On the Minimax Complexity of Pricing in a Changing Environment

We consider a pricing problem in an environment where the customers' willingness-to-pay (WtP) distribution may change at some point over the selling horizon. Customers arrive sequentially and make purchase decisions based on a quoted price and their private reservation price. The seller knows the WtP distribution pre- and postchange but does not know the time at which this change occurs. The performance of a pricing policy is measured in terms of regret: the loss in revenues relative to an oracle that knows the time of change prior to the start of the selling season. We derive lower bounds on the worst-case regret and develop pricing strategies that achieve the order of these bounds, thus establishing the complexity of the pricing problem. Our results shed light on the role of price experimentation and its necessity for optimal detection of changes in market response/WtP. Our formulation allows for essentially arbitrary consumer WtP distributions and purchase request patterns.