CHAPTER 12
The War of Wits RAND, Summer 1950 RAND, Summer 1950
Oh, the RAND Corporation is the boon of the world; They think all day for a fee.
They sit and play games about going up in flames, For counters they use you and me, Honey Bee, For counters they use you and me.
- MALVINA R REYNOLDS, "The RAND Hymn," 1961 "The RAND Hymn," 1961
THE DC-3 DC-3 SHOOK SHOOK as it droned past the desert and mountains toward the opaque Pacific and water-colored sky. Los Angeles lay thousands of feet below, resembling some science-fiction vision of a s.p.a.ce colony under its sulfurous blanket of haze. Nash had boarded the TWA flight in New York almost twenty-four hours earlier. He had not slept at all. He was rumpled, sweaty, cramped, and exhausted, but as the plane descended, he hardly registered these discomforts. His attention was wholly absorbed by the exotic panorama and his own intense excitement. as it droned past the desert and mountains toward the opaque Pacific and water-colored sky. Los Angeles lay thousands of feet below, resembling some science-fiction vision of a s.p.a.ce colony under its sulfurous blanket of haze. Nash had boarded the TWA flight in New York almost twenty-four hours earlier. He had not slept at all. He was rumpled, sweaty, cramped, and exhausted, but as the plane descended, he hardly registered these discomforts. His attention was wholly absorbed by the exotic panorama and his own intense excitement.
Flying was still a highly novel experience in 1950, no more so than for a twenty-two-year-old West Virginian whose travels had mostly been limited to the Norfolk & Western runs between Roanoke and Princeton. Nash"s first flight marked the beginning of his career as a consultant for the secretive RAND Corporation. RAND is a civilian think tank in Santa Monica, described by Fortune Fortune in 1951 as "the Air Force"s big-brain-buying venture," in 1951 as "the Air Force"s big-brain-buying venture,"1 where brilliant academics pondered nuclear war and the new theory of games. Nash"s on-and-off encounter with RAND over the next four years was a transforming experience in his life. His a.s.sociation with RAND, at the height of the Cold War, started promisingly in the summer of 1950, just as the Korean War began, and ended traumatically in the summer of 1954, when McCarthyism reached its peak. where brilliant academics pondered nuclear war and the new theory of games. Nash"s on-and-off encounter with RAND over the next four years was a transforming experience in his life. His a.s.sociation with RAND, at the height of the Cold War, started promisingly in the summer of 1950, just as the Korean War began, and ended traumatically in the summer of 1954, when McCarthyism reached its peak.
On a purely personal level, Nash"s view of the world and himself was permanently and subtly colored by the RAND Zeitgeist - its worship of the rational life and quantification, its geopolitical obsessions, and its weirdly compelling mix of Olympian detachment, paranoia, and megalomania. Intellectually, it was another story. From the moment of his arrival, Nash began actively disengaging himself from the interests and individuals that brought him to RAND in the first place, retreating from game theory and moving rapidly into pure mathematics, a process of disengagement that would repeat itself several times over the rest of the decade. retreating from game theory and moving rapidly into pure mathematics, a process of disengagement that would repeat itself several times over the rest of the decade.
Nothing like the RAND of the early 1950s has existed before or since.2 It was the original think tank, a strange hybrid of which the unique mission was to apply rational a.n.a.lysis and the latest quant.i.tative methods to the problem of how to use the terrifying new nuclear weaponry to forestall war with Russia - or to win a war if deterrence failed. The people of RAND were there to think the unthinkable, in Herman Kahn"s famous phrase. It was the original think tank, a strange hybrid of which the unique mission was to apply rational a.n.a.lysis and the latest quant.i.tative methods to the problem of how to use the terrifying new nuclear weaponry to forestall war with Russia - or to win a war if deterrence failed. The people of RAND were there to think the unthinkable, in Herman Kahn"s famous phrase.3 It attracted some of the best minds in mathematics, physics, political science, and economics. RAND may well have been the model for Isaac Asimov"s It attracted some of the best minds in mathematics, physics, political science, and economics. RAND may well have been the model for Isaac Asimov"s Foundation Foundation series, about a RANDlike organization full of hyper-rational social scientists - psychohistorians - who are supposed to save the galaxy from chaos. series, about a RANDlike organization full of hyper-rational social scientists - psychohistorians - who are supposed to save the galaxy from chaos.4 And Kahn and von Neumann, RAND"s most celebrated thinkers, were among the alleged models for Dr. Strangelove. And Kahn and von Neumann, RAND"s most celebrated thinkers, were among the alleged models for Dr. Strangelove.5 Although its heyday lasted a decade or less, RAND"s way of looking at human conflict not only shaped America"s defense in the second half of the century but also made a deep and lasting impression on American social science. RAND had its roots in World War II, when the American military, for the first time in its history, had recruited legions of scientists, mathematicians, and economists and used them to help win the war. As Fred Kaplan writes of RAND"s role in nuclear strategy, Although its heyday lasted a decade or less, RAND"s way of looking at human conflict not only shaped America"s defense in the second half of the century but also made a deep and lasting impression on American social science. RAND had its roots in World War II, when the American military, for the first time in its history, had recruited legions of scientists, mathematicians, and economists and used them to help win the war. As Fred Kaplan writes of RAND"s role in nuclear strategy,6 [World War II was] a war in which the talents of scientists were exploited to an unprecedented, almost extravagant degree. First, there were all the new inventions of warfare - radar, infrared detection devices, bomber aircraft, long-range rockets, torpedoes with depth charges, as well as the atomic bomb. Second, the military had only the vaguest of ideas about how to use these inventions... . Someone had to devise new techniques for these new weapons, new methods of a.s.sessing their effectiveness and the most efficient way to use them. It was a task that fell to the scientists.
Initially, the scientists worked on narrow technical problems - for example, how to build the bomb, how deep to set the charges, the choice of targets. But when it became clear that people didn"t know the best way to use this incredibly expensive and destructive weaponry, they were increasingly drawn into discussions of strategy.
