Automatic Mechanism Design Of Optimal English Auctions With Discrete Bid Levels

In this paper we consider the optimal design of English auctions with discrete bid levels. Such auctions are widely used in online Internet settings and our aim is to automate their configuration in order that they generate the maximum revenue for the auctioneer. Specifically, we address two complimentary problems: (i) that of determining the optimal reserve price and bid increment in these auctions and (ii) that of estimating the values of the parameters necessary to perform this optimal auction design by observing the bidding in previous auctions. To this end, we use a general expression relating the revenue of the auction to the discrete bid levels implemented in order to determine (using a numerical solution) the optimal bid levels in the general case. We then use this result to show that the characteristics of these optimal bid levels are highly dependent on the number of bidders and their valuation distribution. Specifically, we compare two commonly used distributions (uniform and exponential) and show how the optimal reserve price and bid increment changes as the number of bidders increases. When this optimal auction is implemented, improvements result in both the revenue and the duration of the auction, compared to the more common case of fixed bid increments. Finally, given the dependence of this optimal auction design on the number of bidders and their valuation distribution, we show that we can use Bayesian inference to estimate these values through observations of the closing prices of previous auctions.