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Vickrey Auction (wikipedia.org)
66 points by EricButton on June 29, 2023 | hide | past | favorite | 65 comments


The Undercover Economist book mentions these. They're honest but they're publicly embarrassing for governments in auctions with few bidders, because sometimes there would only be two bidders, one bidding $100k and one bidding $4, so people were wondering why the winner who was bidding $100k was only paying $4 for a license. [0]

The book goes on to describe the UK 3G Telecom license auction[1] and explain how it went much better. In summary it was more like a typical auction but instead of bidders proposing bids, the price went up gradually and the the bidders did something like stay as the price went up or leave when the price went too high for them.

[0]: https://blogs.cornell.edu/info2040/2022/10/31/when-an-auctio... [1]: https://www.nuff.ox.ac.uk/economics/papers/2002/w4/biggest29...


If these auctions were common, it seems like it would be a ripe opportunity for arbitrage.

In a case like this if you thought the market value was $100k, someone with no interest in the license should go ahead and bid something like $60k anyways. If everybody else placed silly bids like $4 "just in case nobody else bids for real", you'll win and resell it and walk away with $40k profit.

Of course this assumes there is an actual market for the thing -- that a telecoms company really will take it off your hands for $100k.

Although if there really is only one person in the world who wants something and they would pay $100k for it... and literally nobody else has any interest in it at all... then there's a good argument to be made that it really is worth $0. Like a remote island that is utter perfection for one hermit, but of zero interest to anyone else.


A key property of a Vickrey auction is that it is incentive compatible, i.e. that it isn't possible to achieve a better expected outcome by bidding something other than your true valuation.

Your example relies on the telecom company (or any secondary buyer) not bidding in the auction or bidding only $4. A strictly dominant strategy for the telecom company would be to bid $100k in the auction, winning it for $60k (the second-highest price).


> In a case like this if you thought the market value was $100k, someone with no interest in the license should go ahead and bid something like $60k anyways. If everybody else placed silly bids like $4 "just in case nobody else bids for real", you'll win and resell it and walk away with $40k profit.

No, in a case like this, you would risk having to fork over 60k, and you would in reality win nothing. The company that bid 100k gets it for 60k, you spend and receive nothing.


What's the difference in the example of the embarrassing public auction? In that example, doesn't one of the two bidders leave the auction when the price rises over $4? Leading to the same outcome?


That's correct, the price at the end is theoretically the same, but the public doesn't know about the high bidder's price in the second option. The second option (or just a regular auction) just saves you some embarrassment, which is nothing in the end, but in the political world embarrassment is not nothing.

The other benefit (for the seller) mentioned was that bidders get a social signal that other companies think the license is apparently worth the current price, which could pressure the price upwards. Versus Vickrey Auctions where it's a completely blind bid.

If you're curious, if you google "undercover economist vickrey auction uk" you may or may not find a ctrl+f searchable pdf where you can read this section yourself.


You don't choose to leave in a Vickrey auction, your participation is limited to one bid.


In Quebec we had an investigation into widespread corruption in construction ( https://en.wikipedia.org/wiki/Charbonneau_Commission ) during which the major government witness made the very strong case that thanks to the lowest-bidder-at-lowest-bid-price auction process used by municipalities you either have to be corrupt or you will go out of business. I couldn't help thinking he should have cited Vickrey at the time (unlikely that he would be aware), and the province should have move to second price auctions for dishing out government contracts, but you would have the small challenge of persuading the populous that paying an amount which isn't actually the lowest bid is actually in the long term interest of everyone, especially if the short term beneficiaries have a track record of organised crime.


But as the article points out, Vickrey-style auctions are vulnerable to collusion. Presumably in an area where there's already lots of corruption you're going to see plenty of this.


They are vulnerable to collusion in the sense that if all partys collude to decide who is going to win, then the winner bids X and the losers never put in a bid, so the pre-determined winner pays $0. In that sense, literally every auction is vulnerable to collusion. The only net downside to the Vickrey auction is that the winner still wins even if there is a defector, they would just pay more. This is in contrast to say a normal first-price auction where the winner values at $100 and the losers value at $99, so they collude to have the winner bid $1 and the colluders bid $0, but then there is a incentive for the colluders to defect and pay $2 to get the thing they value at $99. So, vulnerable to collusion in this sense is more that it is vulnerable to collusion with little to no risk of defection. However, if there are non-colluders, then the best you get is the highest bid of the non-colluders.


