since I was curious, I had to go look it up

And Google AdWords do operate this way. Advertisers use cost-per-click (CPC) pricing, so you pay only for the clicks you've received at a price you've set (choose a maximum CPC from 5 cents USD to US$50). Rank is determined by combination of CPC and clickthrough rate. If an ad is irrelevant to users, they won't click on it and it will move down the page. Your relevant ads will rise, at no extra cost to you.
