We study platform markets in which agents arrive gradually, experience changes to their preferences over time, and are frequently re‐matched. We introduce simple auctions specifically designed for such markets. Upon joining, agents select a status that determines the weight assigned to their future bids. Each match is then assigned a score that depends on the agents' reciprocal bids and status. The matches maximizing the sum of the bilateral scores are implemented. Under certain conditions, such auctions maximize profits, welfare, or a combination of the two. We use the results to shed light on the distortions due to platforms' market power.