Gates' bidding model (revisited)

Gates' (1967) bidding model was one of the earliest proposed for construction bidding. Its most celebrated formula allows for calculating the probability of any bidder submitting the lowest bid when competing against several known competitors. This model has been shown to outperform many recent bidding models. However, it also suffers from important limitations that keep it from being applied in wider contexts. In this paper, we overcome two of such limitations. First, we extend Gates' model to calculate the probability of a bidder ending in any position other than the first (lowest). Second, we propose an approach for extrapolating the probabilities of all bidders underbidding each other, even in those situations of limited access to historical bidding information. Overcoming these limitations significantly enhances Gates' model in two ways. First, it allows anticipating the probabilities of winning an auction in best value auctions where bidders who submitted a competitive but not necessarily the lowest bid can still win. Second, our extension allows applying Gates' formula in situations of incomplete information. This is especially interesting when some bidders have not met in previous auctions and there is no information from them individually underbidding each other.