Determining the final price from the set of bids can be done in different ways. Depending on whether the auction Format is multiple- or single-item, and whether the auction type is static or dynamic, different pricing rules are possible.

Policy makers often discuss at great length which pricing rule to choose for their auction. However, while the choice of pricing rule can of course affect the auction outcome, this effect is not nearly as strong as that of other factors, such as for instance the level of competition, or whether ceiling prices, prequalifications, and penalties are designed well.

Overview of different pricing rules

Depending on whether you chose a single-item or multiple-item auction format, and a static or dynamic auctionauction type, different pricing rules are possible.

  • For single-item static auctions, possible pricing rules include the first-price auction and the second price auction, in which the bidders each submit one sealed bid.
  • For single-item dynamic auctions, pricing can be done according to the Dutch auction or the English auction
  • For multiple-item static auctions, possible pricing rules include pay-as-bid auctions as well as uniform-price auctions paying either the amount of the lowest rejected bid or the highest accepted bid. Bidders all submit one sealed offer per project.
  • For multiple-item dynamic auctions, pricing options include ascending clock auctions and descending clock auctions. Clock auctions are quite established because of their fast realization. For instance, in the Netherlands, flowers in wholesale are sold via clock auctions within seconds.

Single-item static auctions

In such an auction, the winning bidder can either be paid the price set in his own bid (first-price auction) or the price offered by the second-cheapest bidder (second-price auction).

The main drawback of a first-price auction is that the winning bidder will only realise a positive profit if her bid exceeds her true costs. Bidders are thus likely to exaggerate their costs and benefit from a higher rent in case of winning. However, this comes at the expense of a lower winning probability. How a bidder addresses this trade-off depends on her risk attitude. The auction outcome may thus not be efficient in the sense that the bidder with the lowest cost is awarded.

On the other hand, the first-price rule has the advantage that bidders face no uncertainty on which price they will receive in case of winning. In contrast, the second-price rule is incentive-compatible (Mochón and Sáez, 2015, p.31), meaning that each bidder has an incentive to bid at her true cost, since her bid price never directly determines the award price in case of winning. For this reason, we conclude that a second-price rule is preferable to a first-price rule for static single-item auctions.

Mochón, Asunción, Sáez, Yago (2015) Understanding Auctions. ISBN 978-3-319-08813-6

Single-item dynamic auctions

Dutch or English pricing is possible for this kind of auctions. In a Dutch auction, the auctioneer starts by offering a support level which is too low for any bidder to accept. The price is then gradually increased until the first bidder accepts the offer. This bidder is then awarded. In an English auction, the auctioneer starts with a very high support level which is gradually reduced, causing bidders to drop out one by one. The last remaining bidder is awarded. The main drawback of a Dutch auction is that a winning bidder will only realise a positive profit if her bid exceeds her true costs. Bidders are thus likely to exaggerate their costs and benefit from a higher rent in case of winning. However, this comes at the expense of a lower winning probability. How a bidder addresses this trade-off depends on her risk attitude. The auction outcome may thus not be efficient in the sense that those bidders with the lowest costs are awarded.

In contrast, the English auction is incentive-compatible, meaning that a bidder has an incentive to bid at her true cost, since her bid price never directly determines the award price in case of winning. Because of this characteristic, we recommend English auctions rather than Dutch auctions.

Multiple-item static auctions

In such an auction, the awarded bidders can each be paid the price which they submitted (pay-as-bid) or they can all be paid the same price: This uniform price can be the price of the last project which was awarded (uniform pricing with highest accepted bid) or of the first project which was not awarded (uniform pricing with lowest rejected bid).

One drawback of the pay-as-bid pricing rule is that a winning bidder will only realise a positive profit if her bid exceeds her true costs. Bidders are thus likely to exaggerate their costs and benefit from a higher rent in case of winning. However, this comes at the expense of a lower winning probability. How a bidder addresses this trade-off depends on her risk attitude. The auction outcome may thus not be efficient in the sense that those bidders with the lowest costs are awarded. On the other hand, the pay-as-bid rule has the advantage that bidders face no uncertainty on which price they will receive in case of winning.

Uniform-pricing with highest accepted bid comes with a similar problem, as each bidder is faced with the probability that her project will be the last awarded project, thus determining the price. There is thus the same incentive to bid at a price above true costs. In contrast, the uniform-price rule with lowest rejected bid is incentive-compatible, meaning that a bidder has an incentive to bid at her true cost, since her bid price never directly determines the award price in case of winning. This is true if each bidder only has one single project in the auction. In case of multi-project bidders, this auction format is not incentive-compatible. Both uniform-price varieties come with a risk of irrational underbidding: Bidders may bid below costs (even at a price of zero) just to ensure that their project is awarded, assuming that the price-determining project (either last-accepted or first-rejected) will have a bid high enough to ensure a cost-covering price for all winning projects. If enough bidders follow this strategy, the winning price may well be zero. While in theory, rational bidders would thus refrain from such risky bidding behaviour, observations from real applications show that it does happen, especially if bidders are inexperienced. In conclusion, uniform pricing with highest accepted bid has more drawbacks than benefits. The benefits and drawbacks of pay-as-bid and of uniform pricing with last rejected bid tend to balance each other out. It is difficult to predict how bidders will behave in real auction applications. Experiences with PV pilot auctions in Germany have shown that alternating between the pricing rule throughout several rounds seems to have no significant influence on the resulting price. Furthermore, making small changes to auction design, such as alternating pricing rules, can help avoid implicit collusion as bidders have less chance to get too used to one auction mechanism. For most real-life applications, we therefore cannot clearly recommend either pricing rule but would rather advise to test both of them in consecutive auction rounds. In case of inexperienced bidders, it may be more appropriate to start the auction scheme with a pay-as-bid rule. The pay-as-bid rule is most commonly applied in multiple-item auctions and has been used in France, some auction rounds in Germany, Ireland, California, and South Africa. uniform pricing elements have been used in the Netherlands, the UK, and some PV auction rounds in Germany.

Multiple-item dynamic auctions

In the case of multiple-item dynamic procurement auctions, the procedure for an ascending clock auction is as follows: The clock starts with a support level so low that no participant is willing to accept. Then the price is increased continuously within predefined fractions of time and bidders signalize successively their acceptance of the recent price. That is, bidders are awarded one after another by accepting the price until the demanded volume is reached. The award price will be determined by the last bidder who accepted. A descending clock auction starts with a high support level which gradually decreases. Bidders drop out as support levels become unacceptably low for them, until the remaining bidders are just enough to fill the auctioneer’s target volume. In a descending clock auction, the price of the last dropped-out bidder (lowest rejected bid) will thus determine the price for all awarded projects. However, a variant with highest accepted bid (last auction price) exists as well.

The main drawback of an ascending clock auction is that a winning bidder will only realise a positive profit if her bid exceeds her true costs. Bidders are thus likely to exaggerate their costs and benefit from a higher rent in case of winning. However, this comes at the expense of a lower winning probability. How a bidder addresses this trade-off depends on her risk attitude. The auction outcome may thus not be efficient in the sense that those bidders with the lowest costs are awarded. The same is true for the descending clock auction with highest accepted bid. In contrast, the descending clock auction with lowest rejected bid is incentive-compatible for single-project bidders: A bidder’s own bid price never directly determines her award price, and bidders thus have an incentive to bid at their true cost. Given that the descending clock auction with lowest rejected bid is incentive compatible, we recommend to apply this pricing rule rather than the two others.