‘The game theorist reading this book does not need another lecture on the importance of the book and the development of game theory. Very few other books in economics have been as highly praised and influential. Only a handful of topics have received as much attention or been surveyed as intensively in contemporary economics as game theory. The reader of the book who is not a scholar of game theory, and is interested in catching up with the development of the discipline since the book was published, can choose from a number of excellent introductory books. They are written in a variety of styles and levels of mathematical sophistication and are directed at laypersons as well as scholars of economics, law, political science, management theory, mathematics, and biology…’ ARIEL RUBINSTEIN
Game Theory was originally propagated by John von Neumann and Oskar Morgenstern in their work, ‘Theory of Games and Economic Behaviour,’° to deal with economic problems. They expounded ‘the mathematics of probability and of decisional sequences’ under ‘conditions of complete information’)’
It has been applied to international politics by Morton Kaplan and Thomas Schelling.
The period of the late ’40s and early ’50s was a period of excitement in game theory. The discipline had broken out of its cocoon and was testing its wings.
Giants walked the earth.
At Princeton, John Nash laid the groundwork for the general non-cooperative theory and for cooperative bargaining theory.
Lloyd Shapley defined a value for coalitional games, initiated the theory of stochastic games, coinvented the core with D. B. Gillies, and together with John Milnor developed the first game models with an infinite number of players.
Harold Kuhn reformulated the extensive form and introduced the concepts of performance strategies and perfect recall. A. W. Tucker invented the story of the Prisoner’s Dilemma, which has entered popular culture as a crucial example of the interaction between competition and cooperation.
It is important to recognize that the results that Aumann enumerated did not respond to some suggestion of von Neumann; rather they were new ideas that ran counter to von Neumann’s preferred version of the theory.
In almost every instance, it was a repair of some inadequacy of the theory as presented in the TGEB.
Indeed, von Neumann and Morgenstern criticized Nash’s non-cooperative theory on a number of occasions. In the case of the extensive form, the book contains the claim that it was impossible to give a useful geometric formulation.
Thus, game theory was very much a work in progress, in spite of von Neumann’s opinion that the book contained a rather complete theory. Through the efforts at RAND and at Princeton University, many new directions of research had been opened and the way had been paved for the applications to come.
The game theory has been defined as ‘a body of thought dealing with rational decision strategies in situations of conflict and competition, when each participant or player seeks to maximise gains and minimize losses”.
It is a mathematical model in which the player is placed in a certain fixed situation and tries to make maximum gains out of his opponents.
The situations visualised are of four kinds:
(1) zero-sum two persons games;
(2) non-zero-sum two persons games;
(3) zero-sum n-persons games; and
(4) non-zero-sum n-persons games.
In situation (1) the gain of one is equal to the loss of the other. In (2) and (3) the outcome is shared and the losses of one are not necessarily equal to the gains of another.
In (4) the situation is tremendously multifarious and the gains and losses are shared by both sides to some extent.
There are definite assumptions and rules of the game. The assumptions are that the players are guided by rational behaviour and choose the best course of action that brings them maximum gains.
The rules are that the equation between the players is straight and the losses of one are the gains of another. The theory is built up with the help of five important conceptions: strategy, opponent, pay-off, rules and information. Players are engaged in choosing alternatives which can be used in the future situations. These are known as the outcomes.
The full ranges of possible outcomes are prospects. The gain and loss result of prospects is pay-off which is maximum when one wins, second- best when the game is drawn and third-best when it is lost.
Just as rationality in the behaviour of a player is assumed, his ability to make maximum gains by designing the best strategies is also taken for granted.
The theory is highly abstract and works only under assumed conditions. The players are rarely as rational as presumed by this theory.
The theory can be applied with some success only to cases of two- person zero-sum games, but, as Morton Kaplan has pointed out, there are few such situations in real life and the theory ‘has only limited applicability to most problems of international politics’.
One of the reasons for its limited applicability has been suggested by Karl W. Deutsch — ‘Game Theory usually assumes that most games have an end but international politics is rather an unending game in which no great power can pick up its marbles and go home’.