The advent of the bomb turned the temporary wartime partnership between the military and the scientific establishment into a continuing relationship. The Air Force, which controlled the new weaponry, emerged after the war as the linchpin of the national defense. "Whole conceptions of modern warfare, the nature of international relations, the question of world order, the function of weaponry, had to be thought through again. n.o.body knew the answers," Kaplan writes.7 Again the military turned to the academic community. As Oskar Morgenstern, also a RAND consultant during the 1950s, put it in his book on defense Again the military turned to the academic community. As Oskar Morgenstern, also a RAND consultant during the 1950s, put it in his book on defense issues: "Military matters have become so complex and so involved that the ordinary experience and training of the generals and admirals were no longer sufficient to master the problems... . More often than not their att.i.tude is, "here is a big problem. Can you help us?" And this is not restricted to the making of new bombs, better fuel, a new guidance system or what have you. It often comprises tactical and strategic use of the things on hand and the things only planned." issues: "Military matters have become so complex and so involved that the ordinary experience and training of the generals and admirals were no longer sufficient to master the problems... . More often than not their att.i.tude is, "here is a big problem. Can you help us?" And this is not restricted to the making of new bombs, better fuel, a new guidance system or what have you. It often comprises tactical and strategic use of the things on hand and the things only planned."8Fortune magazine put it more succinctly: "If World War II was a war of weapons, another conflict would include on both sides a war of wits at the highest level of knowledge." magazine put it more succinctly: "If World War II was a war of weapons, another conflict would include on both sides a war of wits at the highest level of knowledge."9 In the final days of the war, the Air Force generals began to worry about the brain drain of top scientists.10 How to keep the best and brightest thinking about military problems was far from obvious. Men of the caliber of John von Neumann would hardly sign up for the civil service. But scientists would have to have access to secrets so one couldn"t just rely on contracts with universities. The solution was a private nonprofit organization outside the military but with close ties to the Air Force. In the fall of 1945, General Henry "Hap" Arnold promised to give Douglas Aircraft $10 million of leftover wartime procurement funds for a research venture to be called Project RAND (for "research and development," though wits later insisted the acronym stood for "research and nondevelopment"). The project was housed on the third floor of Douglas"s Santa Monica plant. Friction between Douglas and the new ent.i.ty led to a spinoff as a private nonprofit corporation in 1946, which was when RAND moved to its downtown offices. How to keep the best and brightest thinking about military problems was far from obvious. Men of the caliber of John von Neumann would hardly sign up for the civil service. But scientists would have to have access to secrets so one couldn"t just rely on contracts with universities. The solution was a private nonprofit organization outside the military but with close ties to the Air Force. In the fall of 1945, General Henry "Hap" Arnold promised to give Douglas Aircraft $10 million of leftover wartime procurement funds for a research venture to be called Project RAND (for "research and development," though wits later insisted the acronym stood for "research and nondevelopment"). The project was housed on the third floor of Douglas"s Santa Monica plant. Friction between Douglas and the new ent.i.ty led to a spinoff as a private nonprofit corporation in 1946, which was when RAND moved to its downtown offices.
RAND"s Air Force contract gave it an amazingly free hand, according to William Poundstone"s history of RAND. The contract called for research on intercontinental warfare, which, given the dominant role of nuclear weaponry, effectively gave RAND an unrestricted license to roam over the front lines of the U.S. defense strategy. Within these guidelines, RAND scientists could study anything that interested them. RAND could also refuse specific studies requested by the Air Force.
From the beginning, RAND"s work was a curious mix of narrowly focused engineering, cost-benefit studies, and blue-sky conjecture. A now-famous 1946 study, completed more than a decade before the launch of Sputnik Sputnik in 1957, proved remarkably prescient. In "Preliminary Design of an Experimental World-Circling s.p.a.ceship," RAND scientists argued that "the nation which first makes significant achievements in s.p.a.ce travel will be acknowledged as the world leader in both military and scientific techniques. To visualize the impact on the world, one can imagine the consternation and admiration that would be felt here if the US were to discover suddenly that some other nation had already put up a successful satellite." in 1957, proved remarkably prescient. In "Preliminary Design of an Experimental World-Circling s.p.a.ceship," RAND scientists argued that "the nation which first makes significant achievements in s.p.a.ce travel will be acknowledged as the world leader in both military and scientific techniques. To visualize the impact on the world, one can imagine the consternation and admiration that would be felt here if the US were to discover suddenly that some other nation had already put up a successful satellite."11 RAND"s civilian scientists soon made a mark on American defense policy. Poundstone reports that RAND played a leading role in the development of the ICBM; RAND convinced the Air Force to adopt in-flight refueling of jet bombers; it was responsible for the fail-safe protocol whereby bombers are kept in the air at all times and during a crisis head for targets in an enemy nation. Its worry that a psychotic individual in a position of power could trigger a nuclear war convinced the Air Force to adopt a safer b.u.t.ton that required cooperation of several individuals to arm and detonate a nuclear warhead. psychotic individual in a position of power could trigger a nuclear war convinced the Air Force to adopt a safer b.u.t.ton that required cooperation of several individuals to arm and detonate a nuclear warhead.
To be plucked from academe and initiated into the secret world of the military had become something of a rite of pa.s.sage for the mathematical elite. In World War II, the very best had traveled into the New Mexico desert to Los Alamos to work on the A-bomb alongside von Neumann, and to Bletchley Park north of London to help Turing and his team break the n.a.z.i code.12 Many others, less well known or simply younger, wound up at dozens of less famous sites working on weapon design, encryption, bomb targeting, and submarine chases. Many others, less well known or simply younger, wound up at dozens of less famous sites working on weapon design, encryption, bomb targeting, and submarine chases.13 The recruitment of scientists by the military hadn"t stopped when the war ended, much to everyone"s surprise. Many of the mathematicians and scientists did not return to their quiet prewar routines but instead took on military research contracts, made frequent visits to the Pentagon and the Atomic Energy Commission, and, in a few cases, stayed on at Los Alamos and the other government weapons labs. For an elite cadre of applied mathematicians, computer engineers, political scientists, and economists RAND was the equivalent of Los Alamos.14 The problems the military asked the scientists to solve called for new theories and new techniques, which in turn attracted the top scientific talent on which RAND"s credibility depended. "We had so many practical problems that involved mathematicians and we didn"t have the right tools," said Bruno Augenstein, a former RAND vice-president, years later. "So we had to invent or perfect the tools."15 Mostly, according to Duncan Luce, a psychologist who was a consultant at RAND, "RAND capitalized on ideas that surfaced during the war." Mostly, according to Duncan Luce, a psychologist who was a consultant at RAND, "RAND capitalized on ideas that surfaced during the war."16 These were scientific, or at least systematic, approaches to problems that had been previously considered the exclusive province of men of "experience." They included such topics as logistics, submarine research, and air defense. Operations research, linear programming, dynamic programming, and systems a.n.a.lysis were all techniques that RAND brought to bear on the problem of "thinking the unthinkable." Of all the new tools, game theory was far and away the most sophisticated. These were scientific, or at least systematic, approaches to problems that had been previously considered the exclusive province of men of "experience." They included such topics as logistics, submarine research, and air defense. Operations research, linear programming, dynamic programming, and systems a.n.a.lysis were all techniques that RAND brought to bear on the problem of "thinking the unthinkable." Of all the new tools, game theory was far and away the most sophisticated.
