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The Ideal Auction - Numberphile - YouTube
Channel: Numberphile
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So an auction is a method of price
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discovery, a method of figuring out what
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someone's gonna pay for an item; and
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who's gonna get it. So if I've got a
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coca-cola to sell and I've got six
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people who want it, who's gonna get that
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coca-cola and how much are they gonna
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pay? And any sort of mechanism in which
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the potential buyers express desire in
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some way, and then that turns into both a
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price and a determination of who gets it;
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we call that an auction. The Latin root
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of auction came from 'to increase' and
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your, kind of, standard auction says we're
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gonna let competition push the price up
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until one person is left standing. So
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probably the most important factor is
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price discovery - I don't know what this
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item is worth. You have paintings for
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sale and no one really knows, you know,
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what- the value of those paintings is
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pretty much determined by what people
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are willing to pay for them. It would be
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a- really a frustrating thing if when I
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went to buy shampoo in the grocery store
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I had to go bid on it and wait and, well,
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let other people bid; all the while
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waiting for my shampoo. And so we
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typically wouldn't run auctions when we
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have enough of the supply that we're
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pretty sure we can sell to everybody and
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we have a good enough sense of the price
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or the value that there's no need to run
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through a price discovery method.
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(Brady: How come we know the price of
shampoo but we)
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(don't know the price of the Mona Lisa?)
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In essence th- they can make more shampoo
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at roughly the same cost, so that we can
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have as much shampoo as we need - if we
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need 10% more shampoo that's not a
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problem for the shampoo manufacturer. So
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as a result while there could be a
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shortage, and you see this often if
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there's a storm coming; people come in
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they buy all the stuff off the shelves,
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that would be a time where well
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there's gonna be people who go without,
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as a result you might think about
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holding an auction. Now let me say most
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states have laws that prevent sellers
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from holding an auction in that
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circumstance, they're they're not allowed
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to take advantage of people who are in
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some sense desperate. You know, otherwise
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you know, you can go- if you need ten
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bottles of shampoo you go buy 10 bottles
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of shampoo, the grocery store doesn't run
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out. Probably the most popular auction is
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called an oral ascending auction. You see
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it in movies where somebody
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tugs their ear and they buy a Ming vase
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by accident. The item is put on for sale,
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there's a minimum bid perhaps or a low
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bid that the auctioneer starts with, and
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then they start with this chatter going
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'do I have $10? Do I have $20? I got $20, do I
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have $30? Do I have $30?'
and so on and they- the
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price rises until at some point there's
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only one bidder who's willing to bid at
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that price. And that is no one is willing
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to go up any more. It's sometimes called the
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English auction, it was common in
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England but it's actually common around
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the world as a method of auctioning. I
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believe it was used as far back in time
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as the Babylonians. This auction has been
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around a really long time. Sealed bid
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auction. In this case bidders say 'here is
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my bid' - they write it on an envelope,
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those envelopes are all opened
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simultaneously. The high bidder wins and
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they pay their bid. Sometimes that's
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called a pay as bid auction; sometimes-
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usually with the word sealed bid, and
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sometimes it's called a first price;
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meaning the high bidder paid the high
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bid. Typically it's governments that use
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sealed bids. Much more common to be
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governments, sometimes large corporations
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will also use sealed bid. The beauty of a
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sealed bid, relative to an English
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auction, is that it's hard for the
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auctioneer themselves to cheat. So our
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big concern with the government holding
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an auction is that the government
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officials might collude with one of the
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bidders. If the government official did
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that there would be a paper trail that
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allows it to be audited. When I was at
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the Department of Justice a bidder
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submitted a bid that contained copies of
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all their rivals' bids in the same
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envelope. And so we were able to show
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really easily that the bidders
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themselves were colluding with each
other;
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price-fixing, it's against the law. The
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bidder had inadvertently submitted a
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copy of the rivals bids which they
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shouldn't have been able to see.
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Dutch auction, sometimes called a tulip
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auction, is well known for being used in
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the Dutch tulip auctions. It's an oral
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auction, that is it's used with an
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auctioneer and all the bidders assembled
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together. And it starts high and then
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runs low. If we're selling tulips we'll
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say, 'is anybody willing to pay $10,000?'
