Ex post Nash consistent representation of effectivity functions

We consider effectivity functions for finitely many players and alternatives. We assume that players have incomplete information with respect to the preferences of the other players. Our main result is the characterization of effectivity functions which have an ex post Nash consistent representation, i.e., there is a game form such that i the distribution of power among coalitions of players is the same as in the effectivity function and ii there is an ex post Nash equilibrium in pure strategiesfor any preference profile.