How can game theory help us to understand the allocation mechanism in the competitive environment of advertising slots and is there an optimal strategy to place bids in Facebook ad auctions?
Without consciously perceiving it, we encounter auctions daily, when browsing through Google, Facebook, Instagram etc. With every website call, advertising slots are auctioneered in the background. There are no publicly available statistics on the number of ad auctions performed per day, but Facebook, for example, reports 1.56 billion active daily users1. Assuming that every user accesses different sites/profiles while visiting Facebook, and each page shows multiple advertising slots, the maths adds up to billions of auctions performed every day, and that’s just for Facebook. How can game theory help us to understand the allocation mechanism in the competitive environment of advertising slots and is there an optimal strategy to place bids in Facebook ad auctions?
BEFORE PLACING YOUR BID STRATEGY, YOU MUST UNDERSTAND THE RULES
Given advertisers (bidders) are selling different products or services, they must first define a target audience, i.e. choose characteristics their potential audience must have. Hence, a Facebook user (customer) can fall into multiple target audiences. Whenever a person within a certain target audience accesses the website, all relevant advertisers compete in the auction for advertising slots. To maximise its long run revenue, Facebook is not only interested in bidders’ willingness to pay for advertising slots, but also in non-monetary criteria, such as the probability of interaction of the customer and the user experience. Therefore, the winner of the auction is determined through a total value score. This total value score combines three major factors:
- Bid: The advertiser’s willingness to pay
- Estimated Action Rate: Probability that customer interacts with displayed ad
- Ad quality: Measurement for user experience
As more relevant ads are more likely to have higher interaction rates and come with better user experience, it could be that more relevant ads are shown to the customer for a lower price (advertiser’s bid) than less relevant ads with higher bids. An allocation mechanism/procedure that also considers non-monetary criteria to determine the winner is called ‘scoring auctions’.
HAVING UNDERSTOOD THE SELECTION CRITERIA, WHAT IS THE ALLOCATION MECHANISM?
Every ad placed on the social network is in competition with multiple other potential advertisements. Facebook must not only factor the value of one single ad, but also the opportunity costs of not showing a competing ad to the targeted audience.
Therefore, Facebook is using the Vickery-Clarke-Groves (VCG) auction. Facebook’s Chief Economist, John Hageman, explains the mechanism:
If you’re an advertiser and you’re getting a chance to show your ad, you’re going to take away the opportunity from someone else. The price [of the ad] can be determined based on how much value is being displaced from those other people. An advertiser will only win this placement if their ad really is the most relevant, if it really is the best ad to show to this person at this point in time.2
A VCG auction is a second-price sealed-bid auction format. Bidders only know their own bid and report their bid to the auctioneer. All bids are collected and the mechanism assigns the advertising slot in a socially optimal manner, according to the advertiser’s bids (or in Facebook’s case, according to their total value score).
SO, HOW MUCH SHOULD AN ADVERTISER BID?
One of the most interesting properties of the VCG mechanism for auctioneers is that it is an optimal strategy for bidders to bid their true valuation. Also, Facebook recommends bidding your true valuation for the ad slot as an optimal bidding strategy3. But is this really optimal for advertisers?
To answer this question, let’s see how the mechanism works in practice and analyse the optimal bidding strategy by means of an example (for simplicity, let’s exclude non-monetary criteria):
There are four bidders for two equal advertising slots, with the following willingness to pay for the ad:
- Bidder A: $10
- Bidder B: $8
- Bidder C: $7
- Bidder D: $1
The VCG mechanism determines the winners with the highest bids for the two available slots, bidder A and B. Therefore, bidder A pays $10 and bidder B pays $8 for the slot? No, because a VCG auction is a second-price mechanism. The VCG auction determines the payment of the winners by calculating the harm of their existence. This sounds complicated? Let’s continue with the example. The payment of the winner is determined by:
= sum of remaining winning bids without winner in auction
– sum of remaining winning bids with winner in auction
In our example, payments would be:
Payment of bidder A:
- Without A in the auction bidder B and C would win, with bids of $8 and $7 respectively. Therefore, the sum of winning bids is equal to $15
- The sum of other winning bids with A in the auction would be $8
- So, the price A must pay would be $7 ($15 – $8)
Payment of bidder B:
- Without B in the auction bidder A and C would win, with bids of $10 and $7 respectively. Therefore, the sum of winning bids is equal to $17
- The sum of other winning bids with B in the auction would be $10
- So, the price B must pay would be $7 ($17 – $10)
We observe that the bidder’s optimal strategy is to bid their true valuation for the ad, since they will be charged less than their bid if they win an advertising slot. Facebook calls the strategy a “bid cap”, which seems to be optimal at least in a one-shot setting.
THEN, WHY DOES FACEBOOK OFFER MORE BID STRATEGIES THAN THE “BID CAP”?
As an advertiser, however, one-shot settings are not really your daily business. To reach more than one person with your Facebook ad, you must participate in several auctions with other bidders. Game theory literature teaches us that strategies differ if a game is either finitely or infinitely repeated. Hence, the optimal bid strategy on Facebook ad spaces might be different than in the example illustrated above, where it would be best to submit your true valuation for one shown ad. The above-mentioned auction format is a second-price auction (i.e. the bidder with the highest bid does not pay his bid, but a lower price). So, lets analyse the optimal bidding strategy in repeated second-price auctions. Indeed, the optimal strategy in a repeated second-price auction is to bid below your true valuation in earlier auctions and will depend on the anticipated behaviour of other participants.
Further reasons for the use of a different bid strategy is the underlying objective of the advertiser. In the example above, we assumed that the objective is to directly maximise your short-run goal (e.g. revenue on your website). A marketing campaign goal might be more long-term, for example to increase brand awareness. Marketing campaigns often work with budget constraints that affect the bidding strategy in repeated second-price auctions.
Hence, although the second price auction is a simple allocation mechanism, placing a bid strategy for a repeated second price auction on Facebook is not straightforward and therefore multiple bidding options must be available, as offered by Facebook.