The spirit of quantification, however, was contagious, and it was at RAND, more than anywhere else, that game theory in particular and mathematical modeling in general entered the mainstream of postwar thinking in economics. At that point, the military was the only government sponsor of pure research in the social sciences - a role later taken over by the National Science Foundation - and it bankrolled a great many ideas that turned out to have little true relevance for the military but a great deal for other endeavors. RAND attracted a younger generation of mathematically sophisticated economists who embraced the new methods and tools, including the computer, and attempted to turn economics from a branch of political philosophy into a precise, predictive science.
Take Kenneth Arrow, one of the early n.o.bel Laureates in economics. When Arrow came to RAND in 1948, he was an unknown youngster.17 His famous thesis, His famous thesis, written in the as-yet-unfamiliar language of symbolic logic, was a product of a RAND a.s.signment. The a.s.signment was to demonstrate that it was okay to apply game theory, which is formulated in terms of individuals, to aggregations of many individuals, namely nations. Arrow was asked to write a memorandum showing how it could be done. As it turned out, the memorandum became Arrow"s dissertation, an attempt to restate the theories of British economist John Hicks in modern mathematical language. "That was it! It took about five days to write in September 1948," he recalled. "When every attempt failed I thought of the impossibility theorem." written in the as-yet-unfamiliar language of symbolic logic, was a product of a RAND a.s.signment. The a.s.signment was to demonstrate that it was okay to apply game theory, which is formulated in terms of individuals, to aggregations of many individuals, namely nations. Arrow was asked to write a memorandum showing how it could be done. As it turned out, the memorandum became Arrow"s dissertation, an attempt to restate the theories of British economist John Hicks in modern mathematical language. "That was it! It took about five days to write in September 1948," he recalled. "When every attempt failed I thought of the impossibility theorem."18 Arrow showed that it is logically impossible to add up the choices of individuals into an unambiguous social choice not just under a const.i.tution based on the principle of majority rule, but under every conceivable const.i.tution except dictatorship. Arrow"s theorem, along with his proof of the existence of a compet.i.tive equilibrium, which also owes something to Nash, earned him the n.o.bel Prize in 1972 and ushered in the use of sophisticated mathematics in economic theory. Arrow showed that it is logically impossible to add up the choices of individuals into an unambiguous social choice not just under a const.i.tution based on the principle of majority rule, but under every conceivable const.i.tution except dictatorship. Arrow"s theorem, along with his proof of the existence of a compet.i.tive equilibrium, which also owes something to Nash, earned him the n.o.bel Prize in 1972 and ushered in the use of sophisticated mathematics in economic theory.
Other giants of modern economics who did seminal work at RAND in the early 1950s included Paul A. Samuelson, probably the most influential economist of the twentieth century, and Herbert Simon, who pioneered the study of decisionmaking inside organizations.
RAND"s location was part of its allure. The corporation"s headquarters, in a once-sleepy beach colony, lies five miles to the south of the Santa Monica Mountains at the far end of the Malibu Crescent, just west of Los Angeles. In the early 1950s, Santa Monica looked the way Nash imagined that certain towns in Italy or France might look. Wide avenues were lined with pencil-thin palm trees. Cream-colored houses were topped with tiled roofs and encircled by shoulder-high walls. Seaside hotels and rest homes were across from a seaside promenade. The magentas and reds of the bougainvillea and hibiscus were improbably intense. The breeze, surprisingly cool, smelled of oleander and seawater. Some of the best work was done in beach chairs.
RAND itself was tucked out of sight of the ocean on Fourth and Broadway at the edge of Santa Monica"s slightly rundown business district. The 1920s bank building was a white stucco affair ornamented with Victorian flourishes. The building had recently housed the presses of the Santa Monica Evening Outlook; Santa Monica Evening Outlook; the newspaper had moved catty-corner to a former Chevy dealership when RAND moved in. By 1950, RAND was already spilling over into several annexes located over storefronts, including ones occupied by the the newspaper had moved catty-corner to a former Chevy dealership when RAND moved in. By 1950, RAND was already spilling over into several annexes located over storefronts, including ones occupied by the Outlook Outlook and a bicycle shop. A year later, when and a bicycle shop. A year later, when Fortune Fortune magazine discreetly introduced RAND to the wider public, it described "bright walls shining through fog-sunny days and its wide, white-lighted windows shining on uninterruptedly through the night. The building is never closed, nor is it ever really open." magazine discreetly introduced RAND to the wider public, it described "bright walls shining through fog-sunny days and its wide, white-lighted windows shining on uninterruptedly through the night. The building is never closed, nor is it ever really open."19 It was one of the most difficult buildings in the United States to get into, Fortune Fortune said. On Nash"s first day, members of RAND"s uniformed, armed police force stood guard in front of the building and in its lobby, scrutinizing him closely said. On Nash"s first day, members of RAND"s uniformed, armed police force stood guard in front of the building and in its lobby, scrutinizing him closely and memorizing his face. and memorizing his face.20 After that, for the rest of the summer and in subsequent years, the guards always greeted him with a cool, respectful "h.e.l.lo, Dr. Nash." There were no ID cards in those days. Inside were a series of locked doors, with offices cl.u.s.tered by types of security clearance needed to gain access to them. The math division occupied a group of small private offices in the middle of the first floor, upstairs from the electronics shop where von Neumann"s new computer, the Johnniac, stood. After that, for the rest of the summer and in subsequent years, the guards always greeted him with a cool, respectful "h.e.l.lo, Dr. Nash." There were no ID cards in those days. Inside were a series of locked doors, with offices cl.u.s.tered by types of security clearance needed to gain access to them. The math division occupied a group of small private offices in the middle of the first floor, upstairs from the electronics shop where von Neumann"s new computer, the Johnniac, stood.21 Nash got an office to himself, a small windowless cubicle whose walls didn"t quite extend to the ceiling, with a desk, blackboard, fan, and, of course, a safe. Nash got an office to himself, a small windowless cubicle whose walls didn"t quite extend to the ceiling, with a desk, blackboard, fan, and, of course, a safe.
