Question: My ten-year old, while playing, did some damage to a neighbor's property and now my neighbor claims that I am responsible for compensating him. What is the right thing to do?
Answer: While it would be a nice thing for you to offer compensation, there is no halachic responsibility for damage caused by a minor. Your son, as well, has no responsibility to pay even when he grows up, but it is a good idea for him to repent his act at that time.
Minors who behave as juvenile delinquents and cause ongoing trouble must be dealt with by the rabbinical court which has the authority to take proper measures to keep them under control.