If they run and you chase them then most times they will keep running as they think you are following them to where they are going, or they have learned that if they come back right away they will be scolded or tied up.
  Playing tug a war with a dog can create a dog that loves to grab on to items and pull until the item is theirs.
Certain breeds where trained to tug and pull. in some applications of training the handler or trainer wants the dog to grab on and hold on, police dogs are a good example.

However in the home the dog may get confused with an article a child has and the consequences can be fatal.

Many owners say after the fact MY DOG NEVER DID THAT BEFORE chances are he was never in that situation before or a member of the family was inadvertently training the dog for an undesirable action.
 
 All play should be supervised and controlled. Its what you the owner/leader allow. Leaving the dog outside to his/her own devices does not constitute play. The dog is learning to his/her environment.

Leaving a child and a dog alone to play together can also have fatal consequences.
 
First train your dog: You cannot expect the dog to come back if you did not train it to recall
An owner cannot expect the dog to sit and give up the toy it he/she did not teach the dog that a sit is a sit.
 
Yes the dog can have his time to himself and that is when he is on his mat or in his crate or designated area and he has been given a good chew toy to work on. However if the owner says the command to drop or leave it and the dog was taught this command then the dog must follow through and get the job done.
 
If you make the training fun, short training sessions, do not over work the dog. If you and your dog both enjoy the training then this will become play for both of you and you will both learn the lesson that will last a lifetime. Start with a good foundation and build from there.
Every animal learns best on success

Eventually an owner comes to realize that there is much he/she can learn from their companion and it can be used in everyday life.....FIRM, FAIR, CONSISTENT IN ALL THINGS.