Indeed, you would need carrot and stick. The point the witness made was that under the current system you could not profit without collusion. (Edit to add: and that means that all honest people end up driven out of the construction industry). At least under a Vickrey system an honest person can make a profit hypothetically proportional to the social benefit provided.

The flip side is you would have to tell people that while you're going to increase what you pay them your tolerance for collusion (and it is essentially tolerated today) will go down, and mean it.


true. wonder if there's something like the average of the 2 best bids that would mitigate this problem. coupled with anti-corruption enforcement...


I don't think a Vickrey auction would solve this problem.


Vickrey auctions are really neat! It seems like everyone walks away feeling like they got a good deal.

Kevin Lynagh wrote a great blog post about how he convinced a friend to sell a portion of his inventory of small-run of mechanical keyboards via Vickrey auction.[0]

The friend normally sold the keyboards for $500, but the winners of the Vickrey auction paid $1,668. They were all willing to pay substantially more, too, with the highest bidder offering $2,684.

[0] https://kevinlynagh.com/notes/pricing-niche-products/


It would be interesting to see if this model can be applied to other enthusiast-driven markets or if it's uniquely suited to markets with high-value, low-volume products."


I think that using uniform price auctions for nvidias troublesome 3080 launch would have been beautiful, same for other things that have issues with scalpers and whatnot


Makes sense in the context of collectible mechanical keyboards.

FWIW if you Google Brand New Model F Keyboards, they're currently doing a sort-of vickrey auction for some upcoming novel designs.


This is basically how eBay works for auctions.

A pair of headphones is currently bid up to $55, you place a max bid of $100, and at the end, if the final max bid among every else is $80, then you win them for $81.

Which is why I never understand complaints against eBay "snipers", who bid in the last couple seconds of an auction. If you put in your actual honest max bid, the timing simply doesn't matter.


> Which is why I never understand complaints against eBay "snipers", who bid in the last couple seconds of an auction.

If there were only one instance of the thing you wanted, then there would indeed be no reason to complain about snipers. But if there's multiple different auctions, each selling one of the thing you want, you can't bid on a second one until you're outbid on the first one, or you'll risk getting stuck having to buy them both. Snipers thus result in you being "locked out" of the other auctions for way longer than necessary.


People complain about snipers because they only know if they lose the auction at the last minute.

This means you have to wait until the auction finishes, before you can bid at another auction. Constantly failing auctions because of some hidden bidder means you are wasting your time. It is only worth bidding in the last 30 minutes.


This is exactly why people need to put their actual max bid (as the parent explained) instead of trying to lowball, then the timing doesn't matter.


> people need to put their actual max bid

People don't necessarily know their actual max bid.


Yes they do if they stop to think about it. It might take a minute or so of thought, though.

Obviously that max bid can change over time, i.e. if they discover the same item cheaper elsewhere two days later, but at any given point in time people know their actual max bid.


> This means you have to wait until the auction finishes, before you can bid at another auction... It is only worth bidding in the last 30 minutes.

This is definitely true if there's more than one item listed, but it's still got nothing to do with sniping. It's just the fact that eBay auctions usually last for 7 days.


People complaining about snipers are complaining about not being able to snipe - because they could just put in their max bid. They want the second bidder to go away.


This thread [1] covering the 2020 Prize in Economic Sciences, awarded to Paul Milgrom and Bob Wilson for their improvement of auction theory, is a good read.

Vickery Auctions are one of many in the auction format bestiary, and like all classical formats, they predate both computers and modern auction theory. What's really cool these days (and I'm admittedly biased since it's my space) sits at the intersection of computer science and economics. Economic mechanisms and auction formats that use everything from SAT solving and combinatorial optimization to machine learning and function approximation to drive better real-world economic outcomes.

[1]: https://news.ycombinator.com/item?id=24753291


Programmatic advertising used to be vickrey but switched to first price, and now everyone has to use bid shading to predict how much they can reduce their bid in order to still win the auction.

https://snigel.com/blog/what-is-bid-shading#:~:text=Bid%20sh....


