On the optimality of bargaining outcomes in the Collective-Particularistic multilateral bargaining game

This note analyzes the efficiency properties of the equilibrium in a multilateral bargaining game in which a legislature divides a budget among collective and particularistic goods. We extend the model of Volden and Wiseman (2007) by considering smooth utility functions and consensus requirements ranging from simple-majority to unanimity. We show that when the private valuation of the private good is relatively high, only unanimity induces an (ex-ante) Pareto efficient outcome. Moreover, optimality can be easily attained by using sequential negotiations, independently of the majority requirement.