Kids annoying each other on purpose

My kids like to push each other buttons. They even say to me that “I am trying to annoy her on purpose.” Then they laugh and tell me it is a joke. But it feels true. I used to be a permissive parent, and they still allow themselves to do many things in front of me that they would normally not do in front of my husband.
They are seven, nine, and three years old.
Why are they doing it? I feel like it is some revenge or punishment. They want to get back at each other.
What kind of conversations do I need to have with them, and what policy should I put in place to help them build a better bond between each other?
Thank you