Inverse auctions: Injecting unique minima into random sets

Authors:
F. Thomas Bruss;Guy Louchard;Mark Daniel Ward
Affiliations:
Université Libre de Bruxelles, Belgium;Université Libre de Bruxelles, Belgium;Purdue University, West Lafayette, IN
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2009

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Abstract

We consider auctions in which the winning bid is the smallest bid that is unique. Only the upper-price limit is given. Neither the number of participants nor the distribution of the offers are known, so that the problem of placing a bid to win with maximum probability looks, a priori, ill-posed. Indeed, the essence of the problem is to inject a (final) minimum into a random subset (of unique offers) of a larger random set. We will see, however, that here no more than two external (and almost compelling) arguments make the problem meaningful. By appropriately modeling the relationship between the number of participants and the distribution of the bids, we can then maximize our chances of winning the auction and propose a computable algorithm for placing our bid.