I have read a lot of related materials recently, and thought of answering this question as a summary. The reasons mentioned below are definitely not comprehensive, and secondly, some of them have been mentioned by other respondents. I may come back and add to this answer when I have more knowledge.
Here are some theoretical reasons not to opt for secondary price auctions (qualifications are in parentheses):
- Secondary price auctions are more risky than primary price auctions (assuming buyers’ values are independent and identically distributed and risk neutral )
- The first-level price auction yields higher (assuming buyers’ values are independent and identically distributed and risk averse )
- A secondary price auction is equivalent to an ascending price auction (assuming that the buyers’ values are independent and identically distributed)
- Secondary price auctions yield lower yields than up-price auctions (assuming buyers are value- correlated )
- Sellers in secondary price auctions have incentive to fake
- The computational complexity of Vickery auctions is high (given a large number of buyers, a large number of items, a large number of constraints)
Below I will illustrate this with some examples. For specific mathematical proofs, please refer to the references at the end of the text. Some other answerers such as @Richard Xu and @sleepsoft also talked about some reasons in the experiment, which benefited me a lot. I suggest everyone to take a look.
Secondary price auctions are riskier than primary price auctions (assuming the buyers’ values are independent and identically distributed)
Now suppose there is a painting to be auctioned, and several buyers want to buy it and hang it at home. They don’t care how much this oil painting is worth in the eyes of others, the main thing is that it is comfortable to hang in their own home. They are also knowledgeable. They know that such words can be worthless or expensive, but they will not be more expensive than 5 million. In other people’s minds, the price of this painting should be in this range. (risk-neutral, value IID)
If the oil painting is sold at a secondary price auction, then the buyer can just shoot it and think it is worth a few dollars in his heart. Anyway, he has to pay the second highest price. At this time, the distribution of the price everyone auctioned will be between 0 and 5 million.
If you sell this oil painting at a first-level price auction, then the buyer must bid a price lower than the price in your mind, because if you win, you have to pay the price you auctioned. If the price is not lower than the price in your mind, then you can actually buy it back The family only cares about money. At this time, the distribution of the auctioned prices will be between 0 and a number less than 5 million.
In fact, it can be proved that there is the principle of income equivalence in this case, that is, for the seller, the expected income of the two auctions is the same. But if the secondary price auction results in a wider range of prices, the seller is actually at greater risk. If the seller is risk averse, then he prefers to choose the first price auction.
(Mathematically speaking, the expected return of a secondary price auction is the mean-preserving shape of the expected return of a primary price auction)
The first-level price auction yields higher (assuming buyers’ values are independent and identically distributed and risk averse)
The rules of the primary price auction determine that if you bid a low price, the profit will be higher when you win. But if your price is low, your probability of winning will also be low.
A speculator might think, I might as well take 1 bucks, just in case other people don’t want me to make a fortune.
But we consider the opposite type of people, that is, some more cowardly people. They don’t have the idea of turning a bicycle into a motorcycle. The probability of winning is high. Although they earn less, they can only earn if they want to win, even if I earn less. (risk averse)
As for the secondary price auction, no matter what kind of person you are, what you auction is your own value. There’s no such thing as cowardice.
For sellers, if you know that the people who come to the auction are not the type of gamblers, but the big bosses who are steady and steady in their careers, you know why you choose the primary price auction instead of the secondary price auction Come on.
A secondary price auction is equivalent to an ascending price auction (assuming that the buyers’ values are independent and identically distributed)
Raising-price auctions are auctions where the price rises slowly, and then the buyer slowly withdraws. The person who persists until the end does not withdraw wins, and he pays the price when the previous person withdraws. This kind of auction.
What we saw on TV, a person above holding a hammer, and then a group of people shouting “500,000”, “600,000” auctions, can be modeled as an auction of rising prices.
In the story of the oil painting auction above, in fact, the price increase auction and the secondary price auction are equivalent. In an up-price auction, the price rises slowly, but as long as it does not reach the price in your heart, you have no reason to quit, because at this time, no matter how high the price is, as long as you win, you will still make money. But once the price rises to the position of the price in your heart, you have to withdraw, otherwise you should lose money if you win at a higher price. So how much do you pay if you win? Naturally, it is the price at which the second highest-priced person exits. In this way, it is exactly the same as the secondary price auction.