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where we're pretty sure that no one's
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willing to pay $10,000, the price is
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successively lowered until someone says
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I'll take it. And at that moment it sells
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to that bidder at the price that they
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bid. From a theoretical standpoint this
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auction is actually identical to the
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sealed bid auction. And if you think
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about it, when you submit a bid in a
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sealed bid auction you're thinking 'well
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the other bidders will bid whatever they
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bid and I win if I'm the highest.' Now
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imagine yourself in the position of
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bidding in the Dutch auction; you're
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saying I have to choose a bid and when
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the price reaches that bid that's the
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moment I'm going to jump in. I'm thinking,
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will the other one's bid higher than
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that? In which case I'll lose. But if I
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put in a higher bid I might win but I
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pay more - it's exactly the same thought
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process that you face with the sealed
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bid auction. So in fact theoretically the
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same bidder should win at the same price,
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whether I hold a Dutch or a sealed bid.
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When we actually run experiments it's
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not true, people jump a little bit
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earlier in the Dutch auction. That is
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they bid a little bit higher - maybe
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because of the excitement of it, just the
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time while they wait is making them
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nervous or something, they're less
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rational - we don't know. But they bid a
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little bit higher in the Dutch auction
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than they do in the sealed bid.
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The second price sealed bid auction, or
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also known as the Vickrey auction, after
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William Vickrey who won the Nobel Prize
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for its discovery, along with some other
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things about auctions. He did this work
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in 1961.
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So the way Vickrey's auction works is it
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works just like the sealed bid that we
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described before, but now when we open
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the envelopes the high bidder will win
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but they pay the second highest bid, not
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the highest bid. It's the minimum they
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could have bid and still won; is
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one way to think about it. This is the
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price of that. Had they known what all
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the other bids were this is what they
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would have wanted to bid - is that, maybe
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plus a penny to guarantee their win. If
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I am paying the second highest price
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I'll will- I'll be willing to bid a lot
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more aggressively.
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If you've bid in eBay this is how eBay
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works. You submit a bid, let's say for
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$100. When another bid comes in at 40
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they then turn around and give it to you
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at 40 plus the increment, which might be
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45. If that bidder comes back with 60
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they'll then give it again to you for 60
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plus the increment, there around 65. That
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process continues unless someone
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actually bids higher than you. So what
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that's implemented is a second price
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auction, that is to say you don't pay
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your bid - you could have been a million
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dollars - you still pay the next highest
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bid plus a little bit. And the smaller
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that little bit is the more it looks
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exactly like the Vickrey which is paying
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the second highest price.
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It's easy to cheat a second-price
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auction, because you actually see what
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people are willing to pay; so you could
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just go to the high bidder and say oh
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the second highest bid was just a penny
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below your bid, you're gonna have to pay
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approximately your bid.
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Well they've revealed it, and that can be
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dangerous. That's the downside of it; the
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upside of it is that it actually gets
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this competitive pressure of that oral
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auction, which has- you know it's a great
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auction for getting- for extracting lots
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of money out of people but without
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requiring them to be in the same room, or
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even to be humans. And a good example of
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that: the big search auctions won by
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Google and Bing?
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They are second price auctions. You bid
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but what you pay is just what it would
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take to hold your slot. Then let me- let's
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let's just think about the first price
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sealed bid, or the pay as bid, and the
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Vickrey auction. When I'm thinking about
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what I should bid to a first price sealed
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bid I say, 'well I'm gonna pay my bid.' So
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let's say my value is a hundred and I
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think about submitting a bid of $75. That
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means if I win I get $25. If I lower my
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bid a bit - well there's some chance I get
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beat but I make more money when I do win.
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The seal bid auction causes me to cut my
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bid a lot, because that's where my profit
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is. On the Vickrey auction in contrast,
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then I'm gonna bid $100. Because I want
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to win anytime the price comes out below
$100.
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(Brady: And if it comes in lower
that's just gravy?)
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It's all extra money for me, it's
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all money in my pocket. So there's no
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price advantage of lowering your bid,
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there's only a 'did I win?'.
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Well I only want to win whenever the
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price is below my value. Now that's
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assuming I know my value. Somebody came
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along when I was a graduate student and
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offered to sell me a fairly new car for
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$50. You know something's wrong with this,
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like it's stolen - it's too cheap in some
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sense, it's too cheap; I didn't buy
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it by the way. Let's tweak the scenario a
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little bit, now they come in they offer
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you- sell you a car for $2000 that really
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should sell for more like four or five
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thousand dollars. You're kind of nervous,
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there's something that you don't know
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about this car - is it really
worth $2,000?
