Comment by makeitdouble

AFAK each agency/entity manages its staff and can hire accordingly.

For the big project, my mental image is a public call for proposal, followed by one of the bigger groups (e.g. Cap Gemini) coming up with an initial solution that gets deployed. From there it becomes a mix of the public agency staff doing the day to day operation and maintenance, potentially including small bug fixes and updates, and external contracting again for wider range feature additions or changes like system wide security compliance.