Reserve prices eliminate low revenue equilibria in uniform price auctions

Uniform price auctions frequently admit equilibria which raise zero seller revenue. We show that when demand is sufficiently strong — when market supply is more than covered by any bidder's opponents — the introduction of a reserve price improves revenue not only by directly increasing the market clearing price, but also by eliminating low revenue equilibria in which the market clearing price is almost always equal to the reserve. The condition on demand is sharp, and when it is not satisfied there exist equilibria in which the market clearing price almost always equals the reserve. Our results therefore fully characterize the existence of low revenue equilibria in terms of bidder demand at a given reserve price. This sharp characterization extends directly to the case of stochastic supply, and low revenue equilibria also fail to exist when supply is stochastic and elastic.