RAND bristled with self-confidence, a sense of mission, an esprit de corps.22 Military uniforms signaled visitors from Washington. Executives from defense firms came for meetings. The consultants, mostly under thirty, carried briefcases, smoked pipes, and walked around looking self-important. Big shots like von Neumann and Herman Kahn had shouting matches in the hallways. Military uniforms signaled visitors from Washington. Executives from defense firms came for meetings. The consultants, mostly under thirty, carried briefcases, smoked pipes, and walked around looking self-important. Big shots like von Neumann and Herman Kahn had shouting matches in the hallways.23 There was a feeling around the place of "wanting to outrun the enemy," as a former RAND vice-president later put it. There was a feeling around the place of "wanting to outrun the enemy," as a former RAND vice-president later put it.24 Arrow, who was an army veteran from the Bronx, said, "We were all convinced that the mission was important though there was lots of room for intellectual vision." Arrow, who was an army veteran from the Bronx, said, "We were all convinced that the mission was important though there was lots of room for intellectual vision."25 RAND"s sense of mission was propelled largely by a single fact: Russia had the A-bomb. That shocking news had been delivered by President Truman the previous fall, a mere four years after Nagasaki and Hiroshima, and many years before Washington had expected it. The military had hard evidence, the president said in a speech on September 13, 1949, of a nuclear explosion deep inside the Soviet Union.26 n.o.body in the scientific community, especially around Princeton, where von Neumann and Oppenheimer were engaged in an almost daily debate over the wisdom of pushing ahead with the Super, doubted that the Soviets were capable of developing nuclear weapons. n.o.body in the scientific community, especially around Princeton, where von Neumann and Oppenheimer were engaged in an almost daily debate over the wisdom of pushing ahead with the Super, doubted that the Soviets were capable of developing nuclear weapons.27 The shock was that they had succeeded so quickly. Physicists and mathematicians, who were less convinced of Russia"s scientific and technological backwardness, had been warning the administration all along that predictions by senior government officials that America"s nuclear monopoly would persist another ten, fifteen, or twenty years were hopelessly naive, but the sense of being caught off guard was still very great. The shock was that they had succeeded so quickly. Physicists and mathematicians, who were less convinced of Russia"s scientific and technological backwardness, had been warning the administration all along that predictions by senior government officials that America"s nuclear monopoly would persist another ten, fifteen, or twenty years were hopelessly naive, but the sense of being caught off guard was still very great.28 The news effectively ended the debate over the hydrogen bomb more or less immediately. By the time the president delivered the news of the Soviet explosion to the public, he had authorized a crash program at Los Alamos to design and manufacture an H-bomb. The news effectively ended the debate over the hydrogen bomb more or less immediately. By the time the president delivered the news of the Soviet explosion to the public, he had authorized a crash program at Los Alamos to design and manufacture an H-bomb.29 It was unthinkable that such destructive power would be unleashed. Therefore RAND insisted that it was necessary to ponder the possibility.30 The rational life was worshiped to an almost absurd degree. RAND was full of men and women committed to the idea that systematic thought and quantification were the key to the most complex problems. Facts, preferably detached from emotion, convention, The rational life was worshiped to an almost absurd degree. RAND was full of men and women committed to the idea that systematic thought and quantification were the key to the most complex problems. Facts, preferably detached from emotion, convention, and preconception, reigned supreme. If reducing complex political and military choices, including the problem of nuclear war, to mathematical formulae could produce light, why then the same approach must be good for more mundane matters. RAND scientists tried to tell their wives that the decision whether to buy or not to buy a washing machine was an "optimization problem." and preconception, reigned supreme. If reducing complex political and military choices, including the problem of nuclear war, to mathematical formulae could produce light, why then the same approach must be good for more mundane matters. RAND scientists tried to tell their wives that the decision whether to buy or not to buy a washing machine was an "optimization problem."31 RAND was privy to the military"s most highly guarded secrets at a time when the nation was growing increasingly nervous about the safeguarding of those secrets to the point of paranoia. From the summer of 1950 on, RAND would be increasingly affected by the growing alarm over Russian access to American military secrets.32 It began with the Fuchs trial in the winter of 1950. It began with the Fuchs trial in the winter of 1950.33 Fuchs was a German emigre scientist who had fled to Britain during the war and eventually wound up working with von Neumann and Edward Teller at Los Alamos. A clandestine member of the British Communist Party, Fuchs subsequently confessed in January 1950 to pa.s.sing atomic secrets to the Russians and was tried and convicted in London that February. Senator Joseph McCarthy had embarked that same month on his anticommunist campaign, accusing the federal government of security breaches. Fuchs was a German emigre scientist who had fled to Britain during the war and eventually wound up working with von Neumann and Edward Teller at Los Alamos. A clandestine member of the British Communist Party, Fuchs subsequently confessed in January 1950 to pa.s.sing atomic secrets to the Russians and was tried and convicted in London that February. Senator Joseph McCarthy had embarked that same month on his anticommunist campaign, accusing the federal government of security breaches.34 Four years later, in April of 1954, Robert Oppenheimer, the former head of the Manhattan Project, the director of the Inst.i.tute for Advanced Study, and the most famous scientist in America, was declared a security risk by Eisenhower and stripped of his security clearances in the full glare of national publicity. Four years later, in April of 1954, Robert Oppenheimer, the former head of the Manhattan Project, the director of the Inst.i.tute for Advanced Study, and the most famous scientist in America, was declared a security risk by Eisenhower and stripped of his security clearances in the full glare of national publicity.35 The ostensible reason was Oppenheimer"s youthful left-wing a.s.sociations, but the real reason, as von Neumann and most scientists testified at the time, was Oppenheimer"s refusal to support the development of the H-bomb. The ostensible reason was Oppenheimer"s youthful left-wing a.s.sociations, but the real reason, as von Neumann and most scientists testified at the time, was Oppenheimer"s refusal to support the development of the H-bomb.
The fact that McCarthy himself ultimately became a target of censure would do little to dispel the atmosphere of paranoia and intimidation at RAND, which lived on Air Force and AEC money and had projects on the H-bomb and ICBMs.36 Most of what the mathematicians worked on was not in fact cla.s.sified, but that didn"t matter. RAND, which harbored a collection of oddb.a.l.l.s like Richard Bellman (a former Princeton mathematician who had all kinds of communist a.s.sociations, mostly accidental, including a chance encounter with a cousin of Julius and Ethel Rosenberg), would become particularly careful about minding its Most of what the mathematicians worked on was not in fact cla.s.sified, but that didn"t matter. RAND, which harbored a collection of oddb.a.l.l.s like Richard Bellman (a former Princeton mathematician who had all kinds of communist a.s.sociations, mostly accidental, including a chance encounter with a cousin of Julius and Ethel Rosenberg), would become particularly careful about minding its Ps Ps and and Qs Qs.37 Everybody needed a top-secret clearance. People who arrived without a temporary security clearance were banished to "quarantine" or "preclearance" and weren"t permitted to sit with everybody else. Nash"s secret clearance was granted on October 25, 1950.38 His recollection that he had a top-secret clearance - which a large contingent-in the math division did have - is probably faulty. Nash also recalls that he applied for a Q clearance in 1952. His recollection that he had a top-secret clearance - which a large contingent-in the math division did have - is probably faulty. Nash also recalls that he applied for a Q clearance in 1952.39 Any consultant to the math division who worked on Atomic Energy Commission contracts was required to have a Q clearance because of access to doc.u.ments related to the construction and use of nuclear weapons. But despite a November 10, 1952, postcard to his parents telling them that he had applied for a higher clearance at RAND, Nash now says Any consultant to the math division who worked on Atomic Energy Commission contracts was required to have a Q clearance because of access to doc.u.ments related to the construction and use of nuclear weapons. But despite a November 10, 1952, postcard to his parents telling them that he had applied for a higher clearance at RAND, Nash now says it was never approved - meaning that his role at RAND was largely confined to highly theoretical excercises as opposed to applications of game theory concepts to actual questions of nuclear strategy - the province of men like von Neumann, Herman Kahn, and Thomas Sch.e.l.ling. it was never approved - meaning that his role at RAND was largely confined to highly theoretical excercises as opposed to applications of game theory concepts to actual questions of nuclear strategy - the province of men like von Neumann, Herman Kahn, and Thomas Sch.e.l.ling.40 Everyone had a safe in his office for storing cla.s.sified doc.u.ments, and everyone was warned about taking doc.u.ments out of the building or talking out of school.41 Papers had to be put in the safes at the end of every day. There were spot checks. There was a public address system and there were parts of the building that were off-limits to people who didn"t have a Q clearance. Papers had to be put in the safes at the end of every day. There were spot checks. There was a public address system and there were parts of the building that were off-limits to people who didn"t have a Q clearance.
