" What's the best way to organize an auction in which bidders are competing for multiple items? "
define an auction as
"any market that involves a single seller and a group of buyers."
" Figuring out how to extract the maximum amount of money from people with differing abilities to pay"
"According to Daskalakis, the difficulty of finding the optimal multi-item auction suggests that it "has such large complexity that there's no succinct description that gives you the optimal outcome." "
"To maximize revenue, the auctioneer might have to agree to sell an item at some fraction of the highest bid, a fraction that could depend on a host of factors: the difference ..a long laundry list of allocation rules of what you have to do for every possible set of bids"
,
The solution by Daskalakis
"..while the optimal auction might be enormously complicated, it can be described as a probabilistic combination of simple auctions."
consider this analogy
' three points define an equilateral triangle. A point in the center of the triangle
can be thought of as 33 percent the point at the top of the triangle, 33 percent the bottom right corner and 33 percent the bottom left corner. "
"..we view this auction-design problem as a geometric problem...And our auctions lie inside complicated shapes whose corners are simple things."
" In particular, the "corners" are so-called Vickrey–Clarke–Groves (VCG) auctions, one of whose inventors, William Vickrey, won the Nobel Prize "
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"the auctioneer doesn't have to keep track of a complicated set of rules. After the bidders have submitted their bids, the auctioneer randomly chooses one of the VCG auctions — the "corners" — and uses its relatively simple rules to allocate the items in the docket."
"Every randomized algorithm is by definition a distribution over deterministic algorithms, so the crucial thing here is not that," The crucial thing is understanding what deterministic algorithms are in this decomposition... in this decomposition it happens to be of a very simple form — VCG auctions....It is remarkable that they are of this type,"
"In the type of VCG auctions the researchers use, bids are modified according to the populations from which the bidders are drawn: Affluent bidders might see their bids cut in half; middle-income bidders might see theirs boosted by 20 percent."
" The items in the docket are then allocated according to the modified bids — not the actual bids. The difference between the VCG auctions in one of the researchers' decompositions is simply the numerical values of the modifications."
Lose to win
". A movie theater that sells student tickets for $5 and nonstudent tickets for $10 is, in effect, modifying its customers' bids according to their ability to pay — boosting the students' $5 bids so that they're commensurate with the nonstudents' $10 bids."
" By using a tiered pricing model, it makes more money. It may lose the business of a couple nonstudents who would have been happy to pay $5 — or $8 — but not $10, and it may undercharge a few students who would have been happy to pay $10. But overall, it does better business than it would if it had charged everyone the same flat rate."
