In reply to McClennen, the paper argues that his criticism is based on a mistaken assumption about the meaning of rationality postulates, to be called the 'Implication Principle'. Once we realize that the Implication Principle has no validity, McClennen's criticisms of what he calls the 'Reductio Argument' and what he calls the 'Incentive Argument' fall to the ground. The rest of the paper criticizes the rationality concept McClennen proposes in lieu of that used by orthodox game theory. It is argued that McClennen's concept is inconsistent with the behavior of real-life intelligent egoists; it is incompatible with the way 'payoffs' are defined in game theory; and it would be highly dangerous as a practical guide to human behavior. Professor McClennen's arguments against the rationality postulates used in my paper 1 are based, I think, on a serious misunderstanding of what demands a rationality postulate actually makes, and can possibly make, on individual players. Let X be some rationality postulate, and let Y be some state of the world that will obtain if all players succeed in acting in accordance with postulate X. McClennen assumes that, in this case, postulate X, at least by implication, requires each player to help bring about this state Y. I shall call this assumption the Implication Principle. In my own opinion, this principle proposes a wholly unacceptable reinterpretation of postulate X.
If X is a valid rationality postulate and if I am a player of game G, then it will be obviously rational for me to act in accordance with postulate X in this game. But the Implication Principle makes the further claim that it is always rational for me to help the other players also to act in accordance with postulate X. Yet, this second statement in no way follows from the first. If X is a valid rationality postulate, then, by conforming to it, I can presumably make my own behavior more effective in advancing my own interests in the game. Likewise, by helping the other players to conform to postulate X, I can presumably make their behavior more