By 1953, soon after Eisenhower issued a new set of security guidelines, security consciousness, in the sense of not overlooking anyone who might be thought remotely unreliable, grew.42 The Eisenhower guidelines broadened the grounds for denying a clearance or stripping someone of an existing clearance. Without a doubt, fear about potential leaks brought to a boil many simmering antagonisms against individuals and groups who posed little or no actual threat to security. Almost any sign of nonconformity, political or personal, came to be considered a potential security breach. The notion, for example, that h.o.m.os.e.xuals were unreliable, because of either poor judgment or vulnerability to blackmail, was first codified in the Eisenhower guidelines. The Eisenhower guidelines broadened the grounds for denying a clearance or stripping someone of an existing clearance. Without a doubt, fear about potential leaks brought to a boil many simmering antagonisms against individuals and groups who posed little or no actual threat to security. Almost any sign of nonconformity, political or personal, came to be considered a potential security breach. The notion, for example, that h.o.m.os.e.xuals were unreliable, because of either poor judgment or vulnerability to blackmail, was first codified in the Eisenhower guidelines.
Like the decade itself, RAND had a split personality. Its style was informal. It tolerated quirky people. It was in some ways more democratic than a university. Almost everyone, including von Neumann, was called by his or her first name, except by the guards, never Doctor or Professor or Sir. Graduate students rubbed shoulders with full professors in a way unimaginable in most academic departments. RAND"s president, a former Douglas Aircraft executive, was a spit-and-polish man who was almost never seen in a suit and tie. All but one or two of the mathematicians, including Nash, came to work in short-sleeved shirts. Appearances were so casual that one mathematician, who found it all very decla.s.se, felt obliged to rebel by wearing a three-piece suit and a tie to the office every day.43 Practical jokes were as much a part of the RAND culture as pipes and crewcuts. Mathematicians and physicists mixed rubber bands into the pipe tobacco, subst.i.tuted dog biscuits for cookies, and tilted desks so pencils rolled onto the floor.44 Wit was greatly appreciated. When John Williams, the head of RAND"s mathematics department, wrote a primer on game theory, published as a RAND study, it was ill.u.s.trated with funny little cartoon figures and full of jokey examples starring John Nash, Alex Mood, Lloyd Shapley, John Milnor, and other members of the math department. Wit was greatly appreciated. When John Williams, the head of RAND"s mathematics department, wrote a primer on game theory, published as a RAND study, it was ill.u.s.trated with funny little cartoon figures and full of jokey examples starring John Nash, Alex Mood, Lloyd Shapley, John Milnor, and other members of the math department.45 The mathematicians were, as usual, the freest spirits.46 They had no set hours. If they wanted to come into their offices at 3:00 They had no set hours. If they wanted to come into their offices at 3:00 A.M. A.M., fine. Shapley, who had come back from Princeton for the summer and continued to insist on the sanct.i.ty of his sleep cycle, was rarely seen before midafternoon. Another man, an electrical engineer named Hastings, typically slept in the "shop" next to his beloved computer. Lunches were long, much to the annoyance of RAND"s engineers, who prided themselves on sticking to a more respectable routine. The mathematicians mostly took their bag lunches to a conference room and pulled out chessboards. They invariably played Kriegspiel, usually in total silence, occasionally punctuated by a wrathful outburst from Shapley, who frequently lost his temper over an umpire"s or opponent"s error. Even though the games typically lasted well into the afternoon, they were rarely finished and finally reluctantly abandoned midgame. Poker and bridge groups met after hours. Lunches were long, much to the annoyance of RAND"s engineers, who prided themselves on sticking to a more respectable routine. The mathematicians mostly took their bag lunches to a conference room and pulled out chessboards. They invariably played Kriegspiel, usually in total silence, occasionally punctuated by a wrathful outburst from Shapley, who frequently lost his temper over an umpire"s or opponent"s error. Even though the games typically lasted well into the afternoon, they were rarely finished and finally reluctantly abandoned midgame. Poker and bridge groups met after hours.
There were no afternoon teas, formal seminars, or faculty meetings at RAND. Unlike the physicists and engineers, the mathematicians usually worked alone. The idea was that they would work on their own ideas but would help solve the myriad problems encountered by researchers, picking up problems to solve as the spirit moved them.47 People would drift into each other"s offices or, more frequently, simply stop to chat in the corridors near the coffee stations. The grids and courtyards of RAND"s permanent headquarters - to which the mathematics group moved in 1953, the year before Nash"s final summer at RAND - were designed, by John Williams, as it happens, "to maximize chance meetings." People would drift into each other"s offices or, more frequently, simply stop to chat in the corridors near the coffee stations. The grids and courtyards of RAND"s permanent headquarters - to which the mathematics group moved in 1953, the year before Nash"s final summer at RAND - were designed, by John Williams, as it happens, "to maximize chance meetings."48 Through such encounters new research was "announced" and mathematicians got hooked on problems that colleagues in other departments wanted solved. Most of the work wasn"t reported formally, and even when it was published as RAND memoranda, there was no formal approval process. A consultant would simply go to the math department secretaries, hand over a handwritten paper, and a day or two later a RAND memorandum would appear. Through such encounters new research was "announced" and mathematicians got hooked on problems that colleagues in other departments wanted solved. Most of the work wasn"t reported formally, and even when it was published as RAND memoranda, there was no formal approval process. A consultant would simply go to the math department secretaries, hand over a handwritten paper, and a day or two later a RAND memorandum would appear.49 Published reports for outside circulation didn"t go through a much more rigorous vetting process. Published reports for outside circulation didn"t go through a much more rigorous vetting process.
