Any Pay Per Search Ads Network?

Looking thru Google Search Box that some sites are having, when someone perform search using the box, and actually click on the link at the result page, the webmaster earned some CPC from google. What if they don't click on any link on the result page? Well, webmaster earn nothing isn't it??!

So, would there be some ads network that actually offer Pay Per Search model?? Meaning, whether or not a visitor click on the link listed on the result page, the webmaster has earned as long as the visitor perform a search query using the ads network's search utility??

Would there be such company offering this monetization option for webmasters?? Anyone could help to provide more information if they do found this type of ads network?

Thanks!

There may be some out there.. but it seems like the payout would be so low to not be worthwhile and so ripe for abuse that not sustainable.

Plus you would have to push inferior search results on your visitors.