Talk:Vickrey auction

Factual Errors

I don't think it has much to do with EBay auctions at all, I don't see that it is "similar strategically" to English auctions, and I can't see that shill bids give any advantage at all, since it is a sealed auction! (I suspect that bullet point was added by someone who though vickrey auction = EBay) 213.184.192.82 12:03, 30 March 2007 (UTC)

Actually, EBay is an approximation of a Vickrey auction if you use the strategy of bid sniping. If all bidders are using snipe bids (and it is their optimal strategy to do so), then the winner will pay the true valuation of the participant with the second highest valuation, plus a small epsilon based on the minimal bid increment. The reason this occurs is that because auctions will end at a certain time, it's a player's best strategy to bid a small increment at the last possible moment. Now, this is also assuming a one-shot auction, so the fact that there can be simultaneous auctions of perfectly substitutable items makes the one-shot Vickrey less applicable. Other auction sites, such as amazon.com, use rules that extend the auction a certain amount of time after the last bid. Such auctions are not equivalent to a Vickrey auction. I first found out about this idea in Mike Wellman's tutorial at the AAAI conference last summer (2006). The abstract can be found at [1]. Halcyonhazard 20:33, 1 April 2007 (UTC)

Ebay?

Isn't eBay's auction model based on a variation of this concept? Whereas the winner pays an amount derived from the second highest bidder? -- Des Courtney 21:41, 8 Mar 2005 (UTC)

I don't know; I haven't used Ebay. I'll go look at the rules on their site and tell you for sure. The distinction is simple, though: if the winning bidder pays what he bid, it's a first-price auction. If the winning bidder pays the second-highest bid, it's a second-price (or Vickrey) auction. Isomorphic 21:45, 8 Mar 2005 (UTC)

OK, not quite as simple as I thought. Ebay seems to be running what's called a proxy auction, in which you give an upper limit and the bids are placed automatically. However, Ebay auctions run over a period of time, and you can adjust your bid if you discover that someone has bid over your limit. In a true Vickrey auction, the bids are all collected at once with no opportunity to revise them after learning what others are bidding. These two are strategically equivalent if you use very simple auction models, but there can be differences once you add in psychological factors and the possibility that bidders adjust what they think the good is worth after seeing other peoples' bids. I hope that answers your question. Isomorphic 21:58, 8 Mar 2005 (UTC)

Vickrey auction reduces winner's curse?

I am a bit confused. As far as I know winner's curse comes from overestimating in a common value auction the value of the good. The English and the Vickrey auction are strategically similar and I know that winner's curse will show up in the English auction. Thus I don't see how winner's curse is reduced by a Vickrey auction. -- mkrohn 23:03, 25 May 2005 (UTC)

It's not. In fact, the winner's curse should actually be smaller in an English auction, because bidders can gain information during the auction by watching other bidders drop out. Vickrey auctions are sealed-bid and do not give bidders this information. What a Vickrey auction does is avoid bid shading in auctions where there is no common value (and thus no winner's curse.) Thanks for pointing this out; I don't know why I didn't catch it earlier. I shall correct the article. Isomorphic 04:32, 26 May 2005 (UTC)

The above argument may not be correct. In English Auction, the winner still pays (may be a little) more than what is offered by the runners-up. And by definition, that is "Winner's curse". In Vickrey auction, the winner has the satisfaction of knowing that whatever amount he is paying is seconded by at least one other agent. This article may clarify some doubts. Hiranmay (talk) 16:58, 15 March 2021 (UTC)

Thank you for your fast reply and the correction. In particular it is helpful as I have an exam in about a week and auctions are a (very minor) part of it. So far I have read the chapter in the Varian book, but Wikipedias articles are more interesting :-). Some remarks:

• I have removed the mention of Vickrey auction in Winner's curse.
• The advantage of the Vickrey auction (in comparison to the English auction) is that it is faster to realize (just one bidding round) and that the needed communication is lesser (the English auction requires that all persons can communicate for the time of the auction).
• Perhaps it should be pointed out that it is only the "private value" auction where bidders give their true value for the good while in a "common value" auction winner's curse in general will lead to bid shading.
• While I agree with you that the English auction gives you more information (because it lasts several rounds) I am not so sure (not saying it is wrong) about the conclusion. I try to explain (assuming of course "common value" scenario):

• If the English auction is used without the "open-exit" option than a bidder has often not much more information about the number of remaining bidders and thus can hardly judge the "real" value of the good.
• With "open-exit" things become much more interesting because everyone knows how many persons are still interested to buy the good for the current offer. On the other hand this might lead to higher bids as explained in Experimental economics: "[...] seeing other people bid for the same thing increases its probable value.". And IMHO this is not only an experimental result (from a game theory point of view that would be interesting to analyze). Not sure if my argument is understandable though, sorry.

