Secret reserve prices in first-price auctions

•I study a SIPV auction environment with a risk-averse seller and risk-neutral buyers.•The seller can fix the rules of the auction before or after she learns her value.•Rules consist of a bid space and whether a secret reserve price is set later on.•Bidding behavior may exhibit jumps which can be controlled by holes in the bid space.•It may be optimal to fix rules early and to set a secret reserve price.

This article offers a theoretical explanation for the use of secret reserve prices in auctions. I study first-price auctions with and without secret reserve price in an independent private values environment with risk-neutral buyers and a seller who cares at least minimally about risk. The seller can fix the auction rules either before or after she learns her reservation value. Fixing the rules early and keeping the right to set a secret reserve price can be strictly optimal. Moreover, I describe the relation of using a secret reserve price to phantom bidding and non-commitment to sell.