Previously, we saw that if a player could reject an offer and make a counteroffer, he could force his opponent to offer concessions in the initial proposal. But what causes those concessions: the power to reject or the power to make a counteroffer?
This lecture answers that question by investigating a model in which a player can reject an initial offer. If he chooses to do so, he receives a second offer. (Thus, there is no counteroffer. The same individual makes both offers.) Under these conditions, the receiver captures none of the surplus, just as in the ultimatum game. This is because the second offer stage is functionally an ultimatum game, in which the receiver earns a payoff of 0. In turn, the receiver is willing to accept any amount at least as large as 0 in the first stage, which allows the proposer to capture everything.