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 (Axiomatic models of bargaining. Springer, Berlin, 1979) 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 over several rounds. In each round, an increasing share of the total amount is negotiated over in accordance with the NBS, the disagreement point being determined by the outcome of the previous round. In line with Roth’s result, the final amount received by the more risk averse player is still bounded by half the total amount. As a new feature, however, this player does not lose from bargaining for more rounds if his opponent exhibits non-increasing absolute risk aversion. What is more, both players’ risk profiles become essentially irrelevant if successive bargaining takes place over sufficiently small commodity increments. Each player then gets approximately half of the commodity.