* To be a nuisance and cause trouble: Prince Brat is, as his name suggests, a spoiled and mischievous child. He enjoys causing chaos and disrupting the lives of those around him. Tying wigs to hair is a silly but annoying prank that fits his character.
* To assert his power: As a prince, he can get away with things that others can't. Tying the wigs shows that he has power over the lords and that he can disrespect them without facing serious consequences. It's a way for him to remind them (and himself) of his higher status.
* For entertainment: The prince is bored and seeking amusement. He lacks empathy and doesn't consider the feelings of those he pranks. The lords' reactions likely entertain him, further fueling his misbehavior.