AdWords Ad Ranking System and AdWords Discounter explained

During a discussion about the ad ranking system of the Google AdWords advertising program and the associated AdWords Discounter feature, a friend of mine has happened to tell me the other day that according to Google you will pay only a bit more for a particular ad position on the user's search result page than the "owner" of the ad position that is below you. (If anyone of you accrues a clickthrough.) He concluded that it would make an actual CPC column like this one for example:

• 1st position: $1,04
• 2nd: $1,03
• 3rd: $1,02
• 4th: $1,01

The question is not stupid at all, my friend is following the right path, with a little misunderstanding, though. Google says that the AdWords Discounter monitors your competition and automatically reduces your actual cost-per-click so you pay the lowest possible price for your ad's position on the page. It also says that eligible ads are arranged according to their Ad Rank where

Rank = Bid x QS,

where QS is the Quality Score that is determined by various factors, but first of all by the Clickthrough Rate and some relevance factors.

For various reasons, Google does not disclose every aspect of their algorithm but it is widely believed that the QS is in fact a number in Google's algorithm while for us, AdWords advertisers, it is only a concept. (We know which factors it depends on but do not know how.) Now let's say, that you and your only competitor both meet the minimum requirements set by the min. CPC bids and have the following data:

It is also widely believed that Google follows the rules of the so-called second-price auction and we'll follow this model for now. In the above case, of course, you are the winner of the auction with your Rank=63, which means that your ad will show as first on the user's search result page. Though your bid is 9, you will only be required to pay 3 because in that case your Rank is 3x7=21 that exceeds your competition's Rank by an increment of 1. If suddenly your competitor changes his bid to 105, he will, of course, win the auction but will not be required to pay more than 16 because 16x4=64 which exceeds your Rank.