7
The Think Tank by the Sea
Gaming nuclear war
‘What are we to make of a civilization which has always regarded ethics as an essential part of human life, and … which has not been able to talk about the prospect of killing almost everybody, except in prudential and game-theoretic terms?’
Robert Oppenheimer, 1960
The Soviet newspaper Pravda once branded the organization based at the pink and white stucco building the ‘American academy for death and destruction’. Despite moving to more modern headquarters in 2003, RAND remains synonymous with the Cold War and the icy logic of nuclear deterrence.1 At the peak of RAND’s notoriety in the 1960s, a folk song recorded by Pete Seeger summed up the organization’s reputation for cold-blooded strategizing:
Oh, the Rand Corporation’s the boon of the world,
They think all day long 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 … 2
If any one man can be regarded as the founding father of the RAND Corporation, then that man would be Henry ‘Hap’ Arnold, the commanding general of the US Air Force during the Second World War. Arnold was an early believer in the importance of a powerful and independent air force and never stinted from hitting his enemy with everything at his disposal during the war. ‘We must not get soft,’ Arnold warned Stimson when he heard the secretary of war had doubts about the firebombing of Dresden. ‘War must be destructive and to a certain extent inhuman and ruthless.’ Arnold’s only regret was that the area bombing of German cities was proceeding too slowly. He was impatient for his scientists to invent ‘explosives more terrible and more horrible than anyone has any idea of’.3 They would duly oblige. Arnold’s nickname was attributed to his sunny demeanour: ‘Hap’ was short for ‘Happy’.
Months before the end of the war, Arnold began to worry that the scientific expertise assembled to aid the American military would quickly disperse after the conflict was over. Something of a visionary, Arnold foresaw the advent of intercontinental ballistic missiles (ICBMs). ‘Someday, not too distant,’ he wrote in 1943, ‘there can come streaking out of somewhere – we won’t be able to hear it, it will come so fast – some kind of gadget with an explosive so powerful that one projectile will be able to wipe out completely this city of Washington.’4
Arnold urged the Air Force to prepare for a future in which scientists would play a leading role in warfare. ‘For the last twenty years we have built and run the Air Force on pilots,’ he told the Navy top brass. ‘But we can’t do that anymore. We’ve got to think of what we’ll need in terms of twenty years from now.’5 On 7 November 1944, he wrote to his chief scientific adviser: ‘I believe the security of the United States of America will continue to rest in part in developments instituted by our educational and professional scientists. I am anxious that the Air Force’s post war and next war research and development be placed on a sound and continuing basis.’6
The man to whom his memo was addressed was none other than Theodore von Kármán, the same aerospace engineer that Max von Neumann had asked, unsuccessfully, to prevent his son devoting his life to the fruitless pursuit of mathematics. In the midst of the bloodiest war in history, Arnold urged his adviser, now a US citizen and director of the California Institute of Technology’s aeronautical institute, to devote himself entirely to the task of investigating ‘all the possibilities and desirabilities for post war and future war’s development’.7 ‘I told these scientists’, Arnold wrote in 1949, ‘that I wanted them to think … about supersonic-speed airplanes, airplanes that would move and operate without crew, improvements in bombs … defenses against modern and future aircraft … communication systems … television … weather, medical research, atomic energy.’ In short, anything that ‘might affect the development of the airpower to come’.8
Thirteen months later, von Kármán and his colleagues presented Arnold with a massive thirty-three-volume report entitled Toward New Horizons.9 It did not disappoint him. ‘The scientific discoveries in aerodynamics, electronics and nuclear physics open new horizons for the use of air power,’ von Kármán wrote. His introduction preceded hundreds of pages of remarkably foresighted technical analysis, charting the way to developments such as intercontinental ballistic missiles and drones. Much of the information was culled from captured German scientists. The seeds of what would become the RAND Corporation appeared in a small section on the application of science to operations analysis – the brains of the war machine. The United States had assiduously developed expertise in mission-planning during the war. Ending that work, the report warned, would be ‘a great mistake’. Instead, there should be established ‘in peacetime a nucleus for scientific groups such as those which successfully assisted in the command and staff work in the field during the war. In these studies experts in statistical, technical, economic and political science must cooperate.’
Toward New Horizons was everything Arnold was expecting and more. But he had a war to win. He would not act on the report’s recommendations until Frank Collbohm arrived in his office in September 1945. Collbohm was a tough, fit former test pilot and engineer who had joined the Douglas Aircraft Company in 1928. At the end of the war, Douglas was America’s largest aircraft-maker, and Collbohm was the right-hand man of Donald Douglas, the company’s founder. Collbohm had Arnold’s ear too. During the war, he had alerted the general to the cutting-edge radar systems being developed at MIT. Later, he was asked to improve the performance of the B-29 bomber in raids over Japan. The team he helped lead calculated that stripping away most of the aeroplane’s armour plating and leaving only a tail-gun would allow the B-29 to fly further and faster with a bigger payload. The Air Force accepted the recommendations, and the modified B-29s firebombed Japan’s cities at a fiercer pace. Collbohm understood as well as anyone that science would play a pivotal role in any future conflict and was dismayed to see scientists drifting back to their universities at the end of the war.
When, a few weeks after the surrender of Japan, Collbohm met Arnold in Washington, D.C. to air his concerns, the general cut him off. ‘Frank, I know what you’re going to say,’ he exclaimed, slamming his hand down on the table. ‘It’s the most important thing we have to do right now.’10 Collbohm had also come with a proposal from Douglas himself: his company would be willing to house an independent group of scientists who would assist the Air Force with weapons research. Arnold liked the idea. He was good friends with Don Douglas, and a couple of years earlier, his son had married Douglas’s daughter. Unperturbed by possible conflicts of interest, Arnold told Collbohm to get Douglas and meet him for lunch at Hamilton Field, an Air Force base just north of San Francisco on the opposite coast, in two days’ time.
Collbohm caught the first plane he could – a B-25 bomber – to company headquarters in Santa Monica, where he rounded up Douglas and a few other company executives. The deal was done quickly. Arnold told the group he had $10 million of unspent funds from his wartime research budget which he was willing to give Douglas Aircraft to fund the new outfit. Douglas agreed to find space for the organization at their Santa Monica offices. Arthur Raymond, Douglas Aircraft’s chief engineer, suggested the name: RAND for ‘Research ANd Development’. Collbohm volunteered to lead it until a more suitable candidate could be found. His ‘temporary’ appointment as director would last twenty years. No tangible weapon would ever emerge from the think tank, only a slew of reports, prompting the joke that ‘Research and No Development’ was a more appropriate moniker. Some Army chiefs would forever think of the place as a coterie of ‘pipe-smoking, trees-full-of-owls’ intellectual types.
Project RAND was officially born on 1 March 1946, at the stroke of a pen on an Air Force contract. The terms specified the cash was for ‘a continuing program of scientific study and research on the broad subject of air warfare with the object of recommending to the Air Force preferred methods, techniques and instrumentalities for this purpose’. Initially, the scientists and mathematicians hired by RAND worked on technical projects ranging from nuclear propulsion to the design of new aircraft. The think tank’s very first report was released on 2 May 1946. Preliminary Design of an Experimental World-Circling Spaceship concluded that ‘modern technology has advanced to a point where it now appears feasible to undertake the design of a satellite vehicle’. Such a craft would be ‘one of the most potent scientific tools of the Twentieth Century’ and the achievement ‘would inflame the imagination of mankind, and would probably produce repercussions in the world comparable to the explosion of the atomic bomb’. Eleven years later the Soviet Union put Sputnik into orbit, humbling the United States – and turbocharging both the space race and the arms race.
RAND’s relationship with Douglas Aircraft quickly soured. Douglas complained that the Air Force was unfairly awarding contracts to its competitors to avoid accusations of favouritism. Meanwhile, RAND’s growing cadre of mathematicians and social scientists felt straitjacketed by the firm’s stiff corporate ethos. ‘Academic people’, commented Collbohm’s fifth hire, the astronomer John Williams, ‘have irregular habits and have never taken kindly to the eight-to-five routine.’11 There was even resistance to the idea of ordering blackboards and chalk (which the academics wanted in four different colours). The break with Douglas Aircraft came on 14 May 1948, when, to the satisfaction of both parties, ‘Project RAND’ became the RAND Corporation, an independent, non-profit organization employing more than 200 people.
RAND’s focus on engineering and physics would soon be widened enormously under Williams’s stewardship. He was recruited in 1946 on the advice of Collbohm’s close friend Warren Weaver, the wartime director of the Applied Mathematics Panel (AMP).12 The AMP had carried out during the war exactly the kind of research that Collbohm thought RAND should be doing in peacetime.
Weaver was himself a former mathematics professor but had little time for the ‘dreamy moonchildren, the prima donnas, the asocial geniuses’ that he felt dominated the higher echelons of academic science.13 Williams was another of Weaver’s practically minded recruits. After graduating from the University of Arizona in 1937, he started a PhD in astronomy at Princeton University but became so busy with war work that he never finished.
During the Second World War, the AMP supported the new field of ‘operations research’, pioneered in Britain by the physicist Patrick Blackett. Operations research brought the methods of the sciences to bear on wartime problems. The idea was simple: collect and analyse as much data as possible, test hypotheses in the field and use the results to home in on solutions. In nine short months after he joined Coastal Command as a science adviser in 1941, Blackett used this approach to turn around the Royal Air Force’s unsuccessful campaign against German U-boats. Blackett and his team calculated, for example, that setting the Air Force’s depth charges to explode at a depth of 25 feet rather than 100 feet (as they had been) would result in two and a half times more hits. The change was so effective that captured U-boat crews thought the British had started using a new and more powerful explosive.14 The idea caught on quickly. By the end of the war, around 700 scientists in the United States, Canada and Britain were employed in operations research.
With the war over, the question facing military planners was: how could all that expertise now be put to use? With defence budgets tightening, spending on new weapons systems or military operations would have to be weighed carefully against other demands. Weaver’s solution to this problem was the notion of ‘military worth’, a simple score that captured all the complex pros and cons of such choices so that decisions could be made more easily. And the mathematical apparatus to carry out military worth calculations was that of game theory. ‘Military worth, as the phrase is here used, is closely related to the general concept of utility in economic theory,’ Weaver explained in a report in 1946, referring his reader to the relevant section of von Neumann and Morgenstern’s Theory of Games. ‘This pioneering and brilliant book is, it should be pointed out, connected in a most important way with the viewpoint here being presented, for it develops a large part of the mathematics necessary for theories of competitive processes.’15
In September 1947, at a RAND-sponsored conference in New York, Weaver set out a manifesto for the nascent organization. Operations research had ‘resulted only from the pressure and necessity of war’, he said. RAND would provide in peacetime an environment where similar techniques could be more widely used for ‘analyzing general theories of warfare’. Chess master Emanuel Lasker’s Jazz Age dreams of a ‘science of contest’ were at last taking shape. ‘I assume that every person in this room is fundamentally interested in and devoted to what can broadly be called the rational life … as compared with living in a state of ignorance, superstition and drifting-into-whatever-may-come,’ Weaver continued.
I think that we are not interested in war but in peace … I assume that every person in this room is desperately dedicated to the ideals of democracy, and to so running our own business, so cleaning our own house, and so improving our own relations with the rest of the world that the value of those ideals in which we believe becomes thereby evident.16
RAND analysts pride themselves on their dedication to the ‘rational life’ to the present day. The organization’s commitment to peace and democracy – at least beyond the borders of the United States – would be brought into question again and again.
When Weaver’s protégé Williams was hired, the new section at RAND he headed was devoted to the ‘Evaluation of Military Worth’. An aficionado of game theory himself, Williams would write a humorous primer on the subject, The Compleat Strategyst, strewn with in-jokes and featuring many of RAND’s analysts, transformed into comic characters. Translated into at least five languages including Russian, the book would become one of RAND’s most popular publications.
Williams swiftly began recruiting experts in the field. In 1950, RAND’s annual report would proclaim:
the analysis of systems for strategic bombardment, air defense, air supply, or psychological warfare, pertinent information developed or adapted through survey, study or research by RAND is integrated into models, largely by means of mathematical methods and techniques … In this general area of research … the guiding philosophy is supplied by the von Neumann-Morgenstern mathematical theory of games.17
Williams would shape both the intellectual and physical environment of RAND for the next twenty years until his death, aged fifty-five, in 1964. He campaigned successfully for two new divisions to be created at RAND – one for social science, the other for economics. In 1953, the rapidly growing outfit moved to purpose-built quarters by the beach. The new building’s lattices of courtyards and corridors, designed to increase chance meetings between staff from different divisions, were built to specifications drafted by Williams. In this, as in so many things, Williams would prove to be ahead of his time.
Rotund, weighing close to 300 pounds, Williams enjoyed the good life. He had RAND’s machinists fit a Cadillac supercharger to the engine of his brown Jaguar, taking it out for midnight runs down the Pacific Coast Highway at more than 150 miles per hour. At his house in Pacific Palisades, the booze flowed so freely that his erudite guests would be rolling around on the floor drunk by the end of his parties. If that all sounds rather familiar, it is no coincidence. Williams had attended von Neumann’s lectures at Princeton and worshipped him. Von Neumann’s spirit suffused RAND from its inception. All that was missing was the great man himself. On 16 December 1947, Williams wrote to his old professor.
‘The members of the Project with problems in your line (i.e. the wide world) could discuss them with you, by mail and in person,’ von Neumann read. ‘We would send you all working papers and reports of RAND which we think would interest you, expecting you to react (with frown, hint, or suggestion) when you had a reaction.’ For his services, von Neumann would receive US$200 a month – the average monthly salary at that time. The offer from Williams came with a charming stipulation: ‘the only part of your thinking time we’d like to bid for systematically is that which you spend shaving: we’d like you to pass on to us any ideas that come to you while so engaged’.18
Von Neumann began consulting for RAND the following year, holding court there much as he did at Los Alamos and Princeton. As he ambled through the criss-crossing corridors, people would call him aside to pick his brains about this or that. Williams would throw demanding maths problems at his hero in an effort to trip him up. He never succeeded. At one of his ‘high-proof, high-I.Q. parties’19 one analyst produced a fat cylindrical ‘coin’ that was something of a RAND obsession at the time. Milled by the RAND machine shop at the behest of Williams, their proportions were carefully chosen so that the chances of falling heads, tails or on its side were equal. Without blinking an eye, von Neumann correctly stated the coin’s dimensions.20
Like RAND’s analysts, von Neumann was fascinated by war strategy. As a child he’d played the eighteenth-century game Kriegspiel with his brothers, drawing terrain for battles on graph paper, and he found that a version of the game was popular during lunchbreaks at RAND. He was also familiar with the idea of ‘military worth’ and had helped forge its links to game theory. On 1 October 1947, just a couple of months before he received the letter from Williams, the statistician George Dantzig had paid him a visit. Dantzig, a former liaison between the Air Force and AMP, wanted to solve the daunting logistical problem of matching the military’s needs to the resources available as quickly and efficiently as possible. Air Force budgeting in the 1940s was so baroque that producing a plan to requisition the appropriate manpower and materiel for a task could take seven months or more. Eventually Dantzig would help to invent an entirely new discipline called ‘linear programming’ to deal with the process. But in 1947, he had begun with a relatively simple objective: to devise a diet that met a soldier’s nutritional needs as cheaply as possible.21 The numbers involved in even this supposedly straightforward problem had, however, spiralled rapidly out of control, and he had decided to ask von Neumann, expert in computing techniques, for help. Dantzig, who would join RAND in 1952, had begun describing the matter in detail when, uncharacteristically rudely, von Neumann impatiently told him to ‘Get to the point.’ Annoyed himself, Dantzig then ‘slapped the geometric and the algebraic version of the problem on the blackboard’ in ‘under one minute’. Dantzig recalls what happened next:
Von Neumann stood up and said, ‘Oh that!’ Then for the next hour and a half, he proceeded to give me a lecture on the mathematical theory of linear programs.
At one point, seeing me sitting there with my eyes popping and my mouth open – after all I had searched the literature and found nothing, von Neumann said: ‘I don’t want you to think I am pulling all this out of my sleeve on the spur of the moment like a magician. I have just recently completed a book with Oscar Morgenstern on the theory of games. What I am doing is conjecturing that the two problems are equivalent. The theory that I am outlining for your problem is the analog of the one we have developed for games.’22
Von Neumann had instantly recognized that Dantzig’s optimization problem was mathematically related to his minimax theorem for two-person zero-sum games. The insight helped determine the conditions under which logistical problems of the type Dantzig was interested in could or could not be solved. Linear programming is now a staple approach to such problems – from the placement of servers inside data centres to the purchase and distribution of vaccines.
The twin influences of these military mathematicians and the Air Force meant that RAND’s interests in 1948 were completely aligned with von Neumann’s three main obsessions of the time: computing, game theory and the bomb. For a while, there was no other setting that von Neumann enjoyed more and for the next few years, until his interests diverged, von Neumann would often visit the Santa Monica think tank. Even when he was not physically present, his influence was felt. ‘Everybody knew that von Neumann was king,’ recalled Jack Hirshleifer, who was employed in the economics division.23
Early computing work on the ‘Super’ required random numbers for Monte Carlo simulations, so RAND engineers built an electronic device to generate them. This was compiled into a surprise best-seller entitled A Million Random Digits and 100,000 Normal Deviates. In 1949, Williams headed a RAND team that visited various firms to gauge their ambitions for developing electronic computers. ‘It was a dismal scene,’ Williams complained in a memo after he found out that their plans were non-existent.24
RAND turned to von Neumann, by now considered the foremost expert on computing in the United States. With his tongue firmly in his cheek, von Neumann questioned whether a computer was needed at all. According to journalist Clay Blair, RAND scientists came to him with a problem they thought too difficult to solve by conventional means:
After listening to the scientists expound, Von Neumann broke in: ‘Well, gentlemen, suppose you tell me exactly what the problem is?’
For the next two hours the men at Rand lectured, scribbled on blackboards, and brought charts and tables back and forth. Von Neumann sat with his head buried in his hands. When the presentation was completed, he scribbled on a pad, stared so blankly that a Rand scientist later said he looked as if ‘his mind had slipped his face out of gear,’ then said, ‘Gentlemen, you do not need the computer. I have the answer.’
While the scientists sat in stunned silence, Von Neumann reeled off the various steps which would provide the solution to the problem. Having risen to this routine challenge, Von Neumann followed up with a routine suggestion: ‘Let’s go to lunch.’25
RAND pressed ahead with building their own machine – piggybacking on von Neumann’s computer project at the IAS. A team from RAND travelled to Princeton to learn from the IAS experience and, like others around the world, they eagerly read Goldstine and von Neumann’s updates. In 1952, RAND hired Willis Ware, an electrical engineer who had worked on the IAS machine from 1946 to 1951. He stayed for fifty-five years, serving as head of RAND’s Computer Science department from 1960.
RAND’s machine started work in 1953, often running Monte Carlo bomb simulations and Dantzig’s logistical problems. They called it the JOHNNIAC (John von Neumann Numerical Integrator and Automatic Computer). A framed photograph of the man himself hung on the wall next to the machine.
To begin with, von Neumann’s energies were focused on deepening the mathematics of game theory at RAND. A letter from Williams in December 1947 promised that his department planned to make ‘major efforts on applications of game theory’. Von Neumann’s response is encouraging. ‘The work on game theory, which you have been pushing so energetically and successfully interests me greatly,’ he wrote back. ‘I don’t think that I need tell you this again.’26 Von Neumann reviewed the work of RAND’s mathematicians on the subject, and his own early publications for the organization looked at solutions of two-person and n-person games. Like other game theorists there, von Neumann was now less interested in proving new theorems about game theory than coming up with ways to compute actual solutions. ‘I have spent a good deal of time lately on trying to find numerical methods for determining “optimum strategies” for two-person games,’ von Neumann reported to Weaver in March 1948. ‘I would like to get such methods which are usable on an electronic machine of the variety which we are planning, and I think that the procedures that I can contemplate will work for games up to a few hundred strategies.’
One particularly fertile and long-lived area of research at RAND would be the mathematics of ‘duels’ – the subject of nearly a hundred papers and memoranda over two decades. In RAND, the duel served as a simplified model for diverse situations: two aircraft or two tanks closing in for combat, for instance, or a bomber versus a battleship. For analysts, the duel allowed the relatively complete maths of the two-person zero-sum game to be brought to bear on real combat data from the Second World War. In the duels RAND considered, each player wanted to get the best shot by holding off firing as long as possible – but still sooner than their opponent. RAND mathematicians explored many permutations of the duel. If the duellists heard each other’s shots, the duel was ‘noisy’, if neither learned whether or when their opponent had pulled the trigger, the duel was ‘silent’. Opponents might each have one bullet or many, one duellist could be a poorer shot than the other and so on. Each scenario was brought to a precise solution by dozens of RAND’s visiting or resident scholars.27
Some of the papers, including ‘Silent Duel’ and ‘One Bullet Versus Two, Equal Accuracy’, were written by a mathematician called Lloyd Shapley, son of astronomer Harlow Shapley, one of the most famous scientists in America. The younger Shapley’s mathematics degree at Harvard University had been interrupted by the war. He spent the next two years in China, helping the US Air Force decipher coded Soviet weather reports for the region – work that contributed to the forecasts for Japan. After returning to Harvard to finish his studies, and with no interest in postgraduate work, he joined the ‘Military Worth’ section under Williams after hearing about RAND through Air Force connections. He first came to von Neumann’s attention in dramatic fashion during a packed RAND seminar in the summer of 1948.28
Von Neumann had been asked to prove that a particular duel – one involving two fighter aircraft – had no formal solution. After his customary minute or so of staring into space, von Neumann had raced away on the blackboard when he was suddenly interrupted by a voice from the back of the room.
‘No! No! That can be done much more simply!’
Shocked silence settled over the room. Hans Speier had just been appointed head of RAND’s new social science division. His memories of the incident were still fresh in his mind decades later:
‘Now my heart stood still, because I wasn’t used to this sort of thing,’ said Speier.
Johnny von Neumann said, ‘Come up here, young man. Show me.’ He goes up, takes the piece of chalk, and writes down another derivation, and Johnny von Neumann interrupts and says, ‘Not so fast, young man. I can’t follow.’
Now … he was right, the young man was right … 29
Von Neumann was astonished. ‘Who is this boy?’ he asked Williams after the meeting. It was Shapley, who Williams had hired earlier that year. ‘And what’, said von Neumann, ‘has he been doing?’
‘Only John Williams could do this marvellously,’ Speier continued. ‘He said, ‘Oh well, he has written three or four papers, each of which is the equivalent of a doctoral dissertation in mathematics’.
Which was true. Johnny von Neumann looked at that, and he gave him – I don’t know – it was something quite fantastic, a special stipend to Princeton or something like that.
With von Neumann’s encouragement Shapley did indeed go to Princeton in 1950, by now a hotbed of game theory research. While he was there, he solved a key question raised – but not answered – by von Neumann and Morgenstern’s cooperative game theory: how can payouts be divided ‘fairly’ among the members of a coalition? He defined a way to distribute the payouts, now called the Shapley values of a cooperative game, such that no player could do better either by themselves or in any possible splinter groups.
One way to calculate the Shapley values for a game is to imagine that costs or benefits are allocated by a committee on a first-come, first-served basis. Since the order in which players join a grand coalition should not matter in a truly ‘fair’ settlement, the Shapley value for a game actually comprises the payouts that each player gets after averaging over all possible orders in which the players might approach the committee.30
There is something magical in the way the Shapley value elegantly solves what was intractable to the authors of Theory of Games. This was the first hint that the cooperative game theory of von Neumann and Morgenstern could solve real-world problems. And Shapley would do much more. One of his most influential contributions would be forged with fellow Princeton mathematician David Gale, who loved mathematical games and conundrums. Gale was known for quietly scribbling down a grid or pulling a fistful of coins from his pocket at mealtimes and challenging fellow graduate students to solve some puzzle or other. Perhaps in this spirit, Gale sent a few other mathematicians a note in 1960 asking, ‘For any pattern of preferences, is it possible to find a stable set of marriages?’
Shapley sent his answer by return of post.
Let each boy propose to his best girl. Let each girl with several proposals reject all but her favorite, but defer acceptance until she is sure no one better will come her way. The rejected boys then propose to their next-best choices, and so on, until there are no girls with more than one suitor. Marry. The result is stable, since the extramarital liaisons that were previously rejected will be disliked by the girl partners, while all others will be disliked by the boy partners.31
Shapley’s solution applies to any market that requires two sets of people to be paired up so that no one can do better. Gale and Shapley wrote up the findings in a paper, in which they also showed that the method could be used to match applicants to colleges.32 Now known as the Gale-Shapley ‘deferred acceptance’ algorithm, the work was cited as part of the decision to award Shapley a share of the 2012 Nobel Memorial Prize in Economic Sciences, instantly garnering him a reputation in the press as a mathematical matchmaker extraordinaire. He would be one of two game theorists whose striking early contributions did much to make the field useful for economics and other disciplines. At Princeton, the twenty-six-year-old Shapley met the other – a graduate student five years his junior called John Nash. Shapley was cultured, popular, a virtuoso piano player and a decorated war hero. He was also an expert player of Kriegspiel and Go. Nash promptly fell in love with him.
Most people who have heard of John Nash know of him through Ron Howard’s A Beautiful Mind, which is unfortunate because the film romanticizes the man and somewhat mischaracterizes his work. The Nash portrayed in Sylvia Nasar’s biography, upon which the film is nominally based, is a petulant bully who advises his mistress of four years to give up their son for adoption. The physically imposing Nash later threw his future wife ‘to the ground and placed his foot on her neck’ during a maths department picnic.33
When he met Shapley, ‘Nash acted like a thirteen-year-old having his first crush,’ writes Nasar.
He pestered Shapley mercilessly. He made a point of disrupting his beloved Kriegspiel games, sometimes by sweeping the pieces to the ground. He rifled through his mail. He read the papers on his desk. He left notes for Shapley: ‘Nash was here!’ He played all kinds of pranks on him.34
It was to be one of several emotionally tempestuous relationships that Nash had with other men.
Postwar Princeton was a town awash with genius, but Nash implied that he was smarter and from superior stock than his fellow students – particularly those from Jewish backgrounds. ‘He definitely had a set of beliefs about the aristocracy,’ says fellow Princetonian Martin Davis. ‘He was opposed to racial mixing. He said that miscegenation would result in the deterioration of the racial line. Nash implied that his own blood lines were pretty good.’
Still Shapley humoured him, dazzled by the younger mathematician’s obvious brilliance. ‘Nash was spiteful, a child with a social IQ of 12, but Lloyd did appreciate talent,’ recalled Shapley’s roommate, economist Martin Shubik, whom Nash never called anything other than ‘Shoobie-Woobie’. Together with fellow graduate student John McCarthy, Shubik, Shapley and Nash invented a board game in which players had to form alliances – then break them at the last possible minute to win. The game, later named ‘So Long, Sucker’, was designed to push people to their psychological limit: some married couples reputedly went home in separate cabs after a night of play. Once, after Nash ditched McCarthy particularly ruthlessly to win, McCarthy exploded. ‘But I didn’t need you anymore,’ a bemused Nash kept saying. Nash’s name for the game? ‘Fuck your buddy!’
Like Shapley, Nash was drawn to game theory. He attended the popular weekly seminars held on the subject by Albert Tucker, chair of the Princeton maths department. One of the first speakers was von Neumann. It was in these seminars that Nash developed the ideas behind his first game theory paper, written up with the encouragement of Morgenstern, whom Nash referred to as Oskar La Morgue behind his back. Impressively, Nash had first thought of his approach to the problem as an undergraduate at the Carnegie Institute of Technology, during the only economics class he would ever attend. In ‘The Bargaining Problem’, Nash showed that a two-person cooperative game could be brought to a solution if certain conditions were met. 35 He attacked the problem with the axiomatic method championed by Hilbert – and, of course, von Neumann. According to orthodox economic theory, there is no unique solution to how two parties should divide up the ‘surplus’ created when they strike a deal. Von Neumann and Morgenstern got no further with the problem either: they could only give a spectrum of solutions for the two-person game, not a single point at which the players would come to an agreement. Only the simplest ‘symmetric’ version of the problem – when the parties have exactly the same interests and bargaining power – had been shown to have an exact solution. In this case, the net gain would obviously be split equally between the two. Nash was able to show more generally that even in asymmetric cases, assuming that the utilities could be assigned to the two parties in the way Theory of Games described, the bargaining problem has an exact solution – namely, the point at which the product of the two utility scores is a maximum. The result prefigured in a small way Shapley’s contribution, which provides a similar sort of solution for cooperative games with any number of players.
The young Nash had never lacked confidence. In 1948, his very first year as a graduate student, he arranged to see Einstein in his office at the IAS to discuss some pressing ideas on the interaction of particles with fluctuating gravitational fields. Nash spent nearly an hour trying to unwind his thoughts at Einstein’s blackboard but eventually came unstuck. ‘You had better study some more physics, young man,’ Einstein told Nash with a kind smile before sending him on his way. So the following autumn, when the unabashed Nash thought he had made a breakthrough in game theory, he quite naturally scheduled a meeting with the discipline’s founding father.
Just as he had with Einstein, Nash arranged to see von Neumann in his office at the IAS. In 1949, von Neumann was busy consulting for the government, the military, big business and RAND. Behind the scenes, he was campaigning for America to pursue the H-bomb while madly chasing the computing resources necessary to show it was possible. He was also building his own computer at the IAS. An apologetic letter to a friend dictated to his secretary, Louise, that spring read, ‘I am delayed by a siege of work, which I hope will last only for a few days or so. At this point there was a considerable burst of hilarity from Louise. Can you interpret it?’ Still, he made time to see the promising young graduate student.
Nash nervously started to present what would turn out to be his greatest – and final – contribution to game theory. He had come up with a mathematical framework allowing the analysis of any type of game – whether zero-sum or not – with any number of participants, and showed that there are certain outcomes for all games in which no player can do any better by unilaterally changing their strategy. These kinds of solutions to a game are now called Nash equilibria. It was a staggering accomplishment, though no one, least of all Nash, had any idea how thoroughly useful his idea would prove to be. There was one catch: in Nash’s scheme, players were not allowed to communicate or team up – almost as if they were caught in a perpetual final round of ‘Fuck your buddy!’ Von Neumann hated it.36 When Nash started describing his proof, von Neumann interrupted, finished off his chain of reasoning and shrugged away Nash’s accomplishment with a devastating denouement: ‘That’s trivial, you know,’ he said. ‘That’s just a fixed-point theorem.’ And it was. Nash had used the same elegant trick that von Neumann had in his 1937 model of an expanding economy. Von Neumann was underwhelmed, as other mathematicians would be. They would regard Nash’s proof as solid enough, and a great PhD thesis, but not a patch on his later work on nonlinear partial differential equations, for instance, which would net him the Abel Prize in 2015.
What von Neumann disliked most about Nash’s approach, though, was the axioms upon which it was built. The idea that people might not work together for mutual benefit was anathema to him. He was central European to the core, his intellectual outlook shaped by a milieu where ideas were debated and shaped over coffee and wine. At that very moment, he was busily pushing as much as he could about the technical details of his computing project into the public domain. Ruling out communication ran counter to the spirit of his ‘coalitional’ conception of game theory. Even the fact that Nash’s solution could produce a point-solution to a complex game struck von Neumann as unrealistic. He maintained the theory could provide only a spectrum of solutions, with the actual result determined by social mores and the specific circumstances at the time.
Nash would later ascribe von Neumann’s coolness as a defensive response prompted by a Young Turk invading his turf. ‘I was playing a non-cooperative game in relation to von Neumann rather than simply seeking to join his coalition,’ he told the historian Robert Leonard. ‘And of course, it was psychologically natural for him not to be entirely pleased by a rival theoretical approach.’37 ‘Natural’, perhaps, from Nash’s point of view and in keeping with reports that von Neumann could react angrily to being contradicted.38 But von Neumann’s rather more magnanimous reaction to being corrected brusquely, and publicly, by Shapley the year before at RAND suggests there was more at stake for him here than the embarrassment of being outfoxed by a younger mathematician.
A few days after Nash’s meeting with von Neumann, he found a more sympathetic ear. ‘I think I’ve found a way to generalize von Neumann’s min-max theorem,’ he told Gale. ‘And it works with any number of people and doesn’t have to be a zero-sum game.’ Gale urged him to rush the result into print, and he helped draft a paper based on Nash’s proof.39 ‘I certainly knew right away that it was a thesis,’ Gale told Nasar. ‘I didn’t know it was a Nobel.’40
Others were quicker to spot the potential of Nash’s work. By the time he had finished his thesis the following year, he had an offer of a permanent job at RAND. Nash declined, preferring to find a faculty position with the greater intellectual freedom that entailed but elected to spend his summers at the Santa Monica think tank as a consultant instead. His relationship with the think tank would only come to an end in 1954, when he became a victim of one of the many police sting operations that aimed to force gay men to leave town. Nash was caught exposing himself in a public lavatory in the early hours of the morning. When RAND’s head of security came to see him the next morning, he denied he was homosexual and instead told him he had been conducting an ‘experiment’. ‘I like women,’ he insisted, producing a photo of his mistress and illegitimate son. Nash was promptly escorted from the building, and his security clearance revoked.41
Nasar contends that von Neumann’s rejection stung Nash so badly that ‘he never approached von Neumann again’. Yet whatever rift existed between the two men did not prevent them from attending game theory workshops together at RAND. Nor did it stop von Neumann from directing his readers to Nash’s work on non-cooperative games in the 1953 preface to the third edition of Theory of Games. By 1955, relations were cordial enough for von Neumann to chair a presentation by Nash on his ‘Opinions on the Future Development of Theory of n-person Games’ on the last day of a conference held at Princeton University.42 Nash argued again that the theory produced too many solutions for most games. Von Neumann, again, politely demurred.
Surveys of the roots and influence of game theory have generally taken a dim view of its progenitor. ‘Game theory portrays a world of people relentlessly and ruthlessly but with intelligence and calculation pursuing what each perceives to be his own interest,’ says the physicist turned historian Steve J. Heims. ‘The harshness of this Hobbesian picture of human behaviour is repugnant to many, but von Neumann would much rather err on the side of mistrust and suspicion than be caught in wishful thinking about the nature of people and society.’43
Heims attributes von Neumann’s misanthropy to his experience of living under Béla Kun’s regime as a teenager in Hungary. But what von Neumann saw happen in Germany scarred him very much more. ‘His hatred, his loathing for the Nazis was essentially boundless,’ says Klári. ‘They came and destroyed the world of this perfect intellectual setting. In quick order they dispersed the concentration of minds and substituted concentration camps where many of those who were not quick enough … perished in the most horrible ways.’44
By the time von Neumann visited Europe again in 1949, his belief in people had evaporated away altogether. ‘I feel the opposite of nostalgia for Europe,’ he wrote to Klári, ‘because every corner reminds me … of the world which is gone, and the ruins of which is no solace. My second reason for disliking Europe is the memory of my total disillusionment in human decency between 1933 and September 1938.’45
Still, in Theory of Games, arch-rationalist von Neumann had presupposed that even the hard-boiled players he envisaged would collaborate for common advantage. By contrast, Nash would himself describe his thinking, in retrospect, as more individualistic, more ‘American’.46 It is arguably Nash’s conception of game theory, not von Neumann’s, that more closely embodies the kill-or-be-killed paranoia of the early Cold War. And it would be Nash’s powerful solution to games that would for the first few decades after the Second World War take academia, economics and RAND by storm.
In Santa Monica, RAND’s analysts had found themselves bumping up against the limits of game theory. When the mathematics could not provide an answer to a problem, they turned to experimenting – frequently on each other. In the summer of 1949, before Nash’s work had been published, mathematician Merrill Flood had started exploring how well the theory predicted human behaviour by devising games and dilemmas to test his fellow RANDites. Sometimes he turned an everyday problem into a bargaining ‘game’ to see if he could find a ‘rational’ solution. Flood published some of his research in a RAND memorandum entitled ‘Some Experimental Games’.47 The results of his investigations were often surprising. Things did not always go to plan.
In June that year, Flood had tried to buy a used Buick from his friend and colleague, the futurist and nuclear strategist Herman Kahn, who was planning to move back east with his family. Flood recast the situation as a sort of two-player game where the object was to reach an agreement on a fair price for the car. By avoiding a car dealer, they could split the ‘surplus’ profit between themselves. The two men decided to consult a used-car dealer they both knew and were able to ascertain his buying and selling price. Having established the dealer’s ‘cut’, they were now left to agree on how they should divide the sum ‘fairly’ – the classic bargaining problem that Nash had addressed in his paper. Flood suggested an even split: he would pay Kahn the dealer’s buying price plus half of what the dealer would have made by selling the car himself. But both of them knew any other division of the profits was equally admissible – and rational. In the end Kahn, probably fed up with the circularity of the discussion, drove his Buick to the east coast without completing the sale.
News of Nash’s discovery spread to RAND later that year. With two equally valid solutions to choose from, Nash or von Neumann-Morgenstern, the question was which would real humans plump for? In January 1950, Flood and his colleague Melvin Dresher performed an experiment to find out. Transformed into an anecdote by Princeton’s Tucker, who was also a RAND consultant, it would become the most notorious ‘game’ to emerge from the theory: the Prisoner’s Dilemma.
Tucker’s spin on the experiment was to present Flood and Dresher’s game as a choice facing two prisoners being held separately by police. The tale has been refined over the years and now usually runs something like this:48
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:
If A and B each betray the other, each of them serves two years in prison.
If A betrays B, but B remains silent, A will be set free and B will serve three years in prison.
If A remains silent but B betrays A, A will serve three years in prison, and B will be set free.
If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).
The only Nash equilibrium of the dilemma is for the prisoners to rat on each other. To see why, imagine you are prisoner A. If you betray B, and he does the same to you, you both get two years inside. On the other hand, if he stays quiet, you get off scot free. If you refuse to turn stool pigeon, you get a three-year sentence if he betrays you but even if he also opts to stay silent, you still serve a year in prison. Betrayal is the better option no matter what your partner decides – though if both prisoners talk to the police, the outcome is worse than if they both do not.
So much for the ‘rational’ choice. Flood and Dresher wondered what real players would choose to do in this non-zero-sum game.
We conducted one brief experiment with a two-person positive-sum non-cooperative game in order to find whether or not the subjects tended to behave as they should if the Nash theory were applicable, or if their behavior tended more toward the von Neumann-Morgenstern solution, the split-the-difference principle, or some other yet-to-discovered principle.
| Prisoner A\Prisoner B | Stay Silent | Rat |
| Stay Silent | 1 year, 1 year | 3 years, 0 years |
| Rat | 0 years, 3 years | 2 years, 2 years |
Their experiment – dubbed ‘A Non-cooperative Pair’ – presented the players with two strategies each and the payoffs table below. Flood and Dresher roped in Williams (player ‘W’), head of their section, and economist Armen Alchian (player ‘A’). Both were reasonably familiar with zero-sum two-person games but knew nothing of Nash’s proposed solution for non-zero sum games like the Prisoner’s Dilemma. The game progressed for a hundred rounds, and the players were asked to jot down their reactions and reasoning during play.
The experiment is particularly vicious because the winnings are heavily skewed in favour of player W. If the players cooperate, player A gets a half cent, player W gets a cent. If they both choose to defect, player A gets nothing, but player W still wins a half cent. The Nash equilibrium is in the bottom-left corner square – both players should defect. Had they played this strategy throughout the match, Williams would have ended the game with 50 cents and Alchian with nothing. In the end, Alchian came away with 40 cents and Williams won 65 cents. The two cooperated in sixty out of 100 plays – much more often than a ‘rational’ player should. ‘It seems unlikely that the Nash equilibrium is in any realistic sense the correct solution,’ Flood notes.49 Though the participants were prohibited from reaching an understanding on dividing up the winnings, they leaned towards the von Neumann-Morgenstern solution of mutual cooperation.
| Player A\Player B | Strategy 1 Defect | Strategy 2 Cooperate |
| Strategy 1 Cooperate | -1 cent, 2 cents | ½ cent, 1 cent |
| Strategy 2 Defect | 0, ½ cent | 1 cent, -1 cent |
The two players’ notes reveal their thinking. Williams quickly worked out that defecting in every game would net him at least a half cent per round – but that with ‘nominal assistance from AA’, they would both be better off. ‘This means I have control of the game to a large extent, so Player AA had better appreciate this and get on the bandwagon.’50
Alchian did not see things entirely this way. He starts off assuming that Williams will simply defect, as this is his path to a ‘sure win’. When Williams cooperates, he is thrown into confusion: ‘What is he doing?!!’ After playing ‘defect’ a few more times, and getting ‘defect’ back on the next turn from Williams, he eventually responds to Williams’ bid for cooperation by cooperating in turn. But later he appears to grow resentful that Williams gains more through mutual cooperation than he does. ‘He will not share,’ Alchian complains repeatedly. He tries to level things up and plays ‘defect’ a few times with the expectation that Williams will continue to cooperate. When Williams retaliates with ‘defect’, Alchian cooperates for much of the remaining game.
Flood and Dresher canvassed Nash’s opinion on their experiment. He responded by poking holes in their methodology. ‘The flaw in the experiment as a test of equilibrium point theory is that the experiment really amounts to having the players play one large multi-move game,’ he wrote. ‘One cannot just as well think of the thing as a sequence of independent games as one can in zero-sum cases. There is much too much interaction …’ He could not resist taking a swipe at the players. ‘It is really striking however how inefficient AA and JW were in obtaining the rewards,’ he said, adding snidely: ‘One would have thought them more rational.’
Nash was right that the experimental conditions are far from an ideal test of his theory. The problem is that the Nash equilibrium for the 100-move game is for players to defect every time. To see why, imagine that the players are about to play the last round of the game. A rational player should seize the chance to secure a bigger payoff by defecting, since her opponent will not be able to retaliate. But then knowing that her opponent will reason the same way and defect, it is also logical for her to defect in the penultimate round, and so on.51 Yet even the hyper-rational, amoral denizens of RAND did not do this. Flood recalls that von Neumann was quite tickled by their experiment. As he had predicted, players did not naturally gravitate towards the Nash equilibrium.52 Beyond that, however, he seems to have taken remarkably little interest.
The Prisoner’s Dilemma is often portrayed as a paradox of rationality because the most rational course of action for each individual adds up to a worse outcome for everyone. Flood and Dresher hoped von Neumann would ‘solve’ the Prisoner’s Dilemma. He did not. Neither has anyone else – though a lot of ink has been spilt in the effort to do so. Most game theorists now agree there is no ‘answer’ to the dilemma of the sort that Flood and Dresher envisaged. That is because there is no real paradox. The incentives of the game ensure that rational players do not cooperate. The real mystery is why humans faced with a one-shot Prisoner’s Dilemma still sometimes do.53
By 1946, von Neumann was predicting that devastating nuclear war was imminent. ‘I don’t think this is less than two years and I do think it is less than ten,’ he wrote to Klári on 4 October that year.54 His answer was preventive war – a surprise attack that would wipe out the Soviet Union’s nuclear arsenal (and a good number of its people too) before the country was able to retaliate. ‘If you say why not bomb them tomorrow, I say why not today?’ he reportedly said in 1950. ‘If you say today at 5 o’clock, I say why not one o’clock?’55
Some have argued that von Neumann viewed the stand-off between the superpowers as a Prisoner’s Dilemma56 or that his (ultimately unfounded) fears of an imminent Third World War were rooted in game theory. ‘There was perhaps an inclination to take a too exclusively rational point of view about the cases of historical events,’ Ulam noted in his obituary of von Neumann. ‘This tendency was possibly due to an over-formalized game theory approach.’57
There is no evidence that von Neumann explicitly viewed the Cold War or the arms race in these terms. He hated communist Russia and in the wake of the deadliest war that the world had ever known one did not have to be a game theorist to favour preventing another – even by the brutal means of an atom-bombing campaign that left millions of Russians dead. Wigner, who perhaps knew and understood von Neumann better than anyone, put it differently. ‘A mind of von Neumann’s inexorable logic,’ he wrote, ‘had to understand and accept much that most of us do not want to accept and do not even wish to understand.’58
For all its horror, pre-emptive nuclear war was a surprisingly popular idea in the higher echelons of power. Many in the US military were keen.59 ‘The only certain protection against aggression’, Arnold told Secretary of War Henry Stimson in 1945, ‘is to meet it and overcome it before it can be launched or take full effect.’ But they were not alone. Supporters in the press included William Laurence, science correspondent of the New York Times, who wanted the US to force the Soviets to accept nuclear disarmament. If that led to war, Laurence argued, ‘it would be to our advantage to have it while we are still the sole possessors of the atomic bomb’.60 Laurence had more reason than most to fear a nuclear attack on America. He was the only journalist to have been invited to witness the Trinity test and had seen the destructiveness of the atom bomb at first hand.
Senior figures in the Truman and Eisenhower administrations pressed for nuclear strikes privately – and sometimes in public. Truman never seriously considered making an unprovoked attack on the Soviet Union, but Eisenhower did contemplate using atom bombs against China on several occasions during the 1950s. Since the Sino-Soviet Treaty of 1950 included provisions for mutual military assistance should one partner be attacked, Eisenhower knew that an attack on the Chinese would probably need to be coordinated with a pre-emptive strike on the Soviet Union – and he communicated his willingness to escalate indirectly to the two countries.61
Even Bertrand Russell, a lifelong pacifist, pressed for Russia to be given an ultimatum: give up your nuclear ambitions, join a ‘world government’ – or face war. ‘I am inclined’, he said during a talk to the Royal Empire Society in 1947, ‘to think that Russia would acquiesce; if not, provided this is done soon, the world might survive the resulting war and emerge with a single government such as the world needs.’62 Like von Neumann, Russell believed the USSR to be an expansionist, totalitarian regime that, with the demise of Nazi Germany, now posed the biggest threat to world peace.63
Von Neumann appears to have lost his appetite for a pre-emptive strike when it became obvious that the Soviet Union had enough nuclear bombs to retaliate. After a conversation in 1954 with Oswald Veblen, who had come round to the idea, he wrote to Klári. ‘I told him that I felt a “quick” war was academic by now,’ von Neumann said, ‘since it would now – or within a rather short time – hardly be quick.’64
Ironically, just as von Neumann was abandoning the doctrine of preventive war, it effectively became US policy. On 12 January 1954, John Foster Dulles, Eisenhower’s secretary of state, announced that America could meet even the smallest military provocation with the full force of its nuclear arsenal. ‘We want, for ourselves and the other free nations, a maximum deterrent at a bearable cost,’ Dulles said. ‘Local defense will always be important. But there is no local defense which alone will contain the mighty landpower of the Communist world. Local defenses must be reinforced by the further deterrent of massive retaliatory power.’
Dulles may have formed his idea of ‘Massive Retaliation’ as early as 1948. Many in RAND were appalled by the implications of the strategy, which they believed was perilously close to sanctioning a first strike.65
Von Neumann’s early support for preventive war has ensured that he is often remembered as an unremittingly hardline cold warrior. George Kistiakowsky, who worked with von Neumann at Los Alamos, described him in 1984 as ‘a hawk, unmistakable, by modern standards’.66
Von Neumann was, however, a complex character. He loyally served both Democratic and Republican postwar administrations – and hated the paranoiac persecution of leftist and liberal academics that was gathering pace under Senator Joseph McCarthy. At the same time as von Neumann was busily trying to convince the US to bomb the Soviet Union into submission, he was also defending his friend Robert Oppenheimer in secret hearings held by the Atomic Energy Commission (AEC) to determine whether the leader of the US atom bomb project posed a security risk. Oppenheimer was by then director of the IAS. Awkwardly for von Neumann, the chairman of the AEC was Lewis Strauss, a trustee of the IAS who was also his friend. And one of the most damning testimonies against Oppenheimer was to be given by von Neumann’s fellow Budapester Edward Teller.
Von Neumann disagreed with Oppenheimer’s support for the Communist Party.67 Nonetheless, he was always a passionate champion of Oppenheimer’s role in the atom bomb project – and dismissed the idea that he would ever be disloyal to his country as dangerous nonsense. ‘Robert at Los Alamos was so very great,’ he maintained, ‘in Britain they would have made him an Earl. Then, if he walked down the street with his fly buttons undone, people would have said – look, there goes the Earl. In postwar America we say – look, his fly buttons are undone.’68
A particularly damaging accusation made against Oppenheimer during the trial was that he had sought to retard America’s hydrogen bomb programme during his tenure as chairman of the AEC General Advisory Committee, of which von Neumann was also a member. Oppenheimer did in fact oppose it – on technical grounds – and the two men vigorously but respectfully disagreed on the matter. Teller, on the other hand, never forgave Oppenheimer for trying to nix his brainchild.
Von Neumann quickly rounded up some key witnesses: well-respected scientists who had disagreed with Oppenheimer over the Super but were still sure that he was in no way a security risk. When von Neumann’s turn came to testify, he skilfully defended Oppenheimer in front of the panel. Whatever reservations Oppenheimer may have had about the hydrogen bomb, von Neumann said, he put them aside as soon as Truman announced on 31 January, 1950 that the US would develop the weapon. When prosecutors asked him if someone with close communist affiliations should be employed in a sensitive job, von Neumann replied that such connections before the war, when the Soviet threat was not obvious, were irrelevant. ‘We were all little children with respect to the situation which had developed, namely, that we suddenly were dealing with something with which one could blow up the world,’ he told the panel. ‘None of us had been educated or conditioned to exist in this situation, and we had to make our rationalization and our code of conduct as we went along.’69
The four-week hearing had begun on 12 April 1954. Oppenheimer’s security clearance was stripped on 29 June. In 2009, historians with access to the KGB archives found that Soviet intelligence had made many attempts to recruit Oppenheimer – but failed.70 They concluded he was not a spy. When Eisenhower appointed von Neumann to the AEC in 1955, some of his closest friends asked how he could bring himself to join the very agency that had persecuted Oppenheimer. Veblen, who had brought von Neumann to the US in the first place, never forgave him, even refusing to visit the dying von Neumann in hospital despite letters from Klári begging him to come. Oppenheimer was more understanding. He told Klári, ‘There have to be good people on both sides.’71
At RAND, game theory was being applied to the most pressing military problem of the time – how to avoid or survive a nuclear conflict with the Soviet Union. Though there is scant evidence von Neumann viewed international conflicts in game theoretic terms – others did. Game theory, and the Prisoner’s Dilemma in particular, quickly became the analytical instrument of choice for American foreign policy in the febrile atmosphere of fear and paranoia that persisted into the late twentieth century. ‘The Cold War,’ says historian Paul Erickson, ‘came to be seen by many as the ultimate game that game theory was meant to analyze.’ Game theoretical analysis was so ubiquitous, he adds, that ