PRISONER'S DILEMMA

Here's one version: You and your partner are captured. If you rat on him ("defect'') and he is silent, you get off scot-free and he gets three years—and vice versa. If you both rat on each other, you both get less lengthy sentences, two years; but if you both clam up (cooperate with each other), you get one year each. What to do? It is the dilemma posed by the prisoner's dilemma that is the theme of this latest volume from Poundstone (Labyrinths of Reason, 1988, etc.)—an intriguing exercise in point/counterpoint as Poundstone intertwines the development of game theory with a running biography of one of game theory's founders, John von Neumann.

Here again are the tales of the brilliant Hungarian mathematician, the practical joker, the reckless driver and not-so- hot poker player who was a jewel in the crown of the Institute for Advanced Study at Princeton—and also advisor on the Manhattan Project and the hydrogen bomb, consultant at RAND, developer of the digital computer, possessor of a photographic memory, and on and on. Early in his career, von Neumann co-authored the Theory of Games and Economic Behavior with the economist Oskar Morgenstern ("one of the most influential and least-read books of the twentieth century''). Poundstone's point is that for all the beauty of the concepts and theorems derived from game theory (minimax theorem, zero-sum symmetric games, optimal strategies), real games are not played by rational players; often they are not symmetric and, if played not once but in successive rounds, may demonstrate that cooperation is the best strategy. Poundstone's examples of the nuclear-arms race and other instances of the kinds of Pyrrhic victories that can obtain in situations of mutual distrust are apt.

The fact that von Neumann, a lifelong cynic, had a deathbed conversion to Catholicism not so subtly underscores the presence of paradoxes and contradictions that characterize human as opposed to mathematical behavior.