Ex-ante and ex-post strong correlated equilbrium

A strong correlated equilibrium is a strategy profile that is immune to joint deviations. Different notions of strong correlated equilibria were defined in the literature. One major difference among those definitions is the stage in which coalitions can plan a joint deviation: before (ex-ante) or after (ex-post) the deviating players receive their part of the correlated profile. In this paper we prove that if deviating coalitions are allowed to use new correlating devices, then an ex-ante strong correlated equilibrium is also immune to deviations at the ex-post stage. Thus the set of ex-ante strong correlated equilibria of Moreno & Wooders (1996) is included in all other sets of strong correlated equilibria.