A seller running repeated auctions with bidders who have constant valuations over time canexploit the information obtained in past auctions to set reserve prices in future ones. We consideran environment where bidders are naive, losers are replaced by new bidders, and past winnersleave with an exogenous probability. Our model reflects the main characteristics of the marketfor online display advertising, where publishers use real-time first- or second-price auctions tosell impressions to advertisers. The optimal reserve price is either equal to the value of the lastwinner, or lower than it when the last winner’s value is sufficiently high. In this second case, theoptimal reserve price is decreasing in the last winner’s value in a first-price auction, while it isindependent of it in a second-price auction, and often lower than in a first-price auction. For awide range of the model’s parameters, the second-price auction yields a higher seller’s revenuethan the first-price auction, because in the second-price auction a past winner who is outbidacts as a reserve price. We also describe typical paths of reserve prices and characterize thestationary distribution of winners’ values. The probability of trade may be non-monotonic inthe persistence of past winners