Bargaining for Beliefs

There is a scene in Through the Looking Glass in which Alice meets a unicorn who thought humans were fanciful monsters of the imagination. As they confront each other, the unicorn offers Alice a deal,

'if you'll believe in me, I'll believe in you. Is that a bargain?'

A bargain is a contract that both parties have to enter into willingly and with the ability to fulfill their end. Is that the case here? Is belief something we can decide to choose or not? If I offered you $100 to believe in unicorns, is that an arrangement someone could enter into? You could say "I believe in unicorns, but could you choose to really believe? How free are we to determine what we believe?