Third- and Higher-Price Auctions

Abstract

This paper solves the equilibrium bid functions of third- and higher-price auctions for a large class of distribution functions of bidders’ valuations, assuming the symmetric independent private values framework, and risk neutrality. In all these auctions, equilibrium bids exceed bidders’ valuations, and bidders raise their bids when one moves to a higher price auction, and lower bids when the number of bidders is increased.