One-dimensional bargaining with a general voting rule

Abstract

We study a model of multilateral bargaining over social outcomes represented by points in the unit interval. An acceptance or rejection of a proposal is determined by a voting rule as represented by a collection of decisive coalitions. The focus of the paper is on the asymptotic behavior of subgame perfect equilibria in stationary strategies as the discount factor goes to one. We show that, along any sequence of stationary subgame perfect equilibria, as the discount factor goes to one, the social acceptance set collapses to a point. This point, called the bargaining outcome, is independent of the sequence of equilibria and is uniquely determined by the set of players, the utility functions, the recognition probabilities, and the voting rule. The central result of the paper is a characterization of the bargaining outcome as a unique zero of the characteristic equation. JEL classification code: C78