In the basic auction model, the optimal reserve price may depend on the number of bidders

Abstract

A widespread claim in the auction literature about the most well known auction setting with i.i.d. private values is that the optimal reserve price for a second price auction is independent of the number n of bidders. This is indeed the case if the virtual valuation function is increasing, but this result fails to hold if the virtual valuation is non-monotone. In such case the optimal reserve price is weakly increasing in n and, as n tends to infinity, it tends to the highest regular valuation with zero virtual value.