 A couple of observations are important here. First, it is not essential to the game that the offerer know anything about the responder—he or she could be a complete stranger. Second and, as we will see, very importantly, it is not an essential feature of the game that the responder know how much money the offerer has to work with in the first place. So when the offer comes in at $2, the responder might have no idea whether that is all the money that the offerer has to allocate, or whether it is just a small amount out of $100, $10,000, or even higher.  In many versions of the ultimatum game, the responder is told what the offerer has available. But the point to stress here is that this is an optional feature of the game. Finally, it is worth noting that the power dynamic in this game favors the offerer. The responder cannot make any counteroffers back in the hope of getting a bigger offer. He only has the threat of veto power. But if he does veto the offer, then he comes away with nothing himself. That is not a great negotiating position to be in.