A basic assumption of the theory of games is that each player correctly perceives the payoff functions of the other players. This assumption seems highly unrealistic, and it is dropped in this paper and replaced by the assumption that each player has a perception of the payoff function of each of the other players; these perceptions may be incorrect. It is shown that this leads to an analogue of characteristic function theory in which each player has a subjective characteristic function which he believes represents the strength of the several coalitions. It is proposed that the coalitions be treated directly as outcomes and that individual preferences among them be ascertained. If the von Neumann utility axioms plus one other are met, then it can be argued that a simple transformation of the resulting utility function is a player's subjective characteristic function. The beginnings of an equilibrium theory are outlined for this more general model; this theory reduces to a known one when there are no misperceptions. The value of this generalized equilibrium theory is severely limited by two strong assumptions which are made.