Title: Learning to Price with Reference Effects,
Abstract: As a firm varies the price of a product, consumers exhibit reference effects,
making purchase decisions based not only on the prevailing price but also the
product's price history. We consider the problem of learning such behavioral
patterns as a monopolist releases, markets, and prices products. This context
calls for pricing decisions that intelligently trade off between maximizing
revenue generated by a current product and probing to gain information for
future benefit. Due to dependence on price history, realized demand can reflect
delayed consequences of earlier pricing decisions. As such, inference entails
attribution of outcomes to prior decisions and effective exploration requires
planning price sequences that yield informative future outcomes. Despite the
considerable complexity of this problem, we offer a tractable systematic
approach. In particular, we frame the problem as one of reinforcement learning
and leverage Thompson sampling. We also establish a regret bound that provides
graceful guarantees on how performance improves as data is gathered and how
this depends on the complexity of the demand model. We illustrate merits of the
approach through simulations.