# Implementation in Stochastic Dominance Nash Equilibria

Implementation in Stochastic Dominance Nash Equilibria

We study solutions that choose lotteries for profiles of preferences defined over sure alternatives. We define Nash equilibria based on “stochastic dominance” comparisons and study the implementability of solutions in such equilibria. We show that a Maskin-style invariance condition is necessary and sufficient for implementability. Our results apply to an abstract Arrovian environment as well as a broad class of economic environments.