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Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"New kind of auction balances supply, demand and complex bidding strategies,"by Philip Ball. Nature ScienceUpdate, 30 July 2003.

Ball writes about two discoveries in auction theory. The first is in the fieldof combinatorial auctions, in which what a bidder offers for an item may hingeupon such things as whether the bidder purchases another item or on what pricethe bidder has paid for the item. Although an optimal result usually is hardto find for such auctions, David Porter and colleagues present an efficientcombinatorial auction design in "Combinatorial auction design" published July31 in the Proceedings of the NationalAcademy of Sciences USA. The second discovery involves online auctions.Albert-László Barabási and colleagues have determined thatonline auctions that allow an individual to make many simultaneous bids areunfair when compared to conventional auctions. The ability to make a vastnumber of bids increases the bidder's chance to pay less while shutting outthose who bid on only one item. This research appears in "Emerging behavior inelectronic bidding" in the July issue of Physical Review E.

--- Mike Breen

American Mathematical Society