Reaching Consensus Through Simultaneous Bargaining

Abstract

We propose a two-player bargaining game where each player simultaneously proposes a set of lotteries on a finite set of alternatives. If the two sets have elements in common the outcome is selected by the uniform probability measure over the intersection. If otherwise the sets do not intersect the outcome is selected by the uniform probability measure over the union. We show that this game always has an equilibrium in sincere strategies (i.e. such that players truthfully reveal their preferences). We also prove that every equilibrium is individually rational and consensual. If furthermore players are partially honest then every equilibrium is efficient and sincere. We use this result to fully characterize the set of equilibria of the game under partial honesty. KEY WORDS. Approval voting, bargaining, partial honesty, consensual equilibrium.JEL CLASSIFICATION. C70, C72.

Unanimous Implementation: A Case for Approval Mechanisms

“…Having said so, our paper is also related to the literature on Approval Voting (see Brams and Fishburn [1983], Laslier and Sanver [2010] and Bouton and Castanheira [2012] among others), to which Approval mechanisms borrow both its name and its flexibility. Laslier et al [2015] design a bargaining device over lotteries based on Approval voting and derive conditions for consensus reaching in equilibrium with just two agents.…”