Group Bargaining with Representation

We study a strategic bargaining model where two groups of individuals first choose their representatives, who then bargain with each other using a standard alternating-offer protocol, and then the shares of the members of a group are determined by a similar n-person bargaining process within the group. We show that there exists a unique perfect equilibrium outcome of this three-stage game when the breakdown probabilities of both the inter-group bargaining and intra-group bargaining are small. In equilibrium, each group selects as its representative an individual who has the greatest marginal gain from increasing the group's share.