Therefore, the price-raising auction, which is very popular in reality, is a secondary price auction under certain assumptions. From this point of view, it may not be right without widespread application.
Secondary price auctions yield lower yields than up-price auctions (assuming buyers are value-correlated)
Now let’s consider another auction scenario. Several companies are bidding on an oil field in a sea area, and they each survey and assess how much oil is in the field. There is definitely a difference between what you have surveyed and what I have surveyed, but in general, if I surveyed a lot of oil, I guess you have surveyed a lot, and in fact, there should be a lot of oil. (Associated Value)
I can’t tell you how this conclusion came to this time like I told the story before, but it can be proved mathematically that the income of the secondary price auction is lower than that of the ascending price auction. (Hopefully someone can enlighten me)
Sellers in secondary price auctions have incentive to fake
( @Richard Xu talked about this reason, here I also wrote it for the needs of my own summary)
In our previous discussion, the seller seemed to be a selfless and selfless person who strictly enforced his own auction rules. But in fact, the sellers must also have selfish intentions, and they all come out to auction oil paintings, don’t they think about making money?
Now due to the epidemic, the auction has become online. The first thing to consider is an online secondary price auction. Wang always thinks this painting is good, just enter 5 million for brushing the ground, he thinks this painting is worth 5 million, and he also knows that he will definitely not have to pay 5 million. As soon as the results came out, President Wang really won and received a bill: 4.99 million. Mr. Wang was amused when he saw it, and found that the second-highest price was an American Jack who paid 4.99 million. Mr. Wang, who won, happily asked his secretary to beat the money. Who knows sellers are happier and why? In fact, Jack’s auction was 3 million, but it is estimated that this surnamed Wang will never meet Jack on the other side of the world in his life, let alone know how much Jack has auctioned in such an auction. He asked the new interns to adjust Mr. Wang’s payable amount from 3 million to 4.99 million.
Does Mr. Wang have any opinion on this matter? President Wang was happy, he thought he had narrowly beat Jack. Does Jack have an opinion on this? Jack can have any opinion, he knows that someone has made 5 million and only 3 million must lose. No one found out about the fake made by this seller at all, and no one cared. He himself made an extra 1.99 million.
Therefore, the secondary price auction is not credible. Sellers can fake it like this.
What about first-tier auctions? What is being considered now is an online primary price auction. Wang always thinks this painting is good. He thinks this painting is worth 5 million yuan, but he will definitely not make it for 5 million yuan. It is the same if he wins if he shoots 5 million yuan or not. “Then let me pay 4 million yuan.” As soon as the result came out, President Wang won, and found that the second highest price was an American Jack who fetched 2 million.
Can the seller cheat at this time? No, because of the first price auction, if you win, you will pay as much as you bid. President Wang made 4 million, so you have to charge him 4 million. You can’t charge him 4.99 million, right? Mr. Wang should call the police and arrest you when he received a bill of 4.99 million.
So the primary price auction is credible.
The computational complexity of Vickery auctions is high (given a large number of buyers, a large number of items, a large number of constraints)
The previous answers, as well as the description of the question, as well as the answers of other respondents, are limited to the case where a single item auction is considered. In fact, we generally use the term “secondary price auction” in single-item auctions, and “Vickery auction” is more of a word used in multi-item auctions.
(to be continued……)
references
Krishna, Vijay. Auction theory . Academic press, 2009.
Milgrom, Paul, and Ilya Segal. “Deferred-acceptance auctions and radio spectrum reallocation.” Proceedings of the fifteenth ACM conference on Economics and computation . 2014.
Akbarpour, Mohammad, and Shengwu Li. “Credible auctions: A trilemma.” Econometrica 88.2 (2020): 425-467.
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Author: findingnothing
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Further reading:
What does it mean to bid, and why do you want to bid instead of closing at the highest price?
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