Nipping, or sometimes known as “play biting”, is a normal behavior in the dog world. Having been privileged to see over 150 puppies go from birth to 8 weeks, I’ve had the opportunity to see firsthand how this behavior is dealt with appropriately.
In a normal environment when a puppy becomes too rough in play, the other puppies simply stop playing with them. Usually, where the issue comes into play and can become more serious, is after the dog is taken home at 8 weeks. If not properly reinforced by its new owners and/or pack (ie. “Rough play results in no play!”), the dog will not follow the same rules.
I have found in almost all situations the new owners allow the dog to mouth hands while playing. This is a sure way to increase the behavior until play biting/nipping starts to break skin. We as humans do not have a thick coat of fur to protect us, so what might be normal play previously with its littermates can be inappropriate in the human world. It’s only fair to help our new friend succeed by eliminating his/her chance of failure. And, as in all behavior modification – consistency is critical!
Another way to deter this problematic behavior is to simply give the dog a toy or chew to have in its mouth during play time.
Additionally, I never recommend “tug of war”. It has the potential in a high enough percentage of dogs to encourage aggressive behavior that it is a big “NO-NO” in my book! It can also result in accidental biting/nipping, especially with younger children, who have not fully developed eye/hand coordination.