• It should be mentioned that the Vickrey auction is in general Pareto-efficient (if there is no reserve price--if there is it is not Pareto-efficient)
• I do not know the ebay proxy thing which is mentioned in the article but I from what I read it sounds more like an English auction which is handled by an agent.

Hope my points make some sense. I would start editing the article on my own, but my time is very limited for the next ten days, thus if anyone finds the above remarks useful I would be happy if he using this to improve the article further :-) -- mkrohn 09:53, 26 May 2005 (UTC)

My own knowledge of auctions is very much slanted toward theory rather than practice. So I have to admit I don't know what the "open-exit" option is. I'm quite sure about my statement that in pure theory the English auction should reduce the winner's curse. Aside from the fact that it makes sense to me, I got it straight out of Krishna's book. However, in practice I agree that that might not be true. The effect you're talking about is called "bidding frenzy". It occurs for a number of reasons, all irrational at some level, and a lot of it is often just desire to win the auction.

I'd say more, but I'm kind of tired and thinking isn't working real well. Isomorphic 03:14, 27 May 2005 (UTC)

Examples of use

Ebay is listed as an example of a high profile users (though similar, not identical). The Wikipedia entry on AdSense states The source of all AdSense income is the AdWords program which in turn has a complex pricing model based on a Vickrey second price auction. Based on? Adding it as an example, possibly expanding on what the differences are and their impacts would seem useful to me. Any reason this is not done? 85.164.107.7 18:14, 2 Jun 2005 (UTC)

Name misspelled?

The article spells it "Vickrey", but most of the web sources and also an article I have from the Phi Beta Kappa Forum Volume 85, No. 3, P. 4, spells it "Vickery".

Are we certain that the article has it spelled correctly? If not, how do we fix it so that people will find the article and others dependent upon it? (There is a seperate article on William 'Vickrey' that would also have to be fixed if the name is misspelled.) Bill Jefferys 03:27, 4 December 2005 (UTC)

The Nobel Foundation spells it as it is in the Wiki article. This is as authoritative source as I can find easily. Bill Jefferys 03:36, 4 December 2005 (UTC)

Yes, it's spelled Vickrey. I don't know what web sources you're using, but I suggest you compare this google search with this one. Isomorphic 03:40, 4 December 2005 (UTC)

Yes, I'm convinced that the Wiki article has it correct. I trust the Nobel foundation. Googling produces somewhat more with the correct spelling; but about 40% get it wrong even so. Bill Jefferys 15:03, 4 December 2005 (UTC)

I see about 35,000 hits with the right spelling, and about 390 with the wrong spelling. Isomorphic 03:07, 5 December 2005 (UTC)

I did a different search, but forget exactly what I typed in. Both were in the mid to high 10,000s with about a 60:40 break in favor of the correct spelling. Sorry, I cannot resurrect what I did. Bill Jefferys 13:54, 5 December 2005 (UTC)

Ah, here they are: [2] versus [3]. The difference is I failed to use quotes. Bill Jefferys 14:02, 5 December 2005 (UTC)

Unfortunate merging

Vickrey-Clarke-Groves has been merged into Vickrey auction [4][5]. Now we have one article about two related, but different concepts with similar, but different names. The text is confusing, and it has become that much harder to make meaningful links to only one of these concepts. In addition, categories become a problem where they relate only to one of these concepts. Rl 12:28, 4 September 2006 (UTC)

The reason I merged the two together was before the VCG article only had information relevant to network routing (which I felt was somewhat misleading), and VCG is "simply" a generalization of the Vickrey Auction. I agree that they should be split again, but that more content will need to be added to make it worthwhile. Halcyonhazard

I mentioned it here rather than just undoing it because it was obviously done with good intentions. Merging and splitting articles wreaks havocs on article histories, though, so it should be a last resort. We shouldn't merge concepts that deserve separate articles just because they are too small or incomplete. That said, I agree with your assessment of the old VCG article. Maybe use {{expand}} instead? Rl 16:03, 4 September 2006 (UTC)

