Dynamic Pricing When Customers Have Time-Inconsistent Preferences

This paper examines the dynamic pricing decisions of a monopolist seller when customers have time-inconsistent preferences, which is modeled by quasi-hyperbolic discounting. By considering the cases where customers can be sophisticated, naive, or partially naive about their time-inconsistent preferences, we characterize the subgame perfect equilibrium for the full spectrum of customers' naivete. Our results show that cream-skimming pricing strategies emerge as a robust pattern across different scenarios. The firm's profits can be improved when customers have time-inconsistent preferences. However, the firm does not benefit from customers' naivete about their time-inconsistent preferences. Our numerical experiments show that the pricing tactics are non-trivial as we vary the degrees of customers' time inconsistency and naivete, and the seller's ignorance of customers' time-inconsistent behaviors can lead to significant profit loss