This copacetic atmosphere was mostly Williams"s doing.50 Witty and charming, weighing close to three hundred pounds, expensively suited, Williams looked like a businessman always about to reach into his pocket to pull out a wad of twenties. An astronomer from Arizona who had spent a couple of years in Princeton attending lectures in Fine Hall, playing poker, and developing an enthusiasm for the theory of games, Williams had been a dollar-a-year man in Washington during the war and became RAND"s fifth employee afterward. Williams hated flying. He loved fast cars. At one point, he spent an entire year outfitting his chocolate-brown Jaguar with a powerful Cadillac engine. It had taken substantial RAND resources (RAND had a repair shop) and considerable bravado to install the thing. Cadillac and Jaguar mechanics had both dismissed the idea as impractical, but Williams had prevailed. He disproved the mechanics" conventional wisdom in late-night, 125mile-an-hour drives along the Pacific Coast Highway. Witty and charming, weighing close to three hundred pounds, expensively suited, Williams looked like a businessman always about to reach into his pocket to pull out a wad of twenties. An astronomer from Arizona who had spent a couple of years in Princeton attending lectures in Fine Hall, playing poker, and developing an enthusiasm for the theory of games, Williams had been a dollar-a-year man in Washington during the war and became RAND"s fifth employee afterward. Williams hated flying. He loved fast cars. At one point, he spent an entire year outfitting his chocolate-brown Jaguar with a powerful Cadillac engine. It had taken substantial RAND resources (RAND had a repair shop) and considerable bravado to install the thing. Cadillac and Jaguar mechanics had both dismissed the idea as impractical, but Williams had prevailed. He disproved the mechanics" conventional wisdom in late-night, 125mile-an-hour drives along the Pacific Coast Highway.
Williams"s approach to management would have made him very much at home in Silicon Valley today: "Williams had a theory," recalled his deputy, Alexander Mood, also a former Princetonian. "He believed people should be left alone. He was a great believer in basic research. He was a very relaxed administrator. That"s why people thought the math division was pretty weird."51 Williams"s letter to von Neumann offering the mathematician a two-hundred-dollar-a-month retainer conveys the man"s style. The letter said, "The only part of your thinking we"d like Williams"s letter to von Neumann offering the mathematician a two-hundred-dollar-a-month retainer conveys the man"s style. The letter said, "The only part of your thinking we"d like to bid for systematically is that which you spend shaving: we"d like you to pa.s.s on to us any ideas that come to you while so engaged." to bid for systematically is that which you spend shaving: we"d like you to pa.s.s on to us any ideas that come to you while so engaged."52 When Williams first arrived, RAND was a tiny annex inside a mammoth Douglas Aircraft factory where thirty thousand workers punched time cards every day. Williams was the one who freed the mathematicians from the clock and then proceeded to demand coffee and blackboards for his mathematicians, explaining that not providing these would guarantee that none of them would produce anything worthwhile. After RAND and Douglas Aircraft parted company, Williams went further. He insisted that the building be open twenty-four hours a day instead of just between eight and five. He got private offices. He set up coffee stations that had their own special full-time maintenance crew. He mollified the engineers and the Air Force generals, who wondered why the h.e.l.l the mathematicians had to be allowed to be themselves. When Williams first arrived, RAND was a tiny annex inside a mammoth Douglas Aircraft factory where thirty thousand workers punched time cards every day. Williams was the one who freed the mathematicians from the clock and then proceeded to demand coffee and blackboards for his mathematicians, explaining that not providing these would guarantee that none of them would produce anything worthwhile. After RAND and Douglas Aircraft parted company, Williams went further. He insisted that the building be open twenty-four hours a day instead of just between eight and five. He got private offices. He set up coffee stations that had their own special full-time maintenance crew. He mollified the engineers and the Air Force generals, who wondered why the h.e.l.l the mathematicians had to be allowed to be themselves.
Everyone soon knew Nash by sight. He roamed the halls incessantly.53 He was usually chewing an empty paper coffee cup that was clamped firmly between his teeth. He would glide through the corridors for hours at a time, frowning, lost in thought, shirt untucked, his powerfully built shoulders hunched forward, his sharp Nixonian nose leading the way. Sometimes he wore a small, ironic smile that suggested some secret amus.e.m.e.nt not likely to be shared with anyone he might encounter. When he did meet someone he knew, he rarely greeted him by name or even acknowledged his presence unless spoken to first, and then not always. When he wasn"t chewing a coffee cup, he whistled, often the same tune, from Bach"s He was usually chewing an empty paper coffee cup that was clamped firmly between his teeth. He would glide through the corridors for hours at a time, frowning, lost in thought, shirt untucked, his powerfully built shoulders hunched forward, his sharp Nixonian nose leading the way. Sometimes he wore a small, ironic smile that suggested some secret amus.e.m.e.nt not likely to be shared with anyone he might encounter. When he did meet someone he knew, he rarely greeted him by name or even acknowledged his presence unless spoken to first, and then not always. When he wasn"t chewing a coffee cup, he whistled, often the same tune, from Bach"s The Art of the Fugue, The Art of the Fugue, over and over again. over and over again.54 His legend had preceded him. In the eyes of his new colleagues, Arrow recalled, Nash was "a young genius who could do anything, a guy who liked solving problems."55 Mathematicians who were struggling with tricky problems quickly learned to collar him by planting themselves squarely in his path. Nash"s curiosity was easily piqued, they discovered, provided that the problem struck him as interesting and the speaker mathematically competent. He was usually more than willing to step around to their offices to look at ma.s.ses of messy equations on their blackboards. Mathematicians who were struggling with tricky problems quickly learned to collar him by planting themselves squarely in his path. Nash"s curiosity was easily piqued, they discovered, provided that the problem struck him as interesting and the speaker mathematically competent. He was usually more than willing to step around to their offices to look at ma.s.ses of messy equations on their blackboards.
