The Ideal Auction - Numberphile

Summary

Highlights

• An auction helps determine who gets an item and at what price, with competition often pushing prices up.📈
• The oral ascending auction, or English auction, increases prices until only one bidder remains.🎩
• Dutch auctions start high and lower the price until someone accepts, mirroring a sealed bid process in theory.🌷
• Vickrey auctions uniquely involve paying only the second highest bid, driving competitive but honest bidding.📨
• Auctions for multiple items, like those on eBay, require strategy in selecting which auction to participate in.⌛

Key Takeaways

• Auctions are a key method for price discovery and involve multiple formats like English, Dutch, and Vickrey auctions.🛍️
• The English auction is popular for its transparency, allowing bidders to adjust their valuation based on others' bids.🏷️
• The Vickrey auction encourages bidding close to actual value by only requiring the winner to pay the second highest bid.📩
• Collusion and manipulation are risks in auctions, making transparency and rules crucial.🔍
• Online platforms, like eBay, employ auction mechanics that mimic traditional auctions, helping users potentially snag a good deal.💻

Overview

Chapters

• 00:00 - 01:00: Introduction to Auctions An auction is a method of price discovery, determining the price someone will pay for an item and who will receive it. It involves interested buyers expressing their desire, resulting in both a price formation and allocation decision. The term 'auction' originates from the Latin word meaning 'to increase.'
• 01:00 - 02:30: Why We Don't Auction Everyday Items The chapter discusses why everyday items are not sold through auctions. The main reason is price discovery; auctions are used when the value of an item is not clearly known, allowing people to determine its worth based on what they are willing to pay. In contrast, everyday items like shampoo have fixed prices because their value is well understood and it would be inconvenient and frustrating to bid on such items in daily life.
• 02:30 - 04:00: Oral Ascending Auction In this chapter titled 'Oral Ascending Auction,' the discussion revolves around the reasons why auctions are not always the preferred method of selling items. It is explained that auctions are typically not run when there is sufficient supply of a product, such as shampoo, that can be easily produced in larger quantities at roughly the same cost. This ensures that everyone can receive the product without needing to determine its value through price discovery methods. The chapter highlights the difference between commodities like shampoo and unique items like the Mona Lisa, whose value isn't as easily determined or replicated, making price discovery methods like auctions more relevant for the latter.
• 04:00 - 06:00: Sealed Bid Auction The chapter titled 'Sealed Bid Auction' explores the concept of using auctions in situations of imminent shortages, such as before a storm. It discusses the ethical and legal implications associated with auctions in these scenarios, noting that many states have laws against exploiting desperate consumers during times of scarcity. This suggests a general prohibition on holding auctions when it could be seen as taking advantage of vulnerable situations.
• 06:00 - 09:00: Dutch Auction The chapter 'Dutch Auction' introduces different types of auctions, focusing primarily on the oral ascending auction commonly depicted in movies. In this type of auction, items are put up for sale with a starting minimum bid, and participants bid against each other in increasing increments until the highest bid is reached. The chapter draws a parallel to common consumer behavior, such as purchasing items in grocery stores.
• 09:00 - 13:00: Second Price Sealed Bid Auction (Vickrey Auction) The chapter explains the concept of auctions, starting with the process where the price increases until only one bidder is willing to continue, often referred to as the English auction, which has historical roots extending back to Babylonian times. It also covers the sealed bid auction, where bidders submit their bids in envelopes, and all bids are opened simultaneously to determine the winner based on the highest bid.
• 13:00 - 18:00: Comparing First Price and Vickrey Auctions This chapter discusses the differences between first price and Vickrey auctions. In a first price auction, also known as a pay as bid auction, the highest bidder pays their bid amount. This type of auction is commonly used by governments and sometimes by large corporations. The advantage of a sealed bid auction, compared to an English auction, is the reduced potential for cheating by the auctioneer, which is a significant concern when the government is involved.
• 18:00 - 22:30: Advice for eBay Buyers This chapter provides advice specifically targeted towards those buying on eBay. It highlights the risks associated with auctions, such as the potential for government officials to collude with bidders; however, such actions can be audited due to the existence of a paper trail. An example from the Department of Justice illustrates a case where a bidder unknowingly included their rivals' bids, thereby exposing a price-fixing scheme among the bidders. This incident underscores the importance of transparency and the illegality of collusion in auctions.
• 22:30 - 24:30: Conclusion and Acknowledgements The chapter titled 'Conclusion and Acknowledgements' discusses the Dutch auction, often referred to as a tulip auction, which is a type of oral auction involving an auctioneer and bidders. It starts with a high price and decreases until a bidder accepts. For example, in the context of tulip auctions, the auctioneer might start by asking if anyone is willing to pay $10,000, decreasing the price until it appeals to a bidder. The chapter concludes the discussion with acknowledgements, although the specific acknowledgements are not detailed in the transcript provided.

The Ideal Auction - Numberphile Transcription

• 00:00 - 00:30 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
• 00:30 - 01:00 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
• 01:00 - 01:30 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
• 01:30 - 02:00 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
• 02:00 - 02:30 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
• 02:30 - 03:00 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
• 03:00 - 03:30 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
• 03:30 - 04:00 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
• 04:00 - 04:30 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
• 04:30 - 05:00 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
• 05:00 - 05:30 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
• 05:30 - 06:00 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
• 06:00 - 06:30 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
• 06:30 - 07:00 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
• 07:00 - 07:30 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
• 07:30 - 08:00 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
• 08:00 - 08:30 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
• 08:30 - 09:00 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
• 09:00 - 09:30 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
• 09:30 - 10:00 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
• 10:00 - 10:30 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
• 10:30 - 11:00 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;
• 11:00 - 11:30 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
• 11:30 - 12:00 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
• 12:00 - 12:30 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
• 12:30 - 13:00 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
• 13:00 - 13:30 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
• 13:30 - 14:00 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
• 14:00 - 14:30 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.