There are several tricks one can us to either prevent a dog from running off game or to put a halt to them if they start. Some I have used, some I have not, but they all seem to get the job done.
The shocking collar method is a good one but one needs to be 110% sure the dogs are on off game before you zap them. Some of them swamper's will fool you on the way they run.
One of my favorites with young dogs that are just getting started is to make them terrified of the meer smell of a deer track. A shocking collar can serve this purpose, but I have seen dogs that figure out they get shocked when barking & running a deer & they will start trailing & running them stale mouthed.
A dog cannot run one if they don't trail them. Here is what I do to make them where they don't even want to put their nose to the ground to even smell a deer trail. I take a drag rag & lay a track using deer scent. When you do this, take some mouse traps & set them along in the track you have layed. When the dog goes to trailing the track that track will junp up and bite him. He will learn that scent means something bad is going to happen to him if he sticks his nose in it & follows it. After 2 or 3 times of getting a mouse trap attached to their nose they will advoid the scent of a deer all togather.