Information aggregation in auctions with an unknown number of bidders

Information aggregation, a key concern for uniform-price, common-value auctions with many bidders, has been characterized in models where bidders know exactly how many rivals they face. A model allowing for uncertainty over the number of bidders is essential for capturing a critical condition for information to aggregate: as the numbers of winning and losing bidders grow large, information aggregates if and only if uncertainty about the fraction of winning bidders vanishes. It may be possible for the seller to impart this information by precommitting to a specified fraction of winning bidders, via a proportional selling policy. Intuitively, this could make the proportion of winners known, and thus provide all the information that bidders need to make winner's curse corrections.