Facebook's ad platform famously uses the Vickrey–Clarke–Groves auction [0]. In theory it rewards advertisers for bidding for ads using their true valuation, or rather, the lifetime value of a customer.

In practice, it's a lot more convoluted, but the basic principle is fascinating.

[0]: https://en.m.wikipedia.org/wiki/Vickrey%E2%80%93Clarke%E2%80...


All of programmatic was vickrey up until a few years ago when everyone switched to traditional first price auctions. I miss those days - it was easy to bid outrageous prices ($100 cpms) but still pay a reasonable amount. Now you need deep/machine learning to evaluate each bid value, and then another algo to predict how much you can shave off that bid and still win the auction.


The Handshake [0] project used (uses?) Vickrey auction to auction off the initial supply of names. It had some other cool ideas, such as replacing certificate authorities with self-signed certificates verified by the blockchain.

I know everyone hates blockchain, I kind of do too, but Handshake I found genuinely interesting.

Disclaimer, I own some Handshake names so you could say I'm shilling for it but mostly the project appears dead anyway...

[0]: https://handshake.org/


I almost bought a Handshake domain, but didn't because of the Vickery auction they use. I wanted to register one that matches my best .com. It's not an in demand name, so it's available, but the last thing I want when I'm buying a domain is a big announcement and a bidding war.

Hey look at me! I'm trying to buy a domain over here! Come compete with me!

It has no value to anyone except me and anyone that can usurp it and try to sell it to me. I don't want to compete with a bunch of crypto bros that have tons of paper money (aka coins) in a low liquidity system, so I opted not to bother.

Now I'm glad I didn't bother. It would have been a huge hassle just to get HNS (?) and now there are tons of blockchain TLD startups. With the collisions that creates they're basically recreating the namespace fragmentation and ambiguity that results from every platform having independent handles.


I completely empathise with your situation.

Last time I checked (not very recently), all the other blockchain domain systems were worse than Handshake. Doesn't mean they won't win...


What's the reason behind?


It implements the welfare-maximizing outcome, defined as the outcome that maximizes the sum of the valuations of all of the bidders for the chosen outcome.


Is this not subject to an equivalence theorem just like revenue?


Explain it to me like I’m a 5 year old


I can't talk about the welfare optimising effects but it's a more efficient way to generate a similar outcome to a classic 'bid upwards' English auction - I assume you know the process of that.

Imagine we have four people competing, who each have a max bid of:

Alice: 100, Bob: 150, Charlie: 155, Diana: 180,

In a standard auction bidding would, say, start at 50. When the cost exceeded 100 Alice would drop out, similarly for Bob at 150, and Charlie at 155. So Diana would win and pay 155 (plus maybe one bid-increment, depending on who bid first).

So, if each simply submitted their max bid under the Vikrey auction rules, Diana would win, and pay 155. The whole bidding upwards process can be avoided, which is by some standard more efficient, and everyone pays essentially the same as they would under and English auction.


Great explanation, thank you


In sealed auctions, you want to win by bidding the most. But if you win by more than $1, you could have paid less.

In this version, you just bid to win and the seller lets you adjust down to that perfect "just barely winning" bid afterwards.

It turns out the seller makes more by everyone bidding to win than they lose by letting the winner adjust their bid after winning.

That's because the 2nd place bid ends up being higher than the winner's used to be.


Thank you


The winner pays the price that the 2nd highest bid.

This means all bidders in the auction have a reason to send an honest bid rather than trying to game the system.

The person "selling" in the auction also has an efficient outcome.


Though we should note this only works in the absence of collusion. If a bidder colludes with the seller, then they can increase the amount the highest bidder pays by bidding a very high second-highest bid.

If the bidders collude, they can get a very low price. This is (obviously) true of most auction systems, but for sufficiently public English auctions, bidders that are otherwise uninterested in an item might bid on an item that is going for obviously far below market.


Yeah finally got why it makes sense to make an honest bid. Thanks


In a normal auction you take the highest offer, but stiff competition will cause the final offer to be too high. If we're talking about megarich people buying Rembrandts, who cares. But generally this is a bad thing: we're failing to discover the real value of the thing being auctioned, and we're being wasteful.

