A brief discussion on the design of bidding advertising mechanism

Regarding bidding ads , many people have two extreme views:

• The first view is that bidding advertising is very simple. Isn’t it just CCTV bidding for prime advertising space every year? Whoever bids the highest will get the advertising space.
• The second extreme is that bidding advertising is too complicated, involving game theory, mechanism design, auction theory, CTR estimation and other advanced theories that ordinary people simply cannot understand , so many people are discouraged from trying it...

However, what is the truth? Which view is correct? Wei Xi, who has been committed to analyzing the underlying logic of Internet business in simple language, will tell you:

The truth is just like the ending of “Little Pony Crossing the River”: the river is neither as shallow as the scalper said, nor as deep as the squirrel said - the basic logic of bidding advertising certainly involves a lot of complex theories, but after reading this article, most people can easily understand the ins and outs of its core principles.

1. From CCTV's top bidder to Google's bidding advertising system

Regarding bidding advertising, many people believe that Baidu is the first company in China to launch bidding advertising. In fact, in a broader sense, CCTV's prime advertising bidding popularized the concept of "bidding advertising" to everyone earlier . As early as 1994, CCTV began to auction advertising space by bidding, giving birth to well-known bid winners such as Qin Chi and Aido VCD.

A typical auction scene goes like this: the auctioneer first marks the ad space and indicates the reserve price, then starts waiting for bidders to bid upwards, "1 million!", "1.2 million!", "2 million!", "2 million once, 2 million twice, deal!"

We are all familiar with such scenes in many film and television works, but not all auctions are conducted in this way. This is just one of many auction mechanisms. This auction method of continuously increasing prices is called the "British auction."

Similar to the English auction, there is also the Dutch auction. The format of the Dutch auction is exactly the opposite. The auctioneer first offers a very high price, and then keeps trying to lower the price until a bidder is willing to accept the transaction price.

So the question is - if traditional advertising can be bid in this way, can online advertising also be bid in the same way? The answer is no . The reason is that online advertising auctions have several important differences from traditional advertising auctions, and these differences will have a significant impact on the design of the bidding mechanism:

• First, whether it is an English auction or a Dutch auction, everyone's bid is public, but many online advertisers may not be willing to disclose their bids , so open bidding becomes inappropriate.
• Second, CCTV’s auction is a one-time action, while online advertising is a repeated game . That is, if one ad space is taken, the advertiser can grab the next one, and the advertiser can constantly adjust his bid.
• Third, online advertising involves multiple objects (each ad request may involve multiple bidding objects) and massive real-time computing.

So what kind of bidding mechanism should online advertising adopt? There are actually a lot of options, let’s look at them one by one:

The first possible option is the "sealed first price" bidding , which is actually a bidding method we are familiar with. Many engineering biddings adopt this method. Its mechanism is that each bidder does not announce his or her bid, but seals it in an envelope and hands it to the seller. The auctioneer allows the highest bidder to win the auction and pays the bid of the highest bidder.

Some people say that this method seems perfect, as it meets the needs of advertisers not to make their bids public, and it has also been proven in many practices. However, in this bidding method, the advertiser's bidding strategy depends on how others bid, but has little to do with their own real valuation . This will cause problems when applied to online advertising auctions.

One of the characteristics of online advertising is repeated game. What does that mean? For example, offline project bidding is one-time, and bidders will tend to be more cautious about their bids because they only have one chance. However, online advertising is multiple-time, that is, advertisers have multiple opportunities to continuously test other people's bids, thereby realizing their optimal strategy.

Let me give you an example - for the ad space under the keyword "running" on Google, Nike believes that a click is worth 10 dollars, while Adidas believes it is worth 6 dollars. At this time, if they adopt a "sealed first price" auction and the reserve price given by the Google advertising system is 2 dollars, then Adidas and Nike will both try to bid.

Adidas started with 2 yuan, Nike offered 2.1, Adidas offered 2.2, Nike offered 2.3, and the two sides kept raising the price until it reached 6 yuan. Then Adidas stopped bidding because it thought the ad was worth 6 yuan at most, so it withdrew.

At this time, only Nike is left. Nike is not stupid. Since no one is competing with it, why should it offer 6 yuan? So it quickly adjusts the price to 2 yuan. At this time, Adidas will enter the market again, and the cycle begins.

If you are careful, you will find that this method has an obvious flaw - instability. The root cause behind this is that from the perspective of game theory, there is no Nash equilibrium in this auction method (this has been proven by economists from a mathematical perspective), that is, there is always a state of chasing each other, because the bid in this auction method depends on the bid of the opponent.

