Multi-issue bargaining under budget-constraints

We analyze a multi-issue bargaining model where the joint production of public goods is budget-constrained. The players must decide the part of the budget that is dedicated to produce any public good. We model the decision process as an alternating offer bargaining game with random proposers. The utilities of the players are assumed separable in any public issue. We show that multiple sophisticated outcomes are (generically) attained when a complete agreement is required for a subset of public projects to be implemented, either if the players bargain globally over the sizes of different public goods or sequentially through partial agreements. However, when public projects are immediately implemented after partial agreements, then uniqueness (which is a necessary condition for efficiency) is generically achieved