Strongly implementable social choice correspondences and the supernucleus

In this paper, we present a characterization of social choice correspondences which can be implemented in strong Nash equilibrium, stated in terms of the power structure implicit in the social choice rule. We extend the notion of an effectivity function to allow for simultaneous vetoing by several coalitions. This leads to the concept of a domination structure as a generalized effectivity function. Using this concept and a solution known from the theory of effectivity functions, the supernucleus, we give a characterization of strongly implementable social choice correspondences as supernucleus correspondence relative to an appropriate domination structure.