The Minimal Dominant Set is a Non-Empty Core-Extension

A set of outcomes for a transferable utility game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. Each game generates a unique minimal (for inclusion) dominant set. This minimal dominant set is non-empty and returns the coalition structure core in case this core is non-empty. We provide an algorithm to find the minimal dominant set.