For bidding on jobs (e.g., highway construction) one normally takes the lowest bid, but the lowest bidder will not make any profit and might lose money on the deal, thus putting the project at risk. What might happen in those cases is that corruption takes root and the lowest bidder gets paid more money illegally.

In any case, sealed bid, second price bidding solves the problem by removing the incentive to offer the best price and instead offer the real value.


Reminds me of this old auction site who's name I can't remember (power in numbers or somesuch?) ... I purchased an Amplifier for my Camaro ... This was in like 1996 ... There were multiple available for purchase (like 25 or so) ... the top X bidders won the right to buy, but we all paid the lowest winning bidder's price ... I think I got that amplifier for like $96


I posted something in the online classifieds this way. In demand but manufacturer was sold out for months. I didn't know how to price it, and I wanted to get a fair price as well as being fair to buyers.

Well, kijiji buyers were not into that. No replies. Just one guy who told me it was the dumbest ad he had ever read. So, I'm still sitting here staring at those ironmaster dumbbells.


Don't obsess over the price you get for used stuff.

If you want, post for sale high, and lower the price over time until you get a sale.


As a tangent, I've heard the Google and others are moving away from second price auctions.

Does anyone have more info on this topic?


I worked for several years in the ad tech space. Display ads on the open web are...something else. IMO, second price auctions don't work well in the online ad world.

In the real world, you know:

(1) all bids are submitted before being reviewed

(2) the highest bidder is actually going to pay the second price, and there's some friction in the form of a buyer's premium that makes it cost inefficient to immediately resell the item

Neither of these hold in the ad space.

Re (1), if you're trafficking ads through GAM, Google gets a chance to see the highest bid before deciding to commit to a bid.

Re (2), a publisher can insert fake line items that dynamically activate on a per-impression level. The goal of the fake line item is to be a stalking horse to artificially inflate the second-highest bid so that the second-price auction is effectively a first-price auction. If the publisher accidentally bids too high and wins the auction, they can just run the auction again.


I also work in ad tech (lead the algo team in job ads).

Second price auctions online are great, but they're not strategyproof. You still need a bidding strategy.

For thin/small/sparse markets they simply don't work. You need a first price auction.

Google definitely game their own 2nd price auction, but this is just one reason amon many they're not strategyproof.


Do advertisers even control their bid in the auction? In my experience, not fully.


My job is to write algos that optimize the bid on behalf of clients.

Most pay per click ad platforms have an API that let you set the bid.


I also work in this field,

> Most pay per click ad platforms have an API that let you set the bid.

even when you are let to set the bid, usually the auction is not conducted just based on your bid but also adjustments from the probability that you will actually pay out


Right, this is why I said it's not strategy proof.

The bid is just an input you control into an opaque function where the output is some cost and conversions


I’ve been a buyer for 8 years are so on ttd and another dsp but haven’t heard of the probably of paying out thing - can you share more info on that?


If you are bidding on a pay per click basis, typically your bid will be adjusted to expected revenue based on the probability someone actually clicks on your ad. For CPM ads this probably doesn't apply.

This is not for open web exchanges, referring more to stuff like adwords, facebook, etc.


Ah shoot that makes sense I was so confused. I was thinking for programmatic the ssp was reducing a bid based on whether they expected the advertiser to actually pay haha


i phrased it poorly


I’m not supply side, but I thought they could just a floor price? Or is that only for pmps?


One problem with second price auctions is their lack of what is known as "credibility". Google has both the incentive and opportunity to lie to the highest bidder about what the second-highest bid was, so they can charge more.

They never literally did this, but ended up doing some convoluted scheme involving subsidies and rebates that, according to a recent lawsuit, amounted to something equivalent.

First price auctions don't have that problem -- you know exactly what you should pay if you win.


Depends a bit on the subcategory, but for programmatic video with real time bidding basically the whole industry started second-price, then moved to first price (different entities, such as exchanges, felt they wanted to extract more profit) and these days it barely qualifies as an auction process due to the amount of "side bidding".


A Vickrey auction is what effectively happens when bidders “snipe” on eBay.


...is another word for sealed-bid second-price auction, to save you a click


I wonder if this would work in the US for housing/real estate?


This is how real estate works. It's called "escalation" in real estate.




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