Online Pricing with Strategic and Patient Buyers

We consider a seller with an unlimited supply of a single good, who is faced with a stream of $T$ buyers. Each buyer has a window of time in which she would like to purchase, and would buy at the lowest price in that window, provided that this price is lower than her private value (and otherwise, would not buy at all). In this setting, we give an algorithm that attains $O(T^{2/3})$ regret over any sequence of $T$ buyers with respect to the best fixed price in hindsight, and prove that no algorithm can perform better in the worst case.