A child was getting into a car parked beside mine and bumped the car door into my car, making a dent in my car, who is obligated to pay for my damages, the driver of the other car? The child’s parents? Nobody?
The Mishna in Baba Kama says that the damages that a child does he is not obligated to pay. Therefore technically no one has to pay for it. However the child would need a kapara medinei shomayim, when he gets older, therefore it would be a correct thing for the father to pay towards the repairing of the dent. In any case, even if the father doesn’t pay for it, you should be mochel the child, as he is only a child and he didn’t mean it, and when he gets older he isn’t going to remember about or be able to find you to ask you mechila.
Baba Kamma 67a in the Mishna, CH:M 424-8. Hagaos H’asrei Baba Basra 87 that when he gets older he has to pay. See Machaneh Yisroel ( R’ Y. Grossman) 23. Rashi Baba Kamma 98b, Taz O:CH 343-2 Bach ibid.