Thanks for the comment. I'm still relatively new here, and it didn't occur to me that the merging and re-splitting should be a last resort (lesson learned). As much as I'd like to, I don't think I'll have time to do justice in splitting the articles for a while (as you might be able to tell from my sporadic Wikipedia contributions). I'd be supportive if you or someone else breaks the two articles back up, and would try for at least a few minor edits/contributions. Halcyonhazard 16:38, 4 September 2006 (UTC)

There may be confusion of terms here. When I studied auctions a few years ago we used the term "Vickrey auction" to mean the mechanism the article now refers to as "Vickrey-Clarke-Groves". The single-unit case we just referred to as a "second-price auction". But then the study of multi-unit auctions is still fairly new, so maybe the terms have been changing? Isomorphic 00:52, 7 September 2006 (UTC)

From Lawrence Ausubel and Paul Milgrom's "The Lovely but Lonely Vickrey Auction" in chapter 1 of Peter Cramton, Yoav Shoham, Richard Steinberg (Eds), Combinatorial Auctions (2006), they say that what we're calling VCG here goes by many names including "extended Vickrey mechanism", Vickrey-Clarke-Groves, and General Vickrey Design. Vickrey's initial work covered second-price auctions and also multi-unit auctions of homogeneous goods. The Clarke-Groves mechanism added to the Vickrey mechanisms the ability to handle heterogeneous goods and also does not require bidders to have nonincreasing marginal values. I've heard the term "second-price auction" many times as well to refer to the single-unit mechanism designed by Vickrey. Halcyonhazard 04:53, 7 September 2006 (UTC)

My mistake, I didn't read carefully enough. The Vickrey-Clarke-Groves can handle non-homogenous goods? That is indeed different from what we called the Vickrey auction, which only handled homogenous goods. (Incidentally, my profs were Ausubel and Cramton, and you've cited both so I guess I got a pretty definitive picture, if only I could remember it all.) Anyway, it seems to me that the Vickrey auction and the Vickrey-Clarke-Groves should probably have separate articles. Vickrey auction covers single good or homogenous goods, the other article covers the more general case (under whatever name we choose from the above options.) Isomorphic 05:57, 9 September 2006 (UTC)

If you agree to split VCG mechanisms and Vickrey auction I could write the base of the VCG article. Let me know.Sebastien Lannez 13:01, 11 April 2007 (UTC)

Yeah, I'd be for re-splitting the articles. If you write the base of the VCG article, I'll try to make a little time to give it at least one editing pass. Halcyonhazard 15:31, 11 April 2007 (UTC)

I don't see that splitting these two articles is going to be useful since (i) most people who need to look on Wikipedia to find out what these things are probably wont know the difference and (ii) they aren't different per se, the VCG mechanism is just a generalised version of a Vickrey auction. As an alternative to splitting, I'd like to propose that we (i) rename this article to "Vickrey-Clarke-Groves Mechanism", (ii) put in some redirects - including from "Vickrey Auction" - and (iii) restructure the article to present the VCG mechanisn, retaining the second price auction as a special case. UbiquitousUK 21:11, 28 August 2007.

I think the example given in the text for VCG is a little confusing. Having A,B, and C not ordered by bid-price makes it tricky to follow, and I certainly don't understand how it works by the end. What if there were hundreds of apples? What's the importance of C wanting both apples? Did he get them both and pay different amounts? I'd have thought that C would have won both apples paying 5 and 2 for them. Although what if A were willing to buy two apples? Grj23 (talk) 07:31, 19 June 2008 (UTC)

I agree the example could use some clarification, and the article should have a formal description in addition to a more fully worked out example. A, B, and C's can't be in strict order; C only wants both apples and is willing to pay $6 for both, but will not pay anything for just one apple. In VCG auctions, each agent gets either a bundle of items (could be just one item) for a single price or get nothing and pay nothing. The problem could be modified such that A is hungry and wants one apple for $5, but the second apple wouldn't do A as much good, so A might only be willing to pay $2 for a second one. Given the current willingness-to-pays, if there were hundreds of apples for sale, then no agent would pay anything because there is no opportunity cost (this is a weakness of VCG in that it does not necessarily maximize seller revenue). If each of the agents had different willingness-to-pays of the hundreds of apples, then it could be solved. Solving large VCG auctions can be difficult because the problem is NP-hard, but in real-world settings, many times they can be solved quickly due to structure in the problem (see Tuomas Sandholm's work and company CombineNet for good examples of this). Also see [6] for a brief mathematical intro to VCG.Halcyonhazard (talk) 01:57, 20 June 2008 (UTC)

Unfortunate Redirect

"Sealed bid auction" should not redirect here. The last thing we want to do is give people the impression that Vickrey auctions and sealed bid auctions are the same thing. UbiquitousUK 21:17, 28 August 2007.

