NASH, John Forbes. Two-Person Cooperative Games.
Chicago: Econometric Society, 1953. First edition.

In 1994 John Nash shared the Nobel Prize in Economics with Reinhard Selten and John Harsanyi "for their pioneering analysis of equilibria in the theory of non-cooperative games". At that time Nash had only written a hand full of short papers in this field during the period 1948-50, and otherwise thereafter been occupied with different topics of mathematics and struggling with mental illness. None the less, these papers today form the foundation of modern game theory and have widely influenced generations of researchers in economics, and other social sciences.

In 1948 John Nash was emitted to Princeton’s elite mathematics department with a letter of recommendation reading nothing else than “This man is a genius”. In search for a topic to write his thesis in, Nash directed his attention to the newly established field of game theory. The modern theory of games had been pioneered by John von Neumann in the 1920’s and then established in his classic monograph Theory of Games and Economic Behavior coauthored with Oskar Morgenstern. Von Neumann and Morgenstern, who were both working at Princeton at the time Nash arrived, had developed a highly successful theory of games, and they predicted that there theory would do the same for economics as calculus had done for physics in Newton’s days. However, most of their work was based on the analysis of the interrelationships of the various coalitions which can be formed by the players in the games. They had also studied possible strategic solutions of various games but for the most part these were either confined to very simple games or of a less satisfying nature.

When Nash entered the field of game theory he based his work on his profound insight that one should distinguish between games were the players act in a cooperative manner (forming coalitions, etc.) and those games were all players act entirely individualistic. This isolation between cooperative and non-cooperative games enabled Nash to propose strategic solutions, of a more useful character, for a broader range of games than von Neumann and Morgenstern had been able to.

Nash submitted his first paper Equilibrium Points in N-Person Games in November 1949. In this short note he introduced for non-cooperative games the decisive concept of an equilibrium point, today called Nash equilibria. In Theory of Games and Economic Behavior von Neumann and Morgenstern had proposed a particular solution for non-cooperative two-person games called minimax solutions, a strategic solution were each player seeks to minimize his maximum possible loss. Nash’s concept generalizes this particularly satisfying solution to games with an arbitrary number of players - a set of strategies for each player which is optimal assuming the strategies of the other players are held fixed. Using Kakutani’s fixed point theorem Nash proved that such equilibrium points exist for all finite non-cooperative games.
In his famous thesis Non-Cooperative Games, which was submitted May 1950 and published in Princeton’s Annals of Mathematics the next year, Nash elaborated on his solution concept and developed a full theory for non-cooperative games. In his concluding remarks Nash wrote the following passage:

“The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to noncooperative form. One proceeds by constructing a model of the pre-play negotiation so that the steps of negotiation become moves in a larger non-cooperative game … describing the total situation.

This larger game is then treated in terms of the theory of this paper … and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation.”

The approach described here was to become a key influence on the future researchers of game theory, and is nowadays known as the Nash program. It was this idea which lay behind Nash’s two papers on cooperative games; The Bargaining Problem and Two-Person Cooperative Games both published in the journal Econometrica. In these works Nash showed how one makes the players’ steps in negotiations in the cooperative game become moves in the non-cooperative model which is then more tractable through the theory of non-cooperative games. This solution concept plays a prominent role in the theory of cooperative games and is known as the Nash bargaining solution.

Von Neumann and Morgenstern had focused their immediate attention towards the interrelationships of coalitions in cooperative games and felt that it was here that the future of game theory lay. When Nash presented his result on equilibrium points to von Neumann he dismissed it as “just another fixed point theorem”. But Nash took his own approach through non-cooperative games and in some sense it was his methods which initiated the revolution in economics which von Neumann and Morgenstern had originally envisioned. 

In: Econometrica, pp.128-140, volume 21, number 1, January 1953. The complete issue offered in original printed wrappers: fine and unmarked.