Google can sell search ads on an ad exchange that they don't operate. They shouldn't be able to simultaneously operate a major seller and the exchange.
Yahoo! and MSFT tried doing same, selling Bing search ads on Yahoo ad exchange. Didn't work well and can't scale it.
And these are Google innovation why should they not use it.
Is it fair to ask some other ad exchanges to run ads on NYTimes or CNN, Fox news?
Is it fair to ask some other ad exchanges to run ads on NYTimes or CNN, Fox news?