Never try arguing with a preteen. Any logic you throw will be judo flipped back at you. Luckily, their teenage hormones will soon shut down most logic functions in their brain, so you can best them there, though they will be mopier than anyone can handle.
You asked if they can cooperate conditionally. To decide, they'd need to cooperate, so this is a fair point to make. If you're confused by this reasoning, you likely don't consistently deal with young siblings.