Every member of the core is as respectful as any other

We strategically separate different core outcomes. The natural counterparts of a core allocation in a strategic environment are the alpha-core, the beta-core and the strong equilibrium, modified by assuming that utility is transferable in a strategic context as well. Given a core allocation omega of a convex transferable utility (TU) game , we associate a strategic coalition formation game with in which omega survives, while most other core allocations are eliminated. If the TU game is strictly convex, the core allocations respected by the TU-alpha-core, the TU-beta-core and the TU-strong equilibrium shrink to omega only in the canonical family of coalition formation games associated with . A mechanism, which strategically separates core outcomes from noncore outcomes for each convex TU game according to the TU-strong equilibrium notion is reported.