Risk optimal single¿object auctions

We analyze the preferences of a risk-averse auctioneer over several auction mechanisms with risk-neutral and symmetric bidders. We obtain the value at risk (VaR) for auctioneer revenue in auction mechanisms belonging to a parametric family which includes two classic mechanisms, the first-price auction and second-price auction. By calculating the VaR for revenue an auctioneer can estimate the amount that will be lost within a given confidence level, depending on the number of bidders and the auction mechanism chosen. The contribution of this paper is the calculation of the VaR for auctioneer revenue in some common auction mechanisms that yield the same expected revenue, including first-price auction and second-price auction and the following mechanisms: Santa Claus auction, sad-loser auction and all-pay auction. We describe how to quantify the maximum loss for an auctioneer at a given probability. We study the value at risk of the auctioneer as a criterion to determine which auctions would best suit the auctioneer's interests.