Williams"s deputy, Alex Mood, was one of the first to try.56 A gentle giant of a man with a dry wit and easy manner, Mood happened to be oppressed by a problem left over from a first, ill-fated thesis attempt at Princeton before the war. He had found a better derivation of a famous solution, he felt, but his proof was overly long, too complicated, and distressingly inelegant. Could Nash come up with something "shorter, simpler"? Nash listened and stared, frowned and walked away. But the very next day, he was back at Mood"s door with a clever and entirely unantic.i.p.ated solution. Nash had "sidestepped the whole induction by regarding integers as variables and sending them to revealing limits." As much as anything else, Mood was charmed by Nash"s style. "When he found a problem," Mood recalled, "he sat down and started attacking it immediately. He didn"t, like some of A gentle giant of a man with a dry wit and easy manner, Mood happened to be oppressed by a problem left over from a first, ill-fated thesis attempt at Princeton before the war. He had found a better derivation of a famous solution, he felt, but his proof was overly long, too complicated, and distressingly inelegant. Could Nash come up with something "shorter, simpler"? Nash listened and stared, frowned and walked away. But the very next day, he was back at Mood"s door with a clever and entirely unantic.i.p.ated solution. Nash had "sidestepped the whole induction by regarding integers as variables and sending them to revealing limits." As much as anything else, Mood was charmed by Nash"s style. "When he found a problem," Mood recalled, "he sat down and started attacking it immediately. He didn"t, like some of his colleagues, browse through the library to see what related stuff had already been done." his colleagues, browse through the library to see what related stuff had already been done."
Williams too was immediately taken with Nash and took him under his wing. He frequently told others that Nash had greater insight into mathematical structure than any mathematician he had ever known, an extraordinary remark from a man who spent the late 1930s in Fine Hajl and was an intimate of von Neumann"s. "He knew which factors of a hundred thousand were the most important," Williams used to say.57 He liked to describe how Nash would come into an office, stare at a blackboard dense with equations, and stand there silently, meditating. "Then," Williams would say, "he"d solve the whole thing. He could He liked to describe how Nash would come into an office, stare at a blackboard dense with equations, and stand there silently, meditating. "Then," Williams would say, "he"d solve the whole thing. He could see see the structure." the structure."
However, Nash mostly kept to himself. He talked about his own research rarely and then only with a select few. When he did, it was not usually because he was looking for help. "It wasn"t so much that he sought advice," another consultant recalled. "You were a reflecting mirror. He was his own creative object."58 The only person he regularly sought out at RAND was Shapley, and fairly soon people around the mathematics division started to think of the two as a pair, RAND"s Wunderkinder. The only person he regularly sought out at RAND was Shapley, and fairly soon people around the mathematics division started to think of the two as a pair, RAND"s Wunderkinder.
Still, Nash"s eccentricity soon became fodder for RAND"s gossip mill. "He reinforced RAND"s idea that mathematicians were a bit crazy," Mood said.59 His office, in which he could rarely be found, was a G.o.dawful mess. When he left at the end of that summer he did so without bothering to clean out his desk. The staffer who was saddled with the ch.o.r.e found, among other things, "banana peels. Bank statements for Swiss bank accounts with thousands of dollars in them. One or two hundred dollars in cash. Cla.s.sified doc.u.ments. The C-1 isometric embedding paper." His office, in which he could rarely be found, was a G.o.dawful mess. When he left at the end of that summer he did so without bothering to clean out his desk. The staffer who was saddled with the ch.o.r.e found, among other things, "banana peels. Bank statements for Swiss bank accounts with thousands of dollars in them. One or two hundred dollars in cash. Cla.s.sified doc.u.ments. The C-1 isometric embedding paper."60 Some people found Nash absurdly childish. He was fond of playing adolescent jokes on his colleagues. Knowing that his whistling irritated one particular musicloving mathematician, who frequently asked him to stop, he once left behind a recording of his whistling on the man"s Dictaphone.61 RAND"s blue-collar police force and maintenance crew found Nash an entertaining subject. They would watch him as he left the building walking north on Fourth Avenue. On several occasions some of them complained to a RAND manager that they had seen Nash tiptoing exaggeratedly along the avenue, stalking flocks of pigeons, and then suddenly rushing forward, "trying to kick "em." RAND"s blue-collar police force and maintenance crew found Nash an entertaining subject. They would watch him as he left the building walking north on Fourth Avenue. On several occasions some of them complained to a RAND manager that they had seen Nash tiptoing exaggeratedly along the avenue, stalking flocks of pigeons, and then suddenly rushing forward, "trying to kick "em."62
CHAPTER 13
Game Theory at RAND
We hope [the theory of games] will work, just as we hoped in 1942 that the atomic bomb would work.
- ANONYMOUS P PENTAGON SCIENTIST to to Fortune, Fortune, 1949 1949
NASH"S NOVEL IDEA about games with many players had preceded him at RAND by several months. The first version of his elegant proof of the existence of equilibrium for games with many players - two skimpy pages in the November 1949 issue of the National Academy of Sciences proceedings - swept through the white stucco building at Fourth and Broadway like a California brushfire. about games with many players had preceded him at RAND by several months. The first version of his elegant proof of the existence of equilibrium for games with many players - two skimpy pages in the November 1949 issue of the National Academy of Sciences proceedings - swept through the white stucco building at Fourth and Broadway like a California brushfire.1 The biggest appeal of the Nash equilibrium concept was its promise of liberation from the two-person zero-sum game. The mathematicians, military strategists, and economists at RAND had focused almost exclusively on games of total conflict - my win is your loss or vice versa - between two players. Shapley and Dresher"s 1949 review of game theory research at RAND refers to the organization"s "preoccupation with the zero-sum two person game."2 That preoccupation was natural, given that these were games for which the von Neumann theory was both sound and reasonably complete. Zero-sum games also seemed to fit the problem - nuclear conflict between two superpowers - which absorbed most of RAND"s attention. That preoccupation was natural, given that these were games for which the von Neumann theory was both sound and reasonably complete. Zero-sum games also seemed to fit the problem - nuclear conflict between two superpowers - which absorbed most of RAND"s attention.
Only it really didn"t. At least some of the researchers at RAND were already chafing at the central a.s.sumption of a fixed payoff in such games, Arrow recalled.3 As weapons got ever more destructive, even all-out war had ceased to be a situation of pure conflict in which opponents had no common interest whatever. Inflicting the greatest amount of damage on an enemy - bombing him back to the Stone Age - no longer made any sense, as American strategists realized during the final phase of the campaign against Germany when they decided not to destroy the coal mines and industrial complexes of the Ruhr. As weapons got ever more destructive, even all-out war had ceased to be a situation of pure conflict in which opponents had no common interest whatever. Inflicting the greatest amount of damage on an enemy - bombing him back to the Stone Age - no longer made any sense, as American strategists realized during the final phase of the campaign against Germany when they decided not to destroy the coal mines and industrial complexes of the Ruhr.4 As Thomas C. Sch.e.l.ling, one of RAND"s nuclear strategists, would put it a decade later, As Thomas C. Sch.e.l.ling, one of RAND"s nuclear strategists, would put it a decade later,5 In international affairs, there is mutual dependence as well as opposition. Pure conflict, in which the interests of two antagonists are completely opposed, is a special case; it would arise in a war of complete extermination, otherwise not even in war. Thepossibility of mutual accommodation is as important and dramatic as the element of conflict. Concepts like deterrence, limited war, and disarmament, as well as negotiation, are concerned with the common interest and mutual dependence that can exist between partic.i.p.ants in a conflict. and dramatic as the element of conflict. Concepts like deterrence, limited war, and disarmament, as well as negotiation, are concerned with the common interest and mutual dependence that can exist between partic.i.p.ants in a conflict.