Reference List

Should the reference to Milgrom's book be more fleshed out? perhaps a link to it on Amazon or the publisher's website? Or the ISBN?129.89.32.111 (talk) 19:22, 20 March 2008 (UTC)

Ex-post efficiency

The article seems to suggest a definition "ex post efficient (the winner is the bidder with the highest valuation)". what does the ex post efficiency exactly mean? 72.0.216.52 (talk) 00:49, 20 June 2010 (UTC)

Empirical validation

The article includes a proof that bidding the true value is optimal. However, it does not discuss empirical validation. Do studies show that Vickrey auctions yield higher selling prices than traditional auctions? Wadler (talk) 09:09, 24 August 2010 (UTC)

Actually, the proof has nothing to do with the optimality of the seller's revenue, especially when compared to other auctions. The proof states that if you are participating in a single-shot Vickrey auction with no externalities, then your optimal strategy is to bid truthfully. In fact, when the primary desideratum is seller's optimal revenue, then Vickrey isn't usually a good choice, especially when price discovery is required because a common public price is not known. Typically, English auctions are good for this. The cited book on the page edited by Cramton, Shoham, and Steinberg has some good chapters on this information. Halcyonhazard (talk) 07:00, 26 August 2010 (UTC)

Math notation style

Please don't write this:

$(6-5)

if you mean this:

$(6 − 5)

A minus sign is not a stubby little hyphen, and proper spacing should be used. See WP:MOSMATH.

Also, notice this difference:

${\begin{aligned}&\max _{1\leq i\leq n}x_{i}\\&{\mbox{max}}_{1\leq i\leq n}x_{i}\end{aligned}}$

The first is standard and correct. The second is what I found in this article. Wikipedians seem to use \mbox promiscuously in place of various other things that are proper usage. There just isn't any proper way to use \mbox within Wikipedia, because Wikipedia's stripped-down version of TeX never has line-breaks, and the proper use of \mbox is to prevent line-breaks. In some contexts \mbox and \text produce quite different results, and I find lots of people here using \mbox instead of \text (in particular \mbox in subscripts and superscripts gives much larger letters than \text does in those contexts). Michael Hardy (talk) 01:09, 12 October 2010 (UTC)

Dr. Said's comment on this article

Dr. Said has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

Too much of a distinction is being made between the Vickrey auction and the VCG mechanism. The Vickrey auction is much more general than what is presented; indeed, Vickrey's original paper looked at multiple (identical) items in addition to the single unit (i.e., second-price auction) case. In addiiton, the generalized second-price auction is not at all a variant of the Vickrey auction -- it is a variant of a second-price auction.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Said has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Said, Maher, 2008. "Information Revelation and Random Entry in Sequential Ascending Auctions," MPRA Paper 7160, University Library of Munich, Germany.

ExpertIdeasBot (talk) 13:26, 7 June 2016 (UTC)

Ethereum Name Service used a Vickrey auction

The Ethereum Name Service (ENS) used a Vickrey auction. As of Aug 2017, the ENS controls assets on the order of US$45+ million in assets locked up to hold the web domain names. (167k+ ETH with ETH currently trading for $280+ per ETH). Seems a rather notable use of this sort of auction mechanism. The Future of ENS Incentives, and CodeTract ENS live tracker. What is the Ethereum Name Service? seems a main stream press coverage article. Google shows a number of others. N2e (talk) 04:47, 20 August 2017 (UTC)

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Weaknesses

Most of the weaknesses listed for both Vickrey auctions and the VCG mechanism in general are factually untrue and largely unsourced. Shilling cannot increase seller profits, nor are there any collusion strategies that benefit buyers. For sellers, shill bids are non-optimal strategy for the same reason that overbidding is a non-optimal strategy for buyers -- the shill bid might win. So far as collusion is concerned, a set of colluding buyers would always do better to only submit a single bid, rather than any other combination of bids. Even the supposed examples of zero price paid by winners are flawed, in that the VCG mechanism is easily modified to take seller costs into account and these function as a reserve price (though this tends to cause budget imbalance in the payments.)

I'd suggest removing all of the listed weaknesses, except for those that can be properly sourced. Wclark (talk) 16:59, 24 May 2023 (UTC)