A good amount of scholarly work exists in the public domain about paid search auctions. I have picked a few that I found most relevant and will try to provide a summary based on their contents here. There are more like my PPC Science Notes :)
The Generalized Second Price (GSP) Auction
This is the auction mechanism on which Google Adwords bidding works. The most common understanding of an auction is the scenario when several bidders place bids for one object and the person with the highest bid takes the booty home for the price he bid at. There are then many (some very complicated) variations of this
and the whole thing explodes into the discipline of Auction Theory. But we will try and focus on just the GSP here.
The Edelman paper is probably the best introductory paper on GSP and I will start with that. The first four pages can be conveniently skipped as they just talked about how big PPC is and how it contributes to 95% of Google's Revenues. On the fifth page they take up an example which illustrates the GSP. I have reproduced that example in excel format. The basic idea behind GSP is that if there are so many advertisers bidding for so many SERP positions, each gets a position basis his bid but pays basis the bid of the guy just below him. That is, what you bid is just used to decide what position you end up at. Once you get that position, what you pay depends on what the other guy, who got the position just below you, was bidding.
Most folks know this about adwords already. But then, what implications does this have on your bidding strategy?
Few Fancy Concepts
Truth Telling: The Edelman paper points out in Remark 3 that truth-telling is not the optimal strategy in GSP. That is, the ROI may not be maximized by bidding exactly at what each click means to you. For e.g. basis your conversion rate and average order value, if you conclude that the value of each click from a keyword to your business is $3, then bidding for that keyword at $3 is not the best thing to do. You could be better off bidding at, say, $2.5
Locally Envy-Free Equilibrium: Another fancy name for a very simple concept. A set of bids are in locally envy-free equilibrium if none of the players could be better off by swapping places with the guy just above it.
The Conclusion
The Edelman paper's end contribution (in my view) is a formula (see right) for a price that any advertiser would be willing to pay in the long run steady state. Note that the long run steady state is when over time advertisers have discovered each other's CTRs and value-per-clicks (Is this possible?).The formula is to be understood as follows.
- The left-hand-side is the maximum price that advertiser k would be willing to pay for position i given the history of bids for all positions below him.
- the first term on the right-hand-side is the value per click for advertiser k
- the second term on the right hand side is the ratio if CTRs for position i and i-1, multiplied by the difference in value per click for advertiser k and bid for position i+1.
Let's say there are 4 advertisers A, B, C and D with value per click of Rs. 10, Rs. 20, Rs. 15 and Rs. 12. Let's say only 3 ad-positions are available with position 1 having a CTR of 5%, position 2 a CTR of 2% and position 3 a CTR of 1%. Let's say for some reason position 3 was bid for Rs. 5 and was taken by advertiser C. Now for position 2, advertiser A would be willing to pay a maximum of 10 - (2%/5%) X (10 - 5) = Rs. 8 while advertiser B would be willing to pay 20 - (2%/5%) X (20 - 5) = Rs. 14.
I cannot go into any more details that this because honestly I haven't spent enough time and energy to understand this deeper. But I am sure algorithmic giants like Marin, Efficient Frontier and ClickEquations etc. would be knowing (and using) stuff like this and making their millions out of it. That is why they have PhD's working in their barracks.
(I will be updating this article as and when I go along further in my reading)
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