What is the ruling on pelting with eggs someone who harms people by making noise with his motorcycle, due to the inability to command or forbid him or ascertain his identity?

Destroying eggs in the manner mentioned is forbidden in Islamic law because it is a waste of money, and Allah dislikes wasting money. Wasting it means spending it in ways not sanctioned by Islamic law and exposing it to spoilage. The reason mentioned does not permit this destruction. The proper way to stop that person's harm is to file a complaint with the authorities.