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And maybe you need a car and you would
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like to buy it but you're still very
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suspicious that this car is worthwhile. If
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it turns out though that ten other
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people who know
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cars pretty well had bid 1600, 1800,
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1900 dollars - you're gonna be a lot more
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willing to pay $2,000. So the effect of
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this is, if I know another bidder is
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willing to pay more for it rationally I
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will actually increase my value, or I
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will be less skeptical that it's
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actually a pig in a poke. What that means
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is the English auction, this oral
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ascending auction, does a good job
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inducing people to bid more. Why? Because
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when the price goes up I say, oh well
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there's another bidder - at least one
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other bidder - willing to pay this. I then
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say, okay good I'm comfortable with that
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and I beat them. That causes them to say
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oh yes well there's another bidder
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willing to pay it and they go up. The
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more of that kind of information that's
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released the more price pressure there
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is and the more we'll push prices up. That
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auction does a good job extracting money
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out of people because of the release of
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information about value from the other
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bidders. The effect of this is is that in
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a Vickrey auction we get some of those
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benefits; not all of them, you know in a
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ascending auction I might see that there
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were ten other bidders - in the Vickrey
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auction all I'm really guaranteed is at
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least one other bidder was willing to
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pay what I'm gonna be asked to pay for
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the item. That tends to drive up values
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and hence tends to drive up prices on
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average. And that's good for the seller.
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It's also good for the buyer in the
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following sense; they wind up getting
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lower profits but they also lower the
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possibility or the likelihood that they
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lose money. So we've only talked about
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one good item so that is
we're only selling
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one item. You know, almost all the
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circumstances I deal with we're selling
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lots of items so there turns out to be a
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version of the Vickrey for that world;
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it's got some defects. New Zealand was
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an early adopter of the Vickrey auction,
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they sold telecom licenses and the
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National Cellular license, the high bid
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was a hundred and ten million dollars and
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the second highest bid, that is the price
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in the Vickrey auction, was 11 million.
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This is like headline news, government
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sells a hundred and ten million dollar
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license for 11 million dollars. Sometimes
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it's actually a bad idea to find out
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what the value is or at least to make it
public.
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Had they run that as an ascending
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auction this wouldn't have happened.
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(Brady: They still would have
missed out on)
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(a bunch of money they could have had)
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(from the person willing to pay a hundred)
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(and ten million. It just wouldn't have)
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(been known.)
- Not necessarily. Let's take
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the case where they ran a sealed bid
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auction, first price - pay your bid. The
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bidder who was willing to pay a hundred
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and ten million certainly wouldn't have
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bid a hundred and ten million, that
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would have left them with no profit.
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Instead they'd have said, who's the
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likely competition here? How much in the
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way of resources does that competitor
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have? And they'd have come up with a
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number; and maybe that number would have
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been 12 million in which case they'd have
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gotten an extra million - but maybe that
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number would have been ten million, in
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which case they'd have lost a million.
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It's not exactly clear. What's true is
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you wouldn't expect it to be a lot more,
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and in fact the mathematics of it
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suggests you would you would expect less
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on average from using that sealed bid
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auction than from using the Vickrey
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auction - but you wouldn't have kept it
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secret. And so you shouldn't think of it
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as being, yes I have gotten all that
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money had I run a seal bid auction; no
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not at all. In fact you might have even
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gotten less.
- (Brady: What's your advice to)
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(someone who wants to succeed on eBay?)
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Most things that sell on eBay there's
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more than one copy of it. So that is to
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say you- there are multiple copies of it
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and so the hard problem on eBay
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is not so much what to bid on the item
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but which auction to bid in. So my first
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advice is, if you want something and
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you're not in a hurry if you're in a
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hurry well buy it now. If you want
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something and you're not in a hurry
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watch what the outcomes are, because eBay
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doesn't really make this all that easy
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to know what what things sell for. Track
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how much it sells for in different
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auctions and that gives you a, well if
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I'm willing to wait six weeks here's
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what I expect to pay. If I'm willing to
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wait three months I will expect to pay
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less, I'll see an auction that shows up
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with a lower price. And so that gives you
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information that arms you about what to
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bid and then sub- figure out that number,
submit it in one
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auction - as soon as it gets beat go
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submit it in another auction. As soon as
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that gets beat, go submit it in a third
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auction. And so on. When you do this you
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should favor auctions that are about to
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expire. Why? Because that way you get the
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information earlier about whether you're
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going to get beat; so you're kind of
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running what we call a search algorithm.
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I'm trying to find which
auction is going to
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get the item to sell at that low price.
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This obviously only applies for items
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that are- where there's more than one
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item but that is the bulk of the things
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that sell on eBay.
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That building behind me? That's the
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Mathematical Sciences Research Institute,
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and that's where today's video was made.
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If you'd like to find out more about
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them, the mathematics that's done here,
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and also the math outreach they support;
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you can find out more via some links I've
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put in the description under the video.
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