Abstract  There is much active research into the design of automated bidding agents, particularly for environments that involve multiple decoupled auctions. These settings are complex partly because an agent’s strategy depends on information about other bidders’interests. When bidders’ valuation distributions are not known ex ante, machine learning techniques can be used to approximate them from historical data. It is a characteristic feature of auctions, however, that information about some bidders’valuations is systematically concealed. This occurs in the sense that some bidders may fail to bid at all because the asking price exceeds their valuations, and also in the sense that a high bidder may not be compelled to reveal her valuation. Ignoring these “hidden bids” can introduce bias into the estimation of valuation distributions. To overcome this problem, we propose an EM-based algorithm. We validate the algorithm experimentally using agents that react to their environments both decision-theoretically and game-theoretically, using both synthetic and real-world (eBay) datasets. We show that our approach estimates bidders’ valuation distributions and the distribution over the true number of bidders significantly more accurately than more straightforward density estimation techniques.