Prisoner’s Dilemma

July 2017

John Von Neumann, Game Theory, and the Puzzle of the Bomb

by William Poundstone; Doubleday; 290 pages.

In 1950 Life magazine quoted the great Hungarian-American physicist John Von Neumann, co-father of both the atom bomb and the digital computer, advocating immediate pre-emptive nuclear war against Russia: “If you say why not bomb them tomorrow, I say why not today? If you say today at 5 o’clock, I say why not one o’clock?” He was hardly alone. Generals and members of Congress were making the same arguments. So, most remarkably, was the British genius Bertrand Russell, today remembered as a crusading pacifist. In 1945, just after Hiroshima, he wrote that “there is one thing and one only which could save the world, and that is … that America should make war on Russia during the next two years, and establish a world empire by means of the atomic bomb.”

Among Von Neumann’s myriad accomplishments he was the inventor of the branch of mathematics called game theory, which is the study of conflict between thoughtful but not necessarily trusting opponents. Game theory is not just about games; it is in fact about all kinds of basic human encounters, including the nuclearsuperpower stand-off. The prisoner’s dilemma of the book’s title is a classic game-theory problem: What should you do when you and an opponent, with whom you cannot consult, will both do best if you both stick your necks out, but he can thrash you if you alone stick your neck out, and vice versa? It is the very quandary of first strikes and of unilateral build-up or disarmament—as theorists at the RAND Corporation in the late forties and early fifties well knew.

By tracing the development of the game theory that studies this quandary and the post-World War II nuclear strategy that tried to resolve it, the author illuminates both, in a book that is at once brisk but solid history, a lucid introduction to the logic of strategy, and a step beyond that into the psychology of basic human exchanges. It turns out there is no correct answer to the prisoner’s dilemma, and that is why Russell and Von Neumann could be so wrong in thinking we had to bomb Russia. But there is a best strategy for repeated prisoner’s dilemmas. The author explains that and its import and goes on to describe other games that point up other conundrums of human interaction.

This is not a history book, or rather it is history only in part. But the history and the other elements all throw light on one another, and the result is greater than the sum of the parts: a vivid profile of Von Neumann, an entertaining lesson in game theory, and an incisive account of Cold War strategizing at the birth of the nuclear arms race.