The von Neumann-Morgenstern theory of games does not yield determinate solutions (corresponding to unique payoff vectors) for two-person variable-sum games and for n-person games. The present paper outlines a general theory of rational behavior in game situations which does yield determinate solutions for all classes of games. The theory is based on two classes of rationality postulates: those defining rational behavior as such, and those defining rational expectations concerning the other players' behavior. It is argued that this new approach greatly increases the possibilities for the application of game theory in economics and the other social sciences.