Recent literature on joint bidding in a single-unit, common-value (CV) auction argues it enhances competition. Information pooling mitigates adverse selection and thus elevates bidding and may even increase revenue despite the reduction in the number of bidders. I analyze joint bidding in a simple CV, uniform-price auction with multi-unit demand, which introduces an opposite force due to (increased) monopsony power of the joint bidders, called demand reduction (DR). I show that even when DR is disallowed, the pro-competitive benefit from joint bidding in single-unit auctions does not generalize to a multi-unit environment. With DR, the scope for improved competition is further eroded.
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