Predicting the probability of winning sealed bid auctions_ the effects of outliers on bidding models

Predicting the probability of winning sealed bid auctions_ the effects of outliers on bidding models

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Construction Management and Economics ISSN 0144-6193 print/ISSN 1466-433X online © 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0144619042000186103 * E-mail: [email protected] Construction Management and Economics (January 2004) 22 , 101–109 Predicting the probability of winning sealed bid auctions: the effects of outliers on bidding models MARTIN SKITMORE * School of Construction Management and Property, Queensland University of Technology, Gardens Point, Brisbane, Queensland 4001, Australia Received 13 November 2002; accepted 8 May 2003 This paper is concerned with the effect of outliers on predictions of the probability of tendering the lowest bid in sealed bid auctions. Four of the leading models are tested relative to the equal probability model by an empirical analysis of three large samples of real construction contract bidding data via all-in (in-sample), one-out and one-on (out-of-sample) frames. Outliers are removed in a sequence of cut-off values proportional to the standard deviation of bids for each auction. A form of logscore is used to measure the ability to predict the probability of each bidder being the lowest. The results show that, although statistically significant in some conditions, all the models produce rather poor predictions in both one-out and one-on mode, with the effects of outliers being generally small. Keywords : Bidding models, bidding theory, construction contracts, empirical tests, predicted probability, probability of lowest bid, sealed bid auctions, tendering theory, logscore test, outliers Introduction The probability of individual contestants winning a bidding auction can be a useful piece of information for many people, not least the contestants themselves. Potential bidders can utilize this information to decide in which auctions to participate, when to try to obtain an invitation to participate, whether to enter a bid and, if so, the dollar value of the bid. Similarly, the auctioneer can also utilize the information in deciding when and how to hold the auction, how many and which bidders to invite, and the criterion for determining the winner. Most of the literature on the subject is concerned with setting a price, x , so that the probability, Pr(x) , of winning the auction reaches some desired level. Several models have been proposed for predicting Pr(x) , and these have been subject to quite lengthy, but as yet inconclusive, discussion based on the theoretical merits of each model. Most of the empirical studies that have taken place have concentrated on fitting a single underlying probability density function to all bids, including the uniform (Fine and Hackemar, 1970; Whittaker, 1970; Grinyer and Whittaker, 1973), normal (McCaffer, 1976; Skitmore, 1986) and gamma (Friedman, 1956; Hossein, 1977) while recent work (Skitmore, 2001; Skitmore and Lo, 2002) uses the single underlying density approach in examining the effects of removing potential outliers – finding the truncated lognormal to be the best fit followed by the truncated normal distribution, with the uniform distribution way behind.
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This note was uploaded on 05/06/2011 for the course BANKING 254 taught by Professor Kumar during the Spring '11 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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Predicting the probability of winning sealed bid auctions_ the effects of outliers on bidding models

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