Magazine article New Statesman (1996)

The Great Game: Simon Singh on "Nash's Equilibrium", the Brilliant Legacy of an Unstable Mind. (Mathematics)

Magazine article New Statesman (1996)

The Great Game: Simon Singh on "Nash's Equilibrium", the Brilliant Legacy of an Unstable Mind. (Mathematics)

Article excerpt

A Beautiful Mind is a film about a mathematician, but it is not a film about mathematics. It concentrates on John Nash's battle with schizophrenia, and barely touches on his great mathematical achievements, which are mentioned only in bar-room scenes or hinted at via arcane equations scrawled on window panes.

To try to complete the picture, it is important to understand Nash's passion-game theory-and how his contribution to that subject has had a huge influence on modern economics. In just a few short years, a man barely out of his teens laid the foundations for a discipline that had an enormous impact on economies all over the world.

Game theory, put simply, is the mathematical study of the strategies used to win games. It began with the study of such games as noughts and crosses and chess, which are relatively easy to analyse because they are games of "complete information" - in other words, each player can see the other's position.

Then mathematicians became interested in games such as poker, which is much more interesting because players cannot see each other's cards. Poker is a game of "incomplete information", so more subtle elements such as bluff come into the analysis.

Eventually, mathematicians attempted to analyse more important games, including economics, warfare and divorce settlement. In each case, you have two parties competing over money or territory; each party develops a strategy based on its own strengths and objectives, and on the perceived mindset and skills of their opponent. Game theory is maths plus a dash of psychology.

And the man who did more than anyone else to apply game theory to the real world was John Nash. Between 1950 and 1953, Nash published four papers that revolutionised game theory. Still in his early twenties, he conducted a deep analysis of a special set of games that were said to be non-zero sum.

In most games, including chess, there is a zero sum, which means that if I win, then you lose, or vice versa. But in a non-zero-sum game, both players can win ... or both can lose. For example, pay negotiation between management and a trade union can be a non-zero-sum game. The result can be a long strike that hurts both sides, or a fair agreement that benefits both sides.

Nash enshrined his theory in mathematical equations; in particular, he identified a situation, later known as the Nash equilibrium, in which both players have a perfect strategy that results in stability. Players maintain this strategy because anything else will only worsen their own position. …

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