All-stage strong correlated equilibrium

A strong correlated equilibrium is a correlated strategy profile that is immune to joint deviations. Existing solution concepts assume that players receive simultaneously correlated recommendations from the mediator. An ex-ante strong correlated equilibrium (Moreno and Wooders, 1996) is immune to deviations that are planned before receiving the recommendations. In this note we focus on mediation protocols where players may get their recommendations at several stages, and show that an ex-ante strong correlated equilibrium is immune to deviations at all stages of the protocol.