Abstract: One aspect of our invention is a new class of rationing rules with disproportionate rationing that motivates bidders to submit more competitive bids. A second aspect of our invention is that competitiveness of bids can be further improved if the rationing rule is different for different price levels. A third aspect is that a bidding format that controls the shape of bids can improve competitiveness of bids, especially when combined with a suitable rationing rule. A fourth aspect is that competitiveness of bids can be further improved if the bidding format and/or rationing rule is automatically updated with regard to new auction relevant information before the auction starts or during the auction process. A fifth aspect is that perceived fairness can be improved if the rationing rule considers the size of bidders. Several aspects of our invention can be combined in an exemplary design. Some aspects of our invention can also be applied to single-object auctions.