Markdown Policies for Demand Learning with Forward-looking Customers

We consider the markdown pricing problem of a firm that sells a product to a mixture of myopic and forward-looking customers. The firm faces an uncertainty about the customers' forward-looking behavior, arrival pattern, and valuations for the product, which we collectively refer to as the demand model. Over a multiperiod sales season, the firm sequentially marks down the product's price and makes demand observations to learn the underlying demand model. Because forward-looking customers create an intertemporal dependency, we identify that the keys to achieving good profit performance are: (i) judiciously accumulating information on the demand model, (ii) preserving the market size in early sales periods, and (iii) limiting the impact of the firm's learning on the forward-looking customers. Based on these, we construct and analyze markdown policies that exhibit near-optimal performance under a wide variety of forward-looking customer behaviors. Moreover, contrary to common intuition, we show that forward-looking customers can improve the performance of a learning policy: if the customers are forward-looking, the firm's profit loss due to demand model uncertainty can asymptotically vanish, whereas if the customers are myopic, the firm's profit loss is nonnegligible in the same asymptotic setting