Scientists At War

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Throughout the late 1940s and early 1950s von Neumann made frequent trips to RAND. John Williams adored him and was “delighted” when, in December 1947, he convinced von Neumann to join the organization as a part-time consultant. Williams, who loved games, would try out immensely difficult math problems on von Neumann but never stumped him. Von Neumann could solve in his head the most elaborate calculations to the second or third decimal point.

THE BIRTH OF GAME THEORY

VON NEUMANN liked games, and in 1928, when he was twenty-four, he had sat in on a fateful bout of poker that set in motion a remarkable train of logical observations. First, he noted that a player’s winnings and losses depended not only on his own moves but also on the moves of the other players. In devising a strategy, he had to take into account the strategies of the other players, assuming that they, too, were rational; that, therefore, the essence of the good strategy was to win the game, regardless of what the other players did, even though what the other players do determines, in part, the playing of the game.

 

Von Neumann then realized that the game of poker was fundamentally similar to the economic marketplace. Economists had been attempting to impose mathematical models on classical economic theory, but with no success. The reason for their failure, von Neumann reflected, was that the theory assumed an independent consumer trying to maximize his gains and independent sellers trying to maximize theirs— whereas, in fact, just as in the game of poker, the consumer and the seller formed a unit, competing but interdependent, and the moves of one could not be systematically analyzed or strategically planned except in the context of the other’s. So it goes with any situation in which two or more players have a conflict of interest and in which a good deal of uncertainty is involved.

Von Neumann developed what came to be called “game theory” as a mathematically precise method of determining rational strategies in the face of critical uncertainties. The classical case of game theory is the Prisoners’ Dilemma. Two prisoners, arrested on suspicion for the same crime, are kept in separate cells with no chance to communicate. They are separately approached by guards and given the following proposition: If neither squeals on the other, they will both serve brief sentences; if Prisoner A tells on B, but B keeps quiet, then A will be let free and B will serve maximum sentence; likewise, if B talks but A remains silent, then B will be freed and A forced to serve full sentence; if both A and B rat on each other, then they will serve half sentences. On the surface, it seems that it would serve both their interests to remain silent. However, there is a great deal of uncertainty: Prisoner A worries that Prisoner B might feel compelled to talk, since it would be to B’s advantage to do so; if, under such circumstances, A does not talk, A serves a full jail sentence. Prisoner B is, of course, thinking similar thoughts about Prisoner A’s possible moves. Therefore, both prisoners will talk and both will serve half jail sentences, even though both would have been better off keeping quiet.

According to game theory, moreover, both prisoners would be perfectly rational if they did talk. Both have to assume that the other prisoner, the other player, will play his best move; thus each has to play the move that would be best for himself given the best move of the other player. That is the essence of game theory: find out your opponent’s best strategy and act accordingly. Such a strategy may not get you the maximum gain, but it will prevent you from taking the maximum loss.

Von Neumann wrote a scholarly paper on game theory in 1928 and created a minor sensation in the scientific and mathematical communities of Europe. The sensation exploded in 1944 when he and a Princeton economist named Oskar Morgenstern collaborated to write an enormous volume called Theory of Games and Economic Behavior, offering mathematical proofs and suggesting applications of the theory to economics and the entire spectrum of social conflict.

It was a conservative theory and a pessimistic one as well. It said that it was irrational behavior to take a leap, to do what is best for both parties and trust that one’s opponent might do the same. In this sense, game theory was the perfect intellectual rationale for the Cold War, the vehicle through which many intellectuals accepted its assumptions. It was possible to apply the Prisoners’ Dilemma, for instance, to the Soviet-American arms race—substituting “build more” for “talk” and “stop building” for “silence.” It made sense for both sides to stop building arms, but neither could have the confidence to agree to a treaty to stop, suspecting that the other might cheat, build more, and go on to win. Distrust and the fostering of international tensions could be elevated to the status of an intellectual construct, a mathematical axiom.

GAME THEORY GROWS UP