Divide the Dollar and Conquer More : Sequential Bargaining and Risk Aversion

We analyze the problem of dividing a fixed amount of a single commodity between two players on the basis of the Nash Bargaining Solution (NBS). For one-shot negotiations, a cornerstone result of Roth (1989) establishes that the more risk averse player will obtain less than half the total amount. In the present paper, we assume that the bargaining procedure occurs along several rounds. In each round, only a share of the total amount is negotiated over according to the NBS, with the disagreement point being determined by the outcome of the previous rounds. In accordance with Roth's result, the amount received by the more risk averse player is still bounded by half the total amount. In addition, this player does not lose from bargaining over more rounds if his opponent exhibits non-increasing absolute risk aversion. Finally, both players' risk profiles become essentially irrelevant if the number of rounds is sufficiently large