Demand Reduction and Inefficiency in Multi-Unit Auctions

Abstract

Auctions often involve the sale of many related goods: Treasury, spectrum and electricity auctions are examples. In multi-unit auctions, a bid for one unit may affect payments for other units won, giving rise to an incentive to shade bids differently across units. We establish that such differential bid shading results generically in ex post inefficient allocations in the uniform-price and pay-as-bid auctions. We also show that, in general, the efficiency and revenue rankings for the two formats are ambiguous. However, in settings with symmetric bidders, the pay-as-bid auction often outperforms. In particular, with diminishing marginal utility, symmetric information and linearity, it yields greater expected revenues. We explain the rankings through multi-unit effects, which have no counterparts in auctions with unit demands. We attribute the new incentives separately to multi-unit but constant marginal utility and diminishing marginal utility.