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Game Theory

  Game theory is perhaps the most important 20th-century development in the formal (or mathematical) social sciences. The landmark work in game theory was John von Neumann and Oskar Morgenstern\'s Theory of Games and Economic Behaviour, which was published in 1944. The insights of game theory are constantly being refined and elaborated, and it remains one of the most vibrant fields in the social sciences.

Game theory is the mathematical study of games and strategy. Its purpose is, essentially, to determine from a given set of rules the likely strategy to be used by each player, and to find the best. In this sense, the theory of games is the analysis of the strategic elements of a game rather than that of the chance elements, which mathematicians have studied over a much longer period in probability. But game theory is not an abstract activity, not pure mathematics. Nor is it a game, though it is useful for explaining the logic of many social games. It is mostly deployed to explore such complex and serious topics as the logic of arms races, the behaviour of agents in imperfect markets, and the behaviour of political parties and coalitions. Game theory studies the logic of interdependent decision-making between individuals or groups on the suppositions that the agents involved in a game are rational, that is, that they have well-formed preferences and pursue their interests efficiently, and that they have strategies, which requires them to have more than one possible course of action. In this sense the whole of economic theory, and much political theory, are subsets of game theory.

Game theorists classify games by their nature and their pay-offs. Co-operative games are those in which the players can communicate and bargain with one another; in non-co-operative games these features are absent. Non-co-operative game theory is the more fundamental and rigorous: it calls for a complete description of the rules of the game so that the strategies available to the players can be studied in detail. The aim of the analyst is to find the equilibrium solutions to the game. Game theorists also classify games by whether or not they are zero-sum or not. In zero-sum games what the winner gets (in whatever units) is exactly equal to the loss of the loser. Non zero-sum games include those in which all players benefit (positive-sum games) or lose (negative-sum games), although not necessarily by the same amounts, and ones in which some players win and others lose, but not by the same amounts (variable-sum games).

In the social sciences most focus has been on non zero-sum games. The most famous is the two-person prisoner\'s dilemma which has an apparently paradoxical property. In this game each player has a dominant strategy, that is, one course of action which leads to the best possible pay-off against whichever of two options the opponent chooses. So both players, if they are rational, must choose these strategies. However, the payoffs of the game are such that both players would be better off if they co-operated and chose ‘dominated strategies’, that is strategies that would leave them vulnerable to being ‘suckered’ by their opponent. This game has been seen by many as a paradigm illustration of the central problems of conflict and co-ordination in politics, economics and psychology.

The prisoner\'s dilemma, like other games, has been formally modelled and used in experimental situations by psychologists, and has been used to explore the logic of arguments used by great political theorists of the past, such as Hobbes, Hume and Rousseau. In the 1970s and 1980s, the use of game theory was increasing across the social sciences, and was perhaps most fruitful in the field of evolutionary biology where it is used to model genetically determined animal behaviour on the assumption that genes behave as if they were rational maximizing agents.

The nature of the problems game theory sets out to solve is such that it is hard to determine in a reasonable amount of time. It is pointless, for example, discovering that the best strategy would have been to raise interest rates six months ago! Analyses of even ‘simple’ games, for example, poker, can only be done for versions of the game which are so simplified that no real-world enthusiast would play them. Another problem is that in most of the game-like situations which interest social scientists, the interest is not in the best thing to do but in the usual thing people do, something about which mathematical game theory can say nothing. In many political or economic situations, the question is what the best thing to do would be assuming that the other players continue to play as usual. (This is also a question to which professional gamblers would like to know the answer.) Because game theory is really about what should be done if every player is playing as well as they can, the number of practical applications of game theory has turned out to be far more limited than those who wish to apply it would desire. TF SMcL BO\'L

See also monopolistic competition; oligopoly.Further reading K. Binmore, Fun and Games: a Text on Game Theory; , R.D. Luce and , H. Raiffa, Games and Decisions.



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