A General Framework for Dynamic Pricing with Patient Customers
We consider a discrete time, finite horizon dynamic pricing model. Customers are assumed to be patient, in that they are willing to wait a given number of periods for the price of the product to fall below their valuation. Customers are assumed to be heterogeneous along two dimensions: valuation and patience level. We make no assumptions on the joint distribution of valuations and patience levels. We show that this model is more complex than a similar model with forward-looking customer behavior, in that it representation involves a higher-dimensional state space. We prove that the problem is tractable and construct a polynomial time algorithm for finding optimal pricing policies. We compare and contrast policies designed for selling to forward-looking customers with policies designed for selling to patient customers.