Abstract: To use market clearing methods to determine market equilibrium, a market clearing situation is established by determining a number of items to be sold at the market price and allotting a number of pseudo items assignable to bids below the market price. Once bids are received for the items, using the number of pseudo items and the actual items as the supply side, and the total funds bid as the demand side, a market clearing price is determinable using a market clearing equilibrium model. Funds assigned to pseudo items are returned or not charged. Further, by selling items only to bids exceeding the market clearing price, such as by setting the market price incrementally above the market clearing price, bidders are encouraged to submit bid prices bid reflecting what the items are worth to them instead of attempting to bid strategically to guess or set the market price.

Abstract: 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.

Abstract: Budget-based advertisement placement is described. Advertisements are selected for display via multiple available ad slots. Click-through prices are calculated for each of the advertisements such that if a particular advertisement is selected by a user, an advertiser is charged the click-through price for that advertisement. The advertisements are assigned to the available ad slots based, at least in part, on budget data associated with the advertisements.

Abstract: Normalized click-through advertisement pricing is described. Advertisements are assigned to advertisement slots on a web page. Click-through prices are calculated for each of the advertisements such that if a particular advertisement is selected by a user, an advertiser is charged the click-through price for that advertisement. Over time, the calculated click-through prices charged to the advertisers result in a normalized return on investment among the advertisements.

Abstract: In auctioning advertising opportunities presented over a network, dual pricing reduces effects of fraudulent behavior causing showing or selection of a bidder's ads. In addition to a per selection bid or per showing bid presented by a bidder, a constructive bid opposite that offered by the bidder is derived from the bid offered and a rate of expected selections per showing. The costs resulting from the number of times the ad is both shown and selected are monitored. The price paid by the bidder is determined by the lower of the two costs. Behavior by another party causing the ad to be fraudulently shown or selected will not affect the bidder unless the party causes both a high number of showings and a high number of selections. Setting a price over a plurality of auction periods reduces the effect of fraudulent behavior perpetrated by the bidder regarding its own ads.

Abstract: Auction prices for a quantity of items, the quantity of which is not determined prior to auction, are equilibrated among bidders to reflect supply and demand for the items. For example, in auctioning Internet advertising opportunities, the first available opportunities are auctioned to a high bidder. Later in the course of the auction period, once the high bidder's budget has been exhausted, the price for advertising opportunities is reduced. The difference in price paid by the high bidder and the reduced price for the quantity of advertising opportunities purchased is credited to the high bidder's account. Once the high bidder's account regains a level sufficient to acquire additional advertising opportunities, the high bidder may continue to acquire advertising opportunities. Other bidders similarly are credited the difference between prices previously paid and the current price. An equilibrium price is reached based on the recursive adjustment of prices paid by the bidders.