Originally, it was called "the Southwest effect".
Numerous studies have shown that when Southwest enters a market, not only do air fares drop, but there is an exponential growth in traffic.
Now that there are more LCC's, it isn't just limited to Southwest.
All the LCC's have a constant parade of city/airport officials asking them to start service to their city - sometimes even when that city already has an LCC.
The big prize is international service. As F9Widebody says, Denver is anxious for flights to Paris, and is offering generous concessions.
They offered a million bucks in concessions to anyone who would start a Denver/Mexico City non-stop. Mexicana took them up on it. Frontier gets between $25,000 and $50,000 for it's service to each of the provincial Mexican cities/resorts.
Denver's big wish is for a non-stop to Asia. The new runway could accomodate such flights, and if any airline starts that service you can bet that DIA would be very generous.
Why? Non-stop service to big international destinations means that the city and it's state is "on the map" for multi-national corporations, which can mean big bucks for the city/state.
if the airport can also offer non-stop connections to other international cities, then it becomes an even more attractive package.
That's the theory.