The government controls the outer districts by regulating everything they can and cannot do. Each district has a small army there to keep them in line. Hunting, etc is forbidden so you'll be forced to accept food from the government which, in turn, makes the odds of your child going to the Hunger Games greater.
The Capitol is where the government is (obviously.). That's where all the tech and food is. The Hunger Games are the Capitol's way of reminding the outer districts that the government is in control.
The first movie is the 74th Hunger Games. You have to figure that everyone from the pre-Hunger Game era is dead, and at this point, the population just bends over and takes it. What are they supposed to do? Attack the "peace keepers" with sticks like Ewoks to Storm Troopers?
As for the holograms, they were better explained in the book and each hologram resembled a fallen tribute. It's my understanding that the arena is basically one big hologram or better yet, like The Grid in Tron. That's how the game makers control everything.
This post was edited on 3/18 at 10:48 am