At the same time, from a deeper level, this mechanism has at least two flaws under the mechanism of repeated games:

• First, it does not conform to Pareto optimality , that is, a good auction mechanism should sell the subject matter to the bidder who has the highest valuation for it. In this case, Nike has the highest valuation, but there is a 50% chance that it will be snatched away by Adidas.
• Second, it is not in the best interest of the seller . Nike and Adidas are both valued at far more than 2 yuan, but the bids start from 2 yuan.

From this we can see that this bidding method is not reasonable for online advertising auctions. So is there a better bidding method? The answer is yes! Next, let’s take a look at it together:

2. A Change in Winning the Nobel Prize

Economist William Vickrey tried to solve this problem. In his classic paper "Anti-Speculation, Auctions and Competitive Sealed Bids" published in 1961, he systematically discussed the "second sealed price" auction method. (Reply to the keyword "bidding" in the backend of the "Wei Xi Chat Advertising" public account to obtain the paper)

William Vickery (left)

It made a small change to the "first sealed price", specifically - bidders still make sealed bids, and the highest bidder still wins the auction, but the winner only needs to pay the second-place bid . That is, if Nike bids 10 yuan and Adidas bids 6 yuan, Nike will still win, but Nike only needs to pay the second-place bid of Adidas - 6 yuan.

This is a small, counterintuitive change - the first place winner only needs to pay the second place's bid. However, don't underestimate this small change. It was because of the systematic discussion of this change that William Vickrey won the 1996 Nobel Prize in Economics . The "sealed second-price" auction is also called the "Vickrey auction" in economics. So what secrets are hidden in this magical little change?

The answer is that it systematically solves the major flaws of the "First Sealed Price". Some people will immediately ask: Why can this defect be overcome by making such a change?

Simply put, in the "sealed second price" bidding mechanism, everyone has a fixed optimal strategy - bidding equal to one's own valuation, or the above pricing strategy. Nike's valuation is 10 yuan, and Adidas' bid is unknown. What is Nike's optimal strategy at this time? The answer is 10 yuan. Why?

We consider two cases:

• First, if Adidas bids more than 10 yuan, Nike will not win no matter what , because Nike cannot bid higher than its own valuation, otherwise it will lose money.
• Second, if Adidas’s price is lower than 10 yuan, Nike should offer the highest price it can to increase its chances of winning , and this maximum value is 10 yuan. In other words, Nike has no motivation to lower its bid because it has no control over the final price paid.

What does that mean? Suppose Nike bids $8, and if Adidas bids $6, Nike wins the auction and only has to pay $6, which is no different from bidding $10. But if Adidas bids $9, it will lose the bid. Therefore, Nike has no incentive to adjust its bid to $8, which may lead to a bidding failure. The only optimal strategy is to bid $10.

In the words of game theory, there is a unique Nash equilibrium for the "sealed second price", which means that the optimal strategy is for everyone to bid their true valuation of the product . Therefore, this mechanism encourages bidders to tell the truth, while also being quite stable, meaning that advertisers have no incentive to frequently adjust their bids.

Under this mechanism, the advertiser with the highest rating for the ad space will always win, while the platform's revenue is guaranteed, and no advertiser will bid a price lower than its own rating. In fact, advertising platforms such as Google, Baidu, and Sina Weibo all adopt this bidding method.

Well, some people may say, is this bidding method the perfect bidding method? In fact, not necessarily. The "sealed second bidding" mechanism has at least one flaw, which is that its anti-cheating features are not strong. If there are colluded accomplices, collusion is easier to achieve under this bidding mechanism. What does that mean?

Let’s still use Nike and Adidas as an analogy. Nike’s psychological bid is 10 yuan, and Adidas’s is 6 yuan. At this time, they collude, Adidas offers 1 yuan, and Nike offers 10 yuan. In the end, Nike only needs to spend 1 yuan to buy the ad space, and the one who gets hurt is the advertising platform. A smart person would immediately say – wouldn’t this happen with the “First Seal Price”? For example, Nike and Adidas have agreed that Nike pays 1 yuan and Adidas pays 0.5 yuan, so Nike still buys the advertising space for 1 yuan!

Haha, that's true, but the "first sealed price" is more likely to lead to betrayal of the conspirators . Although it is agreed that Nike will pay 1 yuan and Adidas will pay 0.5 cents, Adidas has the motivation to violate the conspirator's agreement. As long as Adidas pays 2 yuan, it can win the auction, and Nike will be dumbfounded.

