Ascending auction

In outline, the two steps in a primal-dual approach to the design of efficient ascending auctions are ... 

More recently, Parkes Ungar [79] proposed an ascending auction, /Bundle, which is efficient for the case of buyer-submodular rtftxtncQs, Buyer-submodular is slightly stronger than agents-are-substitutes. As before, let w L) denote the coalitional value for agents L CX. Buyer-submodular requires ... 

Lawrence M Ausubel and Paul R Milgrom. Ascending auctions with package bidding. Frontiers of Theoretical Economics, 1 1-42,2002. 

Here we focus on the class of indirect mechanisms that are called ascending auctions. 

In the auction of a single object, it has long been known that an open (ascending) auction exists that duplicates the outcomes of the Vickrey auction. This is the English auction, in which the auctioneer continuously raises the price for the object. An agent is to keep his hand raised until the price exceeds... 

Ascending auctions also have problems in that they make collusion amongst the bidders easier. This we discuss in section 5.4. 

Ascending auctions come in two varieties (with hybrids possible). In the first, bidders submit, in each round, prices on various bundles. The auctioneer makes a provisional allocation of the items that depends on the submitted prices. Bidders are allowed to adjust their price offers from the previous rounds and the auction continues. Such auctions come equipped with rules to ensure rapid progress and encourage competition. Ascending auctions of this type seem to be most prevalent in practice. 

In order to understand how to design ascending auctions it is important to identify what properties prices must have in order to produce an allocation that solves CAPl. Such an understanding can be derived from the duality theory of integer programs. 

The exposure problem is not the only problem that can occur with an ascending auction. Another is the threshold problem (see Bykowsky et al. [7]) which is an instance of the violation of the agents are substitutes condition. 

Ascending auctions, because of their open nature, allow bidders to signal to one another and so coordinate their bidding. To illustrate suppose two distinct... 

Other ascending auctions that do not fit neatly into our division between primal-dual and lagrangean have also been proposed. Wurman and Wellman [68] propose an iterative auction that allows bids on subsets but uses anonymous, non-linear prices to direct the auction. Bidders submit bids on bundles and using these bids, an instance of CAPl is formulated and solved. Then, another program is solved to impute prices to the bundles allocated that will satisfy a complementary slackness condition. In the next round, bidders must submit a bid that is at least as large as the imputed price of the bundles. 

Why a simultaneous ascending auction We suspect precedent. There are other (open) auction forms one could have suggested. For example, allow bidders to submit simultaneous bids on packets of 2 or 3 blocks (at most one of which would be honored). Alas they have not yet been implemented. Our guess is that the RegTP had no wish to be pioneers. The Simultaneous Ascending Auction (S AA) had been used in the US to much praise and so was a natural choice to consider. 

---