Technical Note—Dynamic Pricing with Heterogeneous Patience Levels

We consider the problem of dynamic pricing in the presence of patient consumers. We call a consumer patient if she is willing to wait a certain number of periods for a lower price and will purchase as soon as the price is equal to or below her valuation. We allow for arbitrary joint distributions of patience levels and valuations. We propose an efficient dynamic programming algorithm for finding optimal pricing policies. We find numerically that optimal policies can take the form of incomplete cyclic policies, mixing features of nested sales policies and of decreasing cyclic policies.