A way to conduct complex transactions by auction efficiently and with a high degree of automation is provided by a methodology for conducting auctions in which bids contain multiple attributes, as opposed to a single attribute (price). Bidders are requested to specify values for each of a set of attributes, which can include transaction terms as well as product and/or service specifications. The bids are evaluated according to criteria that are functions of these attributes in order to reject losing bids and assist the auctioneer in selecting the winning bid(s).