Not as it is the case over here in europe. I just picked out one route ( no time for an deeper analyse ):
ATL-LON feb 7.-9.
The first page on the matrix is full with DL flights only - were's the competion?
Just reversed the flights:
It's US setting the lowest price ( well, that will stop in a few weeks as we know ) and then it's DL - undercutting both home carriers there. That is competition.
If you would follow lets say the LH board here on FT you would know that if you want to fly LH in F or J you start your journey anywhere in the world - just not in Germany! Of course, if you want to lure away (premium) pax from another carrier it works over price.
In the USA it seems that the big 3 have an silent "gentlements agreement" not to attack the others home base(s). Under european conditions the lowest fares ex ATL would always be set by AA/UA/US and DL would lead the market by price ex ORD for example.