Reverse auction: The lowest unique positive integer game

Abstract

A reverse auction can be likened to a tendering process where a contract is awarded to the lowest bidder. This is in contrast to a conventional forward auction where the highest bidder wins. In this paper we analyze a minority game version of the reverse auction where an extra condition is imposed that, namely, the bid must be unique. In other words, the bidder with the lowest positive unique integer (LUPI) wins. We examine and compare two extrema, namely, the case when all players are rational and the case when all players make random selections.