Revenue-maximizing mechanisms with strategic customers and unknown, markovian demand

We show that appropriate dynamic pricing strategies can be used to draw benefits from the presence of consumers who strategically time their purchase even if the arrival process is not known. In our model, a seller sells a stock of objects to a stream of randomly arriving long-lived agents. Agents are privately informed about their values, and about their arrival time to the market. The seller needs to learn about future demand from past arrivals. We characterize the revenue-maximizing direct mechanism. While the optimal mechanism cannot be reduced to posted prices (and requires personalized prices), we also present a simple, "learn and then sell" mechanism that is able to extract a large fraction of the maximal revenue. In this mechanism, the seller first charges a relatively low price that allows learning about the arrival process, and in a second stage, the seller charges the optimal posted price given the previously obtained information.