Rationalizable Strategies and Perfect Equilibria in Common Value Auctions with Variable Supply

Auctions with variable supply are multi-unit auctions, in which the seller determines the supply quantity as a function of the bidding. These auctions are used on various markets ranging from Treasury bills and IPOs to rare wine and art. In this work we compare in a common value model the mixed strategy subgame perfect equilibria and the rationalizable strategies of the uniform price and the discriminatory auction. This allows us to establish a revenue and efficiency ranking of both auctions. The uniform price auction is found to be ex-ante more profitable for the seller and to allocate goods more efficiently.