Space Warfare?

So you hear about spy satelittes being up in space. US spy satts above Chinese airspace and vice versa. Since no one had jurisdiction over space, what stops China have blowing up US spy sats and vice versa?

>>12
Okay need clarification:

So if somebody parks a car in my parking lot that can take pictures of me on the toilet, I can blow it up? Because there's a car parked here I've been suspicious about for a long time.