Theory of Games and Economic Behavior

Our considerations will lead to the application of the mathematical theory of “games of strategy” developed by one of us in several successive stages in 1928 and 1940–1941.1 After the presentation of this theory, its application to economic problems in the sense indicated above will be undertaken. It will appear that it provides a new approach to a number of economic questions as yet unsettled.

To begin with, the economic problems were not formulated clearly and are often stated in such vague terms as to make mathematical treatment a priori appear hopeless because it is quite uncertain what the problems really are. There is no point in using exact methods where there is no clarity in the concepts and issues to which they are to be applied.

A guiding principle cannot be formulated by the requirement of maximizing two (or more) functions at once.

His actions will be influenced by his expectation of these, and they in turn reflect the other participants’ expectation of his actions.

that we feel free to make use of a numerical conception of utility.

We emphasize that the problem of imputation must be solved both when the total proceeds are in fact identically zero and when they are variable.

Our mathematical analysis of the problem will show that there exists, indeed, a not inconsiderable family of games where a solution can be defined and found in the above sense: i.e. as one single imputation. In such cases every participant obtains at least the amount thus imputed to him by just behaving appropriately, rationally. Indeed, he gets exactly this amount if the other participants too behave rationally; if they do not, he may get even more.

These are the games of two participants where the sum of all payments is zero. While these games are not exactly typical for major economic processes, they contain some universally important traits of all games and the results derived from them are the basis of the general theory of games.

The essential feature is that any two players who combine and cooperate against a third can thereby secure an advantage.

Precisely: We shall show that the general (hence in particular the variable sum) n-person game can be reduced to a zero-sum n + 1-person game.

The moves are of two kinds. A move of the first kind, or a personal move, is a choice made by a specific player, i.e. depending on his free decision and nothing else. A move of the second kind, or a chance move, is a choice depending on some mechanical device, which makes its outcome fortuitous with definite probabilities.

in Poker—the interest of the player (we now mean kλ, observe that here kλ ≠ kκ) lies in preventing this “signaling,” i.e. the spreading of information to the opponent (kκ). This is usually achieved by irregular and seemingly illogical behavior (when making the choice at λ)—this makes it harder for the opponent to draw inferences from the outcome of λ (which he sees) concerning the outcome of μ (of which he has no direct news).