introduction
Search ad auction (sponsored search auction) is an advertising auction on the main search engines sell to advertisers search results pages. Each user searches for a keyword, the top and sides of the web page can display some advertising. Each time the ad is clicked, the corresponding advertisers need to pay a fee to the search engine. Typically, more than one advertising, the probability of different locations advertisement is clicked user is not the same, but also want to advertise more than one business. When more advertisers competing advertising click rates of an auction appeared.
A simplified search ad auction scene is this: the seller (search engine) sell m ad slots, advertising click-through rate in descending order of q1 q2 ≥ ≥ ⋯ ≥ qm (nothing to do with the ad's click-through rate assumptions actual content) . There are n buyers (advertisers) per person up to a purchase advertising, their valuations per click of v1, v2, ..., VN . Valuation vi only buyers i myself clear, sellers and other buyers do not know vi values. Quote buyers with sellers b i to represent their valuation vi . B I need not be equal to VI . According to the seller all offers b1, b2, ..., bn to determine which m how the ad slots are assigned to advertisers, and everybody should be how much advertisers pay for each click the p- i . Buyers assume i get the advertising J , then his utility is vi QJ - pi qj , and the seller's income that is all pi qj And. By adjusting the buyers offer to maximize their effectiveness, while sellers want to maximize revenue. Different allocation schemes QJ (⋅) and costs calculated PI (⋅) will affect the buyer's bidding strategy, but also bring different benefits to the seller.
As early as 40 years ago, economist Roger B. Myerson on the design of an optimal auction sellers income program, known as Myerson's auction [1]. In addition to the best seller earnings, Myerson's auction also has properties truthful, that offer buyers b i is exactly equal to the valuation vi when their usefulness is the greatest. This contribution is one of the reasons Myerson won the Nobel Prize in economics in 2007.
It should be emphasized that a classic Myerson's auction depends on the economic assumptions: the buyer's valuation vi obey a probability distribution Fi , and everyone, including sellers are aware of this, including the distribution. Myerson's auction of the distribution plan and the costs are calculated and distributed Fi closely related, that is, buyers i advertising obtained QJ (⋅) and fees paid to him PI (⋅) is about the same time offer ( b1, b2, ..., BN ) and distribution ( F1, F2, ..., the Fn function).
In reality, however, "I know the valuation spread of buyers," this assumption does not hold. The reason is not established are: a complete distribution can not be stored in the computer, information pertaining to the valuation of the advertiser's privacy. Therefore, the search engine can not be used directly Myerson's auction to maximize their returns.
However, unlike traditional economics of the auction it is different, the search ad auction is repeated. Key words are searched every time, it creates an auction, a process that is repeated thousands of times one day. If more than one buyer participated in the auction, search engines can offer through his historical records to estimate the distribution of his valuation. If the data offer more than enough, the seller can still use Myerson's auction to obtain the approximate optimal benefits [2]. Sellers usually means increased earnings decrease utility buyers. In other words, by "big data kill cooked", the seller from the buyer to squeeze more profit.
But buyers willing slaughtered it? Big Data cooked to kill a premise: Quote data must be true portray buyers valuation distribution. However, when the data quoted in the hands of the buyer, even in Myerson's auction had to meet so truthful nature of the auction, honest offer bi = vi may not be a Nash equilibrium (Nash equilibrium that is not the policy of each participant in the other participants the case of change of use of steady state optimal policy). Because the seller and buyer of choice for the distribution and allocation of related pay scheme, so buyers can be modified to affect the distribution of the seller's decision-making, resulting in higher utility. This is the question we want to study:
If the search engine uses historical quotes to approximate the distribution of valuation,
Buyers will use what kind of bidding strategy?
Sellers benefit and how?
Models and results
We consider the two-stage model of an idealized: First, sellers announce an auction scheme M , such as Auction's Myerson, M allocation and payment calculation can be related to the valuation of distribution; then submitted to a group of buyers distribution F1 ', ..., fn ' , specifically, the buyer i according to a bid function βi: R + → R + to estimate vi ~ Fi mapped to bi = BETA i ( VI ), such that the bi distribution obeys Fi' . Buyers i get the advertising qj and fees paid pi by ( b1, ..., BN ) and ( F1 ', ..., the Fn' ) decision. Seller's proceeds are pi qj and the expectations of buyers i utility is vi QJ - pi qj expectations.
In this model, Fi is the buyer's private information, and Fi ' can be seen as a proxy of private information. Buyers can choose any proxy. In the choice of the agent and the auction, among buyers, forming a complex game between buyers and sellers. Therefore, we call this model the "Private Data Agent Game" (the paper as "private data manipulation games, Private Data Manipulation game, PDM" ).
In private data proxy game model, we show that:
Myerson's auction with Generalized First Price auction equivalents.
Generalized First Price auction (GFP) is a single item auction the highest price (first price auction) promotion in the search ad auction scene: In the GFP, the seller will offer advertisers follow in descending order, you may wish to note as b1 ≥ ⋯ ≥ BN , also per-click advertising descending sort, q1 ≥ ⋯ ≥ qm . Allocation is: 1 advertisers advertising obtained 1, 2 get advertisers advertising 2, and so on, advertisers {min n- , m } {get slot min n- , m }; each advertiser i for each pay for clicks and pi is equal to his bid b i . And Myerson's auction is different, GFP itself is not truthful, and its distribution plan and cost calculation has nothing to do with the distribution of valuation. The so-called "equivalence", is said in private data agency game, in Myerson's auction and GFP respective Nash equilibrium, the seller to get the same expected return, each buyer's expected utility are the same. In other words, search engines do not need to restore data after running from the distribution of so-called "earnings optimal" auctions - nothing to do with running a distributed auction is sufficient. The equivalence means that: by skillfully selecting agent distribution, advertisers defeat the "exploitation" of search engine behavior and distribution of certain private Fi improve their own effectiveness (for example under F1, ..., Fn independent and identically distributed when ).
Myerson's auction with GFP equivalent to the conclusion of any set of distribution F1, ..., Fn are established. Further, after the divide valuation Bucharest to some restrictions (such as independent and identically distributed), we came to the conclusion Myerson's auction with the Generalized Second Price auction (GSP) and VCG auction also equivalent (see Figure 1).
discuss
Technically basis, we return in the classical equivalence theorem (revenue equivalence theorem), based on this new perspective game data through private agents to investigate the phenomenon of equivalence between Myerson's auction and GFP, VCG, GSP. We also promote the Tang & Zeng [3] of "Myerson's auction with GFP equivalent in only one auction ad slot" conclusion.
In a practical sense, we repeat the search advertising auction in the actual scene, we discussed the incentive problem in machine learning (incentives in machine learning) - When the output of machine learning algorithms involved in the training data provide stakeholders, data providers It can be profitable by modifying the data. We believe that private data proxy game model can be applied to other practical problems.
references
[1]R. B. Myerson, "Optimal Auction Design," Math Oper Res, doi: 10.1287/moor.6.1.58.
[2]C. Guo, Z. Huang, and X. Zhang, "Settling the Sample Complexity of Single-Parameter Revenue Maximization," in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, doi: 10.1145/3313276.3316325.
[3]P. Tang and Y. Zeng, "The Price of Prior Dependence in Auctions," in Proceedings of the 2018 ACM Conference on Economics and Computation, doi: 10.1145/3219166.3219183.
