Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
A nonparametric estimator for setting: reserve prices in procurement auctions
Proceedings of the 4th ACM conference on Electronic commerce
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Optimal design of English auctions with discrete bid levels
Proceedings of the 6th ACM conference on Electronic commerce
Learn while you earn: two approaches to learning auction parameters in take-it-or-leave-it auctions
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 3
Setting discrete bid levels adaptively in repeated auctions
Proceedings of the 11th International Conference on Electronic Commerce
Adaptive Auction Mechanism Design and the Incorporation of Prior Knowledge
INFORMS Journal on Computing
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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 the problem 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 derive a general expression that relates the expected revenue of the auction when discrete bid levels are implemented, but the number of participating bidders is unknown. We then use this result to show that the characteristics of these optimal bid levels are highly dependent on the expected number of bidders and on their valuation distribution. Finally, we derive and demonstrate an online algorithm based on Bayesian machine learning, that allows these unknown parameters to be estimated through observations of the closing price of previous auctions. We show experimentally that this algorithm converges rapidly toward the true parameter values and, in comparison with an auction using the more commonly implemented fixed bid increment, results in an increase in auction revenue.