Let N be a set of players, C the set of permissible coalitions and G an N-playerstrategic game. A profile is a coalitional-equilibrium if no coalition permissible coalition in C has a unilateral deviation that profits to all its members. Nash-equilibria consider only single player coalitions and...

The paper shows that any sigma-transitive preference can be extended to a complete preference preserving sigma-transitivity. The result has potential applications to the theory of choice and specifically to revealed preference theory.