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  • so in auction is a method of price discovery, a method of figuring out what someone's gonna pay for an item and who's going to get it.

  • So if I've got a Coca Cola to sell and I've got six people who want it, who's going to get that Coca Cola?

  • And how much are they going to pay?

  • And any sort of mechanism in which the potential buyers expressed desire in some wake and then that turns into both a price and determination of who gets it.

  • We call that an auction.

  • The Latin root of auction came from to increase, and you're kind of standard.

  • Auction says.

  • We're gonna let competition push the price up and until one person is left standing.

  • So probably the most important factor is price discovery.

  • I don't know what this item is work.

  • You have paintings for sale, and no one really knows.

  • You know what the value those paintings is.

  • Pretty much determined by what people are willing to pay for them 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 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 the everybody.

  • And we have a good enough sense of the price of the value that there's no need to run through a price discovery method.

  • How come we know the price of shampoo?

  • But we don't know the price of the Mona Lisa, in essence, that they can make more shampoo it roughly the same cost so that we can have as much shampoo is 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 comic people come in, they buy all the stuff off the shelves.

  • That would be a time where there's gonna be people who go without 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 that they're not allowed to take advantage of people who are, in some sense desperate you know otherwise you can go if you need 10 bottles of shampoo would go by 10 bottles of shampoo.

  • The grocery store doesn't run out.

  • Probably the most popular auction is called an aural 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?

  • $20?

  • I got $20.

  • I have $30.1 of $30 and so on.

  • And 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 anymore.

  • Sometimes called the English auction is 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 is the Babylonian Sze.

  • This auction has been around a really long time sealed bid auction in this case, bidder say, Here is my head.

  • They write it on an envelope.

  • Those envelopes are all open simultaneously, the high bidder wins and they pay their bid.

  • Sometimes that's called a pay as bid auction, sometimes usually with the word seal bid.

  • And sometimes it's called a first price, meaning the high bidder paid the high bit.

  • Typically, it's governments that you sealed bids much more common to be government.

  • 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 bitter 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 aural 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 will say, Is anybody willing to pay $10,000 where we're pretty sure that no one's willing to pay $10,000 the prices 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, well, 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 Maur.

  • 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 seal bit.

  • Second price sealed bid auction are also known as the Vickery auction, after William Vickery, who won the Nobel Prize for its discovery along with some other things about auctions.

  • He did this work in 1961 so the way victories 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 bids.

  • It's the minimum they could have bid and still want 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 toe guarantee?

  • There went.

  • If I am paying the second highest price, I'll will it.

  • I'll be willing to bid a lot more aggressively if you've been an 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 bitter comes back with 60 will then give it again to you for 60 plus the increment.

  • They're 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 $1,000,000.

  • 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 victory, 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 bit.

  • 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 aural auction, which has, you know, it's a great auction, forgetting 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 one by Google and being they are second price auctions.

  • You bid.

  • But what you pay is just what it would take to hold your slot.

  • Let me, let's let's just think about the first price he'll bid or the pay is bid and the victory auction.

  • When I'm thinking about what I should bid to a first price, he'll bid.

  • I say, Well, I'm gonna pay my bid, so let's say my value is 100 I think about submitting a bit of $75.

  • That means if I win, I get $25.

  • If I lower my bed a bit.

  • Well, some chance I get beat, but I make more money when I do win.

  • The sealed bid auction causes me to cut my bid a lot, because that's where my profit is on the Vickery auction, in contrast, that I'm gonna bid $100 because I wanna win any time the price comes out below $100 so that comes in love.

  • Oh, that's just great.

  • 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 wanna win whenever the prices below my value.

  • That's assuming I know my value to 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.

  • But I didn't buy it.

  • By the way, let's tweak the scenario a little bit.

  • Now they come and they offer you sell you a car for $2000 that really should sell for more like four or $5000.

  • You're kind of nervous.

  • There's something that you don't know about this car.

  • Is it really worth $2000?

  • 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 10 other people who know cars pretty well had bid 1618 119 $100 you could be a lot more willing to pay $2000.

  • 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 aural ascending auction does a good job inducing people.

  • The bid more.

  • Why?

  • Because when the price goes up, I say, Oh, well, there's another bidder, at least one other bitter willing to pay this.

  • I then say Okay, good.

  • I'm comfortable with that.

  • I beat them.

  • That causes them to say, Oh yes, well, there's another bidder willing to pay it and they go, What the Maur of that kind of information that's released, the more price pressure there is, and the war will 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 victory auction, we get some of those benefits, not all of them in a ascending auction.

  • I might see that there were 10 other bidders in the victory 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 says we're only selling one item in almost all the circumstances I deal with.

  • We're selling lots of items, so there turns out to be a version of the victory for that world, It's got some defects in New Zealand was an early adopter of the victory auction.

  • They sold telecom licenses and the national cellular license.

  • The high bid was $110 million in the second highest bid.

  • That is, the price in the victory auction was 11 million.

  • This is headline news.

  • Government sells $110 million license for $11 million.

  • 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 is an ascending auction.

  • This wouldn't have happened.

  • They still would have missed out on a bunch of money they could have had from the person willing to pay 100 and 10 million.

  • Not 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 100 and 10 million certainly wouldn't have been 110 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 resource is does that competitors hat and they have come up with a number, and maybe that number would have been 12 million, in which case that had gotten an extra 1,000,000.

  • But maybe that number would have been 10 million, in which case they'd have lost a 1,000,000 is 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 Vickery auction.

  • But you would have kept it secret.

  • And so you shouldn't think of it is being Yes, I have gotten all that money.

  • Had I run a sealed bid auction?

  • No, not at all.

  • In fact, you might have even gotten less.

  • What's your advice to someone who wants to succeed on a most things that sell on eBay?

  • There's more than one copy of it, so that is to say, 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, I'll 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 four.

  • Track, how much it sells for in different auctions.

  • And that gives you away.

  • 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 so figure out that number submitted in one election as soon as it gets beat.

  • Go submitted in another auction as soon as that gets beat.

  • Go submitted in the 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, and it was 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 meth outreach they support, you can find out more vice, Um, links.

  • I've put in the description under the video.

so in auction is a method of price discovery, a method of figuring out what someone's gonna pay for an item and who's going to get it.

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理想のオークション - Numberphile (The Ideal Auction - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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