But in the case of the "second sealed price", Nike offers 10 dollars and Adidas offers 1 dollar, and this alliance is very powerful, because no matter how Adidas betrays, it cannot win the auction (its bid cannot exceed 6 dollars), so it has no motivation to betray, so collusion is easier to reach and the probability of cheating will increase.

Well, if there is this flaw, then why do Google and Baidu still use it for online advertising? One important reason is that , unlike a single offline auction, online advertising is a large-scale repeated game. The large scale means that there are a large number of advertisers participating in the bidding, which objectively increases the difficulty of collusion and cheating, and in a sense conceals the defects of this mechanism.

3. VCG, an auction mechanism for multiple ad slots

Above we discussed the basic principles of the bidding mechanism. All the examples are for one ad slot. However, in real advertising systems, there are often multiple ads requested at one time. For example, a search engine has multiple ad slots. How should we set up the bidding mechanism?

Google and Baidu have expanded the "sealed second price" auction. That is, if there are multiple ad spots, the first place will be charged the price of the second place plus one minimum bidding unit (such as 0.01 yuan), the second place will be charged the price of the third place, the third place will be charged the price of the fourth place, and so on. This bidding method is called the "generalized second price auction" (Generalized Second Price auction ), or GSP for short.

GSP Generalized Second Price Auction

This method retains the advantage of the "sealed second price" to the maximum extent, that is, it can form a stable equilibrium, but it also has a disadvantage, it is not a bidding method that maximizes the welfare of all bidders.

Therefore, three economists, Vickrey, Clarke and Groves, proposed a multi-item auction mechanism in three papers respectively, referred to as "VCG auction". This complex bidding mechanism starts from the overall interests of all bidders. It still wins the highest bidder, but the deduction is based on the total loss brought to other bidders by the participation of the high bidder. That is, the total welfare is first calculated when there is no participation of the high bidder, and then the total welfare of others after the participation of the high bidder is calculated. The difference in welfare is the loss of other participants.

In short, when you participate in bidding, you cause losses to other bidders, and you need to pay the cost of reducing the overall welfare of the system in order to ensure the maximization of overall welfare.

This bidding method is relatively complicated to calculate. Let me explain it with a simple example - suppose there are two ad positions, the first and second positions in the search for the keyword "running", the first position can bring 20 clicks, and the second position can bring 10 clicks.

There are three advertisers bidding, Nike pays 6 yuan per click, Adidas pays 4 yuan and Reebok pays 2 yuan . According to the principle of the highest bidder, Nike won the first advertising spot, Adidas won the second advertising spot, and Reebok lost the bid.

Now the question is: How much money should Nike be fined? According to VCG bidding rules:

• First, calculate the revenue of Adidas and Reebok when Nike does not participate in the bidding. That is, Adidas wins the first ad spot and Reebok wins the second ad spot. The revenue is 4*20+10*2=100
• Then calculate the revenue of Adidas and Reebok when Nike participates in the bidding, that is, Adidas wins the second advertising space and Reebok is out, and the revenue is 4*10+2*0=40.
• The difference in welfare between the two is 100-40=60
• Then Nike should pay 60/20=3 dollars for each click.

Facebook's advertising system adopts this bidding method, which maximizes the welfare of bidding participants. However, we can see that the interests of the auctioneer are not maximized. In the above case, Nike's deduction of 3 yuan is less than the 4 yuan charged for the second place under the GSP bidding rules. It can be said that Facebook has sacrificed short-term interests and considered from a longer-term perspective, because bidding advertising is not a short-term behavior. Facebook believes that it is in its own long-term interest to ensure the overall interests of advertisers.

So why doesn't Google also adopt the same VCG bidding method? On the one hand, although VCG can maximize the welfare of bidders, it is very difficult to explain to advertisers and will face huge education costs. Google's chief economist Hal Varian once made it clear that one of the reasons why Google was unwilling to switch from GSP to VCG in 2002 was that the user education costs were too high.

On the other hand, there is a risk of declining income when switching directly from GSP to VCG. Economists have proven that VCG income will not be higher than GSP.

This article mainly introduces the ins and outs of the design of bidding advertising mechanism. In fact, the selection of bidding mechanism is only a small aspect of bidding advertising. I will introduce other aspects of bidding advertising to you in subsequent articles.

Author: Wei Xi Zhi Bei

Source: Weixizhibei