In auctioning items, pseudo bids are determined based on the bid price and auction budget submitted by a bidder. The bid associated with the highest pseudo bid is identified as the winning bid. A consistent pseudo bid function is applied to determine the pseudo bids for each of the bids, or a variable pseudo bid function is selectively applied to some bids. The pseudo bid increases with increased bid prices and/or increased auction budgets. When a winning bid is identified, the winner's auction budget is debited the price of the item won, and the pseudo bid is recalculated using the remaining auction budget. Bidders submitting higher auction budgets are rewarded by being able to win more items because their auction budgets increase their pseudo bids. Recalculating pseudo bids based on remaining auction budgets allows different bidders to alternately win successive rounds as previous winners'auction budgets are reduced.