Third- and Lower-Price Auctions

Abstract

This paper solves the equilibrium bid functions of third — and lower — price auctions. In these auctions, equilibrium bids exceed bidders’ valuations, and bidders raise their bids if one moves to a lower price auction, and lower bids if the number of bidders is increased. Third— and lower—price auctions are unappealing under risk aversion, which in turn may make them appealing when the auction is a substitute for small scale gambling, as in many Internet auctions. Moreover, in the presence of a corrupt agent-auctioneer, an auction may turn out to be third — or lower—price, even though it was set up as a second-price or hybrid English auction.