Double Implementation without No-Veto-Power

Abstract

Abstract We consider the implementation problem with at least three agents. We study double implementability of social choice correspondences in Nash equilibria and undominated Nash equilibria. We prove that “DZ-invariance,” “weak no-veto-power,” and “unanimity” together are sufficient for double implementability. If there is at least one partially honest agent in the sense of Dutta and Sen (2012) , then weak no-veto-power and unanimity together are sufficient for double implementability. If there are at least two partially honest agents, then unanimity is sufficient for double implementability. In addition, we show that if there is at least one partially honest agent and unanimity is satisfied, then “LY-condition” is necessary and sufficient for double implementability. From these results, we obtain several positive corollaries.