Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Developing a bidding agent for multiple heterogeneous auctions
ACM Transactions on Internet Technology (TOIT)
Analysis and Design of Business-to-Consumer Online Auctions
Management Science
A Study of Limited-Precision, Incremental Elicitation in Auctions
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 3
Optimal design of English auctions with discrete bid levels
Proceedings of the 6th ACM conference on Electronic commerce
Auctions with severely bounded communication
Journal of Artificial Intelligence Research
The effects of proxy bidding and minimum bid increments within eBay auctions
ACM Transactions on the Web (TWEB)
Setting discrete bid levels adaptively in repeated auctions
Proceedings of the 11th International Conference on Electronic Commerce
Pricing Rule in a Clock Auction
Decision Analysis
Analysis of an automated auction with concurrent multiple unit acceptance capacity
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types
Artificial Intelligence
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This article considers a canonical auction protocol that forms the basis of nearly all current online auctions. Such discrete bid auctions require that the bidders submit bids at predetermined discrete bid levels, and thus, there exists a minimal increment by which the bid price may be raised. In contrast, the academic literature of optimal auction design deals almost solely with continuous bid auctions. As a result, there is little practical guidance as to how an auctioneer, seeking to maximize its revenue, should determine the number and value of these discrete bid levels, and it is this omission that is addressed here. To this end, a model of an ascending price English auction with discrete bid levels is considered. An expression for the expected revenue of this auction is derived and used to determine numerical and analytical solutions for the optimal bid levels in the case of uniform and exponential bidder's valuation distributions. Finally, in order to develop an intuitive understanding of how these optimal bid levels are distributed, the limiting case where the number of discrete bid levels is large is considered, and an analytical expression for their distribution is derived.