English Auctions with Reentry

Abstract

The English auction is usually modeled (since Milgrom & Weber (1982)) as an open continuously ascending price auction in which bidders choose when to drop out but, once they do so, are forbidden from reentering. It is known that this auction allocates a single object efficiently in many but not all circumstances. In particular, if there are three or more bidders with interdependent values, the English auction may not be efficient. This paper considers a modification of the standard model in which bidders can exit and reenter at will. The main result is that the English auction with reentry has an efficient equilibrium under weak conditions. These are much weaker than the conditions under which the standard English auction is efficient. Thus the modification is not only a more realistic model of the real-world auction but has superior theoretical properties. The failure of the English auction to allocate efficiently stems not from some defect in the institution per se but rather from the way it has been traditionally modeled as a game. JEL Classification Numbers: C72, C73, D44, D82. Keywords: efficient auction, English auction, interdependent values, ex post equilibrium, reentry.