On the lowest unique bid auction with multiple bids

Abstract

© 2015, Newswood Ltd. All rights reseved. This study focuses on the lowest unique sealed-bid auctions in which the winning bidder is the one who places the unique bid that has the lowest value where exactly m bids per bidder are allowed. The problem can be seen as injecting a minimum into a random subset of a larger subset. By assuming that bids are identical and independently placed according to a given probability distribution, we obtain various exact probabilities for the auctions, both as a bidder and an observer, for m = 1, 2. The results are obtained via the inclusion- exclusion principle. The computational results and algorithms to calculate the probabilities are also given.