Dynamic stable set

We study a dynamic vNM stable set in a compact metric space under the assumption of complete and continuous dominance relation. Internal and external stability are defined with respect to farsighted dominance. Stability of an outcome is conditioned on the history via which it is reached. A dynamic stable set always exists. Any covering set by Dutta (1988) coincides with the set of outcomes that are implementable via a dynamic stable set. The maximal implementable outcome set is a version of the ultimate uncovered set.