Sch.e.l.ling goes on to say why this is so: "These are games in which, though the element of conflict provides the dramatic interest, mutual dependence is part of the logical structure and demands some kind of collaboration or mutual accommodation - tacit, if not explicit - even if only in the avoidance of mutual disaster."6 In 1950, at least the economists at RAND were aware that if game theory were to evolve into a descriptive theory that could be usefully applied to real-life military and economic conflicts, one had to focus on games that allowed for cooperation as well as conflict. "Everybody was already bothered by the zero-sum game," Arrow recalled. "You"re trying to decide whether to go to war or not. You couldn"t say that the losses to the losers were gains to the winner. It was a troublesome thing."7 Military strategists were the first to seize on the ideas of game theory. Most economists ignored The Theory of Games and Economic Behavior The Theory of Games and Economic Behavior and the few that didn"t, like John Kenneth Galbraith writing in and the few that didn"t, like John Kenneth Galbraith writing in Fortune Fortune and Carl Kaysen, later director of the Inst.i.tute for Advanced Study, turn out to have had significant contact with military strategists during the war. and Carl Kaysen, later director of the Inst.i.tute for Advanced Study, turn out to have had significant contact with military strategists during the war.8 An article in An article in Fortune Fortune in 1949 by John McDonald made it clear that the military hoped to use von Neumann"s theory of games to work out intelligence missions, bombing patterns, and nuclear defense strategy. in 1949 by John McDonald made it clear that the military hoped to use von Neumann"s theory of games to work out intelligence missions, bombing patterns, and nuclear defense strategy.9 On the lookout for new ideas and with plenty of money to spend, the Air Force embraced game theory with the same enthusiasm with which the Prussian military had embraced probability theory a couple hundred years earlier. On the lookout for new ideas and with plenty of money to spend, the Air Force embraced game theory with the same enthusiasm with which the Prussian military had embraced probability theory a couple hundred years earlier.10 Game theory had already made its debut in military planning rooms. It had been used during the war to develop antisubmarine tactics when German submarines were destroying American military transports. As McDonald reported in Fortune: Fortune:11 The military application of "Games" was begun early in the last war, some time in fact before the publication of the complete theory, by ASWOEG (Anti-Submarine Warfare Operations Evaluation Group). Mathematicians in the group had got hold of von Neumann"s first paper on poker, published in 1928.
But von Neumann actually spent his frenetic visits to Santa Monica almost exclusively with the computer engineers and the nuclear scientists.12 His enormous prestige and Williams"s deft salesmanship led to a major concentration on game theory at RAND from 1947 into the 1950s. The hope was that game theory would provide the mathematical underpinning for a theory of human conflict and spread to disciplines other than mathematics. Williams convinced the Air Force to let His enormous prestige and Williams"s deft salesmanship led to a major concentration on game theory at RAND from 1947 into the 1950s. The hope was that game theory would provide the mathematical underpinning for a theory of human conflict and spread to disciplines other than mathematics. Williams convinced the Air Force to let RAND create two new divisions, economics and social science. By the time Nash arrived, a "trust" of game theory research had grown up at RAND including such game theorists as Lloyd S. Shapley, J. C. McKinsey, N. Dalkey, F. B. Thompson, and H. F. Bohnenbl.u.s.t, such pure mathematicians as John Milnor, statisticians David Blackwell, Sam Karlin, and Abraham Girschick, and economists Paul Samuelson, Kenneth Arrow, and Herbert Simon. RAND create two new divisions, economics and social science. By the time Nash arrived, a "trust" of game theory research had grown up at RAND including such game theorists as Lloyd S. Shapley, J. C. McKinsey, N. Dalkey, F. B. Thompson, and H. F. Bohnenbl.u.s.t, such pure mathematicians as John Milnor, statisticians David Blackwell, Sam Karlin, and Abraham Girschick, and economists Paul Samuelson, Kenneth Arrow, and Herbert Simon.13 Most of the RAND military applications of game theory concerned tactics. Air battles between fighters and bombers were modeled as duels.14 The strategic problem in a duel is one of timing. For each opponent, having the first shot maximizes the chance of a miss. But having the better shot also maximizes the chance for being hit. The question is when to fire. There"s a tradeoff. By waiting a little longer each opponent improves his own chance of scoring a hit, but also increases the risk of being shot down. Such duels can be both noisy and silent. With "silent guns," the duelist doesn"t know the other has fired unless he is. .h.i.t. Therefore, neither partic.i.p.ant knows whether the other still has a bullet or has fired and missed and is now defenseless. The strategic problem in a duel is one of timing. For each opponent, having the first shot maximizes the chance of a miss. But having the better shot also maximizes the chance for being hit. The question is when to fire. There"s a tradeoff. By waiting a little longer each opponent improves his own chance of scoring a hit, but also increases the risk of being shot down. Such duels can be both noisy and silent. With "silent guns," the duelist doesn"t know the other has fired unless he is. .h.i.t. Therefore, neither partic.i.p.ant knows whether the other still has a bullet or has fired and missed and is now defenseless.
A report by Dresher and Shapley summarizing RAND"s game theory research between the fall of 1947 and the spring of 1949 gives the flavor.15 The mathematicians describe a problem of staggered attacks in a bombing mission: The mathematicians describe a problem of staggered attacks in a bombing mission: Problem
A single intercepter base, having I fighters, is located on a base line. Each fighter has a given endurance. If a fighter, vectored out against a bomber attack, has not yet engaged his original target, then at the option of the ground controller he may be vectored back to engage a second attack.
The attacker has a stock of N bombers and A bombs. The attacker chooses two points to attack and sends N1 bombers including A bombers including A1 bomb carriers on the first attack and t minutes later he sends N bomb carriers on the first attack and t minutes later he sends N2 = N N = N N1 bombers including A bombers including A2 = A A = A A1 carriers on the second attack. carriers on the second attack.
The payoff to the attacker is the number of bomb carriers that are not destroyed by the fighters.
Solution
Both players have pure optimal strategies. An optimal strategy of the attacker is to attack both targets simultaneously and distribute the A bomb carriers in proportion to the number of bombers in each attack. An optimum strategy of the defender is to dispatch interceptors in proportion to the number of attacking bombers and not to revector fighters. The value of the game to the attacker will be
V = max (0