Information Aggregation in Auctions with an Unknown Number of Bidders

Abstract

Information aggregation, a key concern for uniform-price, common-value auctions with many bidders, has been characterized in models where bidders know exactly how many rivals they face. A model allowing for uncertainty over the number of bidders is essential for capturing a critical condition for information to aggregate: as the numbers of winning and losing bidders grow large, information aggregates if and only if uncertainty about the fraction of winning bidders vanishes. It is possible for the seller to impart this information by precommitting to a specified fraction of winning bidders, via a proportional selling policy. Intuitively, this makes the proportion of winners known, and thus provides all the information that bidders need to make winner's curse corrections.

Wars of attrition and all-pay auctions with stochastic competition

“…Krishna (2002) investigated this result in another way with an independent private value model. In a recent paper Harstad, Pekec, and Tsetlin (2008) found the same result in multi-unit winner-pay auctions with common value. 2 Pekec and Tsetlin (2008) also investigate multi-unit auctions with unknown number of bidders.…”

“…Harstad, Kagel, and Levin (1990) and Harstad, Pekec, and Tsetlin (2008) show that the form of the equilibrium strategies for winner-pay auctions is such that β(x) = a w a (x)β a (x). However, this result is not obvious for the war of attrition.…”

“…The money spent in this race is not refundable. More generally, the effect of an unknown number of bidders is an important question in auction theory (see the recent papers of Harstad, Pekec, and Tsetlin (2008) and Pekec and Tsetlin (2008)). However, to our knowledge there is no analysis of all-pay auctions with an uncertain number of bidders.…”