- Person
- John von Neumann
- Lived
- 1903–1957
- Field
- Mathematics & computing
- From
- Hungarian-American
The story
How should a rational player act when the outcome depends on what an opponent does? In 1928 John von Neumann, a young mathematician from a Jewish family in Budapest then lecturing in Berlin, published a paper on the theory of board games that answered the question for one important case. He proved the minimax theorem: in any two-person game where one player's gain is the other's loss, each side has a strategy that minimises its maximum possible loss, and the two values match.
Von Neumann later said that he thought there was nothing worth publishing until the minimax theorem was proved, and that without it there could be no theory of games. The theorem is now seen as the starting point of game theory.
Working at Princeton with the economist Oskar Morgenstern, he extended the idea to games with imperfect information and more than two players. Their 1944 book, Theory of Games and Economic Behavior, published by Princeton University Press, attracted so much interest that The New York Times ran a front-page story about it. It argued that economics needed new mathematical tools such as convex sets and fixed-point theorems, and the second edition in 1947 added an influential derivation of expected utility, a way of describing rational choice under uncertainty. The British economist Richard Stone called it the most important publication in economics since Keynes's General Theory.
The book founded game theory as a discipline. Its ideas now shape economics, the design of auctions and markets, evolutionary biology, political science and computer science. Several Nobel Prizes in economics have been awarded for game theory, beginning in 1994 with John Nash, John Harsanyi and Reinhard Selten, and continuing with laureates such as Thomas Schelling and Robert Aumann in 2005.
The mathematical techniques von Neumann introduced, from duality to fixed-point theory, have remained primary tools of mathematical economics ever since.
Why it matters
Game theory gives people a rigorous way to think about cooperation and competition, from setting spectrum auctions to understanding how species evolve.
About John von Neumann
Budapest-born mathematician whose 1945 EDVAC report set out the stored-program design behind almost every computer, and who helped found game theory and modern quantum mechanics.
More about John von Neumann
- Von Neumann warned of CO2 warming in 1955In 1955 John von Neumann noted that carbon dioxide from burning coal and oil might already have changed the atmosphere enough to cause general warming.
- Von Neumann's ergodic theorem earned 'immortality'John von Neumann's 1932 papers on ergodic theory were so important that Paul Halmos said they alone would have guaranteed him mathematical immortality.
- Von Neumann launched computer weather forecastingIn 1950 John von Neumann and Jule Charney used ENIAC to make the first numerical weather forecasts; in 1955 routine computer forecasting began in the US.
- Von Neumann's IAS computer was copied worldwideThe IAS machine John von Neumann built in Princeton from 1946 became the blueprint for early computers worldwide, and its design shaped IBM's first scientific computers.
- John von Neumann invented merge sort in 1945In 1945 John von Neumann invented merge sort, one of the most widely used methods for putting data in order, in what Donald Knuth called his first computer program.
- Von Neumann helped create the Monte Carlo methodWith Stanislaw Ulam, John von Neumann helped develop the Monte Carlo method, using random numbers on computers to solve problems too complex for direct calculation.
- Von Neumann gave quantum mechanics its mathematicsIn his 1932 book Mathematical Foundations of Quantum Mechanics, John von Neumann set out the first rigorous mathematical framework for quantum theory.
- Von Neumann designed a machine that copies itselfIn the late 1940s John von Neumann designed a self-reproducing 'universal constructor' and, with Stanislaw Ulam, created the field of cellular automata.
- John von Neumann wrote the blueprint for modern computersJohn von Neumann's 1945 report on the EDVAC gave the first published description of the stored-program computer, the design behind almost every computer since.
Sources
- John von Neumann Wikipedia
- Theory of Games and Economic Behavior Wikipedia
- Game theory Wikipedia
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