From the answers here, the schulchan aruch h"m 349.3 and the aruch hashulchan 349.1:
it seems that if a child (below 12/13 years old) damages you no one is responsible (but is he stole and the thing still exists or it was exchanged for something that still exist (by the child) we can take it from him).
What can someone do to protect his property (or children) from children?
For example, can he inflict corporal punishment on them (to scare them from doing it again)?
Can he only protect his property when the child is on his property or while the child is doing the damage(Shulchan Aruch Harav Nizkei Haguf 3)?