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Game theory is an application of mathematical reasoning to problems of conflict and collaboration between rational self-interested actors. Developed in the 1940s by Austrian mathematicians von Neumann and Morgenstern, it has been applied to many problems in political science, strategic theory, and even moral philosophy. To some extent it has been used practically by defence planners, and has applications within economics. The essence of all game theory applications is to analyse the interaction between strategies which actors, intent on maximizing their welfare, are bound to take, or likely to take, given certain levels of information. The most crucial distinction is probably between two basic sorts of game, a

distinction that so neatly summarizes a recurrent quality of real life politics that the terminology has entered ordinary political discourse. This is the distinction between zero sum games and non-zero sum. Simply, one might say that a conflict between, for example, an employer and a trade union is zero sum if there is a fixed amount of profit that the firm can make, which cannot be increased by co-operation between them, or, perhaps, that a conflict between university departments for finance is zero sum if there is no chance that the departments can do anything to increase the total university budget. The technical quality of a zero sum game is that the gains to one player (we assume for convenience that this is a two player game) exactly balance the loss to the other. A non-zero sum version of these examples would allow the total amount available for division to be increased by co-operation between the playersÐ profits might actually go up given good labour relations, or the university budget might be increased by an Education Ministry impressed by altruistic university departments, and so on. Most political situations are probably not in fact zero sum, but most are `played' by their actors as though they were. By examining the likely choice of strategies of independent players it is often

possible to show not only what the outcome will most likely be, but where apparently rational interest-maximizing choices, if taken by independent actors, will produce a sub-optimal pay-off for both! This is characterized by the most famous of the simple game analyses in game theory, the Prisoner's

Dilemma. One assumes that two prisoners are held in separate cells, accused of a crime they committed together. To each is made the offer of turning state's evidence against the other, or remaining silent. If a prisoner gives evidence against the other, implicating themself, they will receive a minor prison sentence; if they stay silent, but are convicted on their partner's evidence, they will get a major sentence. But if both remain silent, there being no other evidence, they will both be acquitted.What do they choose? Social psychology experiments have given empirical confirmation of the theoretical prediction that they will both confess, rather than trust the other to co-operate and remain silent. Thus a sub-optimal result arrives, in the absence of malice, out of rational calculation. One point about the prisoner's dilemma game, and it has many real political

applications, is that the results depend crucially on the surrounding context, which changes the effective pay-off matrix. Suppose, for example, that both the accused are members of a criminal gang which ruthlessly punishes informers, once they are let out of prison. In this context the prediction changes. The more complicated the game, and to model any important political situation obviously requires vastly more complicated games, the more unexpected become the predictions, but also the more uncertain. One general result is to show how little our major political actions depend ultimately on rational choice, or how limited is the possibility of rationality, even on major issues, given likely information levels. Game theory is one branch of a whole development of public choice

theories that are said to shed increasing light on social interaction, and they occupy a curious half-way house between being moral philosophy and purely neutral predictive theory. However, the great promise they once showed has not been realized, largely because of the difficulty of building sufficiently accurate empirical assumptions into the models. Where they do work, for example in predicting coalition formation in multi-party governments, the results are often intuitively obvious in any case. It is not so much that game theory does not adequately model rational strategy but that institutional restraints force actors to behave, at best, with what has come to be known as `bounded rationality'.