This paper characterizes neutral social functions that are fully implementable. A necessary condition for full implementation under either the Nash equilibrium concept or the strong Nash equilibrium concept is that the neutral social function being implemented be monotonic and simple. If a neutral monotonic social function is simple and the set of winning coalitions is nondictatorial then the social function is fully implementable by a set of Nash equilibria. For finite alternative sets a neutral monotonic social function will be fully implementable by a set of strong Nash equilibria if and only if it is simple and dictatorial
