Von Neumann

I wouldn't normally make reference to an article about economics in this blog. However, I read an article today from Forbes called A Beautiful Theory. It is about mathematician John Von Neumann who made some important contributions to economic theory. Von Neumann and Oskar Morgenstern were part of my second year microeconomics course at university in the form of expected utility theory.

The article is a very easy read and provides some background on the development of the economic discipline on which my Master Thesis was based - Game Theory.

Here is a printed version of the article.

A condensed version is below:

The revolution in the social sciences began in the 1920s, when the man Time magazine called "the best brain in the world" decided he would work out how to win at poker. John von Neumann's quicksilver genius accelerated the development of the atomic bomb by a year, and he was one of the fathers of the computer.

Von Neumann was only interested in poker because he saw it as a path toward developing a mathematics of life itself. He wanted a general theory--he called it "game theory"--that could be applied to diplomacy, war, love, evolution or business strategy. But he thought that there could be no better starting point than poker: "Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory."

In 1944, Von Neumann teamed up with the economist Oskar Morgenstern to publish the bible of game theory, A Theory of Games and Economic Behavior. The essence of the theory was the mathematical modeling of a strategic interaction between rational adversaries, where each side's actions would depend on what the other side was likely to do.

A Theory of Games and Economic Behavior was widely hailed as an original and rigorous foundation for modern social science.

The admirers were soon disillusioned. To understand why, consider the toy model of poker presented in A Theory of Games. The model certainly meets the challenge that Von Neumann set for himself--bluffing, which seems to be such a psychological affair, emerges from the pure mathematics of the game's equations. Armed with Von Neumann's mathematics, even a computer could learn when to bluff.

But the trouble is that it would take a supercomputer to crunch through the complexities of the model's mathematics. Worse, in order to reach a solution, Von Neumann had to simplify the game of poker dramatically. Real poker is hugely more complicated--and so, too, is real life.

This is a more serious problem than it appears, because game theory is all about "asking yourself what is the other man going to think I mean to do."

Von Neumann and Morgenstern developed a theory of "zero sum" games, such as poker, where one player's loss is the other player's gain. If you play the optimum strategy in that sort of situation, and the other player makes mistakes, you will win.

But real-life games are not usually zero-sum. Consider the plot of the movie "Dr. Strangelove," in which the Soviets rationally create a Doomsday Device which will wipe out the world if they are attacked. Before they can tell anyone, a rogue general launches a strike against them. Peace was a possibility, but instead, the human race is destroyed. That's about as non-zero-sum as you can get.

It is also a reminder that in most situations, the point is not to beat some opponent but to do well for yourself. That will involve understanding the man on the other side of the game. If you think he is rational, and he isn't, your strategy will go badly wrong.

Some brilliant mathematicians and economists have worked hard to patch up these holes in the Von Neumann project, including Nobel prize winners Robert Aumann, John Harsanyi and Reinhard Selten. The most famous of them all is John Nash, who was surprisingly made a celebrity after Russell Crowe played him in the biopic A Beautiful Mind.

Game theory has a lot to contribute to the analysis of life, love and economics. But the game will only go according to plan if you're sure the other fellow knows the rules.