An apparatus includes a computer network including at least one auction server, at least one seller client and at least one buyer client. The at least one auction server, the at least one seller client and the at least one buyer client are executing on a computer system a synthetic continuous double auction having contingent bidding on a plurality of heterogeneous item auctions. The synthetic continuous double auction includes a composite reverse auction, defined to include a bid set including a first contingent bid on a first of the plurality of heterogeneous item auctions and a second contingent bid on a second of the plurality of heterogeneous item auctions, is ended when i) the first contingent bid from the bid set is recognized as a winning bid and substantially simultaneously ii) the second contingent bid from the bid set is withdrawn as a remaining bid.