game theory

game theory The general theory of the rational behaviour of two or more people in circumstances where their interests are, at least in part, conflicting. In The Theory of Games and Economic Behaviour (1947), John Von Neumann and Oskar Morgenstern attempted to develop a theory covering both zero-sum games and non-zero-sum games. In this context a ‘game’ is any social situation where interaction occurs between at least two ‘players’ who are competing with each other at least some of the time. Such situations might include marriage, war, rivalry between political parties, the labour-market, and more specifically employer–worker negotiations. The key contribution of game theory is to provide an abstract mathematical theory to model what choices are possible, or likely, in situations with certain common features (such as the number of participants, or players, and whether the ‘prize’ is of fixed size or is variable).

Zero-sum games represent circumstances in which the gain of one participant is the loss of another; that is, situations where the size of the ‘cake’ is fixed, and everyone seeks to get as large a slice of it as possible. Two-person zero-sum games were the first to be studied by Von Neumann, who showed that in certain cases there would be a relatively stable equilibrium point (or minimax-maximin combination), at which one player's optimum choice met the other's.

In non-zero-sum or non-constant-sum games, it may pay all or some of the participants to co-operate actively to increase the total benefits achieved, so analysis focuses on the formation of coalitions and their outcomes. In effect, collaboration increases the size of the cake, but participants cannot always predict their rival's choice. The most famous examples are the well-known Prisoner's Dilemma and (more recent) Problem (or Tragedy) of the Commons, both of which capture clearly situations in which choices that maximize each individual's self-interest produce the worst possible outcome overall. Only if each participant chooses what is in the collective interest, rather than narrow self-interest, will the collective optimum result be achieved. In most laboratory experiments based on these games, nearly two-thirds of all subjects make the selfish, or distrustful choice; the co-operative outcome is achieved in a small minority of cases. However, they have been run on a vast scale using computer simulations to assess the effectiveness of various strategies pitted against each other; and, on this longer time-horizon, co-operation was found to evolve in a society of completely self-interested individuals.

While few social scientists use the mathematical models of game theory, the general theory and concepts have already had a profound effect on all the social sciences which study situations of conflict, competition, and potential co-operation (notably, for example, in studies of the military and of markets). See Robert Gibbons , A Primer in Game Theory (1992
) and Kenneth G. Binmore , Fun and Games (1992
).