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