yuan-Mao Kao

Pricing a global product differently across multiple regions is a common but controversial practice. While price differentiation helps capture unique market characteristics, it also encourages parallel trade, which may lead to price competition between local business units (LBUs) of a global firm and affect overall corporate performance. We formulate this pricing problem as a two-stage game-theoretic model that consists of a single global business unit (GBU) and multiple LBUs. The GBU designs and manufactures the product and sets the transfer price for supplying the product to all LBUs, while LBUs independently decide retail prices for their respective regional markets. The parallel trade phenomenon emerges naturally when regional prices differ; thus, when LBUs are to set prices for their own regions, they also have to take into account how other LBUs might set their prices, making the pricing problem game-theoretic. Our theoretical results verify the existence of a pure-strategy Nash equilibrium game. A learning-based algorithm is then developed to find a pure-strategy Nash equilibrium for all LBUs. Numerical studies are conducted using data from the fast-moving consumer products industries. Different from most other research that considers only two or three decision makers, the proposed learning-based algorithm is computationally efficient. Even for cases with 100 decision makers, the pure-strategy Nash equilibrium can be obtained within 30 minutes. Moreover, although parallel trades are detrimental to some LBUs, the existence of parallel trade surprisingly leads to higher overall corporate profits, which is made possible through making the product available at different price points in a market. The proposed method also enables the quantitative validation of several conjectures on parallel trading practices.

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 that represents their preferences for the service. The provider has a prior belief about the customer utility model and 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 who knows 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 balances the provider's immediate and future profits from an individual customer. When the provider does not have full information, we find that the 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 can also occur because of offering a suboptimal contract with a long subscription period in the beginning. We propose an information-threshold policy that is adaptive based on the accumulated information, and the provider is guaranteed to have enough information to make decisions when crossing the threshold. We show that our policy achieves asymptotically optimal performance with its regret growing logarithmically in the planning horizon. Our results indicate that offering a long subscription period could be costly when the provider knows little about customers' usage and the service cost is highly uncertain.