The prince didn't know why he had to sign the contract, he just inexplicably signed it.
This brings us to why the prince would sign the contract; many people might find it bewildering, too incredible.
Actually, this involves some psychological aspects, or it could be called psychological suggestion, or something else.
Anyway, when a person is under certain external pressures, they have a stress response to find a way to relieve it, and in such situations, if verbally guided by someone, they can easily be led into another's guidance in thoughts and actions.
This is backed by scientific research. It's like when you are about to drown, if something floats by, you are bound to grab onto it, this is a subconscious action, even if that thing eventually leads you into a crocodile pool, you would still grab it because it's the only thing that offers you a chance of survival at that moment.
