A coalition-proof correlated equilibrium of a game is a pair consisting of a correlation device and a coalition-proof Nash equilibrium of the game extended by the device. A direct coalition-proof correlated equilibrium is a canonical device such that the obedient strategy is a coalition-proof Nash equilibrium of the canonical extended game. The revelation principle may not hold even for two-person games. Direct coalition-proof correlated equilibrium may fail to exist for games with more than two-players. For any game, a (pure) coalition-proof Nash equilibrium is a direct coalition-proof correlated equilibrium. (C) 1996 Academic Press, Inc.
Ray, I. (1996). Coalition-proof correlated equilibrium: A definition. Games and Economic Behavior, 17(1), 56-79. https://doi.org/10.1006/game.1996.0094 (Original work published 1996)