We study a revenue management problem in which a seller operates a markdown setting with a price match guarantee. The seller is endowed with an initial inventory of an item that is depleted over a finite horizon. At the beginning of the selling season, the seller announces a full price and a discount price. Consumers arrive in accordance with a nonhomogeneous Poisson process, and have private valuations for the item. Upon arrival, each consumer must decide whether to buy immediately at the full price, or to wait for an eventual discount and run the risk of not getting the item. At the end of the season, the seller decides whether to discount the item or not. If a discount finally occurs, then the seller will reimburse the price difference to the full-price buyers who claim the refund. We prove the existence of an equilibrium consumer's strategy in this noncooperative game. Then, through a numerical study, we compare the performance of our proposed mechanism with respect to two alternative selling formats: a preannounced fixed-discount mechanism with no price guarantee, and a single price policy. Our experiments show that the price match guarantee can provide substantial additional revenues over the fixed price policy, and even additional revenues over the preannounced fixed-discount policy when the fraction of the refund claimers is less than 40% of the original number of full payers. Joint work with Navaporn Surasvadi, NYU.)