Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. Game theory provides general mathematical techniques for analyzing situations in which two or more individuals make decisions that will influence one another’s welfare. As such, game theory offers insights of fundamental importance for scholars in all branches of the social sciences, as well as for practical decision-makers. The situations that game theorists study are not merely recreational activities, as the term “game” might unfortunately suggest. “Conflict analysis” or “interactive decision theory” might be more descriptively accurate names for the subject, but the name “game theory” seems to be here to stay.
Modern game theory may be said to begin with the work of Zermelo (1913), Borel (1921), von Neumann (1928), and the great seminal book of von Neumann and Morgenstern (1944). Much of the early work on game theory was done during World War II at Princeton, in the same intellectual community where many leaders of theoretical physics were also working (see Morgenstern, 1976). Viewed from a broader perspective of intellectual history, this propinquity does not seem coincidental. Much of the appeal and promise of game theory is derived from its position in the mathematical foundations of the social sciences. In this century, great advances in the most fundamental and theoretical branches of the physical sciences have created a nuclear dilemma that threatens the survival of our civilization. People seem to have learned more about how to design physical systems for exploiting radioactive materials than about how to create social systems for moderating human
behavior in conflict. Thus, it may be natural to hope that advances in the most fundamental and theoretical branches of the social sciences might be able to provide the understanding that we need to match our great advances in the physical sciences. This hope is one of the motivations that has led many mathematicians and social scientists to work in game theory during the past 50 years. Real proof of the power of game theory has come in recent years from a prolific development of important applications, especially in economics.
Game theorists try to understand conflict and cooperation by studying quantitative models and hypothetical examples. These examples may be unrealistically simple in many respects, but this simplicity may make the fundamental issues of conflict and cooperation easier to see in these examples than in the vastly more complicated situations of real life. Of course, this is the method of analysis in any field of inquiry: to pose one’s questions in the context of a simplified model in which many of the less important details of reality are ignored. Thus, even if one is never involved in a situation in which people’s positions are as clearly defined as those studied by game theorists, one can still come to understand real competitive situations better by studying these hypothetical examples.
In the language of game theory, a game refers to any social situation involving two or more individuals. The individuals involved in a game may be called the players. As stated in the definition above, there are two basic assumptions that game theorists generally make about players: they are rational and they are intelligent. Each of these adjectives is used here in a technical sense that requires some explanation.
A decision-maker is rational if he makes decisions consistently in pursuit of his own objectives. In game theory, building on the fundamental results of decision theory, we assume that each player’s objective is to maximize the expected value of his own payoff, which is measured in some utility scale. The idea that a rational decision-maker should make decisions that will maximize his expected utility payoff goes back at least to Bernoulli (1738), but the modern justification of this idea is due to von Neumann and Morgenstern (1947). Using remarkably weak assumptions about how a rational decision-maker should behave, they showed that for any rational decision...