The ultimatum game previously only allowed the receiver of an offer to accept or reject it. What happens if players can reject low offers and make their own demands? The settlement becomes substantially more equitable.
- Rejection of an offer incurs a time delay. We represent this with the discount value δ, which is a number between 0 and 1. If a player rejects an offer and makes a counteroffer, the players now negotiate over a value of δ. This represents the idea that the same division today is more valuable than the same division tomorrow.
- If the receiver of the first offer rejects, she can capture the remaining surplus by making the final offer for herself. This is because the last offer is functionally identical to the ultimatum game.
- Since the proposer of the first offer knows that he will receive a terrible deal if his opponent rejects in the first stage, he makes a generous offer immediately. The opponent accepts.
- Because the receiver only receives δ if she rejects the initial offer, the initial proposer can keep 1-δ for himself.
- Counteroffers do not result in delay or complete bargaining failure, but they do shift the division of the surplus.