On The Centrality of Policy Outcomes in Dynamic Majoritarian Bargaining Games

We analyze an inÞnitely repeated divide-the-dollar bargaining game with an endogenous reversion point. In each session a new dollar is divided among three legislators according to the proposal of a randomly recognized member — if a majority prefer so — or according to previous period’s allocation otherwise. We characterize a Markov Perfect Nash Equilibrium of this game and study the resultant equilibrium dynamics. Contrary to the results of Baron, 1996, for one-dimensional ideological spaces, or the intuition in Baron and Herron, 1999, for a Þnitely repeated analogue of the game over a two-dimensional space, outcomes in distributive policy spaces are considerably more extreme. Irrespective of the discount factor or the initial division of the dollar, equilibrium outcomes are absorbed in an irreducible set that has an empty intersection with the uncovered set (Miller, 1980, Epstein, 1998).