Online advertising has motivated companies to collect vast amounts of information about users, which increasingly creates privacy concerns. One way to answer these concerns is by enabling end users to choose which aspects of their private information can be collected. Based on principles suggested by Feldman and Gonen (2018), we introduce a new online advertising market model which uses information brokers to give users such control. Unlike Feldman and Gonen (2018), our model is dynamic and involves multi-sided markets where all participating sides are strategic. We describe a mechanism for this model which is theoretically guaranteed to (approximately) maximize the gain from trade, avoid a budget deficit and incentivize truthfulness and voluntary participation. As far as we know, this is the first known dynamic mechanism for a multi-sided market having these properties. We experimentally examine and compare our theoretical results using real world advertising bid data. The experiments suggest that our mechanism performs well in practice even in regimes for which our theoretical guarantee is weak or irrelevant.