Introduction

The rationality postulates (axioms) that we will use in our analysis of game situations fall into two main classes:

A. Postulates of rational behavior in a narrower sense, stating rationality criteria for strategies to be used by the players.

B. Postulates of rational expectations, stating rationality criteria for the expectations that rational players can entertain about each other's strategies.

Postulates of Class A in themselves would not be sufficient. We have defined game situations as situations in which each player's payoff depends not only on his own strategy but also on the other players' strategies. If a player could regard the other players' strategies as given, then the problem of rational behavior for him would be reduced to a straightforward maximization problem, viz., to the problem of choosing a strategy maximizing his own expected payoff. But the point is precisely that he cannot regard the other players' strategies as given independently of his own. If the other players act rationally, then their strategies will depend on the strategy that they expect him to follow, in the same way that his own strategy will depend on the strategies that he expects them to follow. Thus there is, or at least appears to be, a vicious circle here. The only way that game theory can break this vicious circle, it seems to me, is by establishing criteria for deciding what rational expectations intelligent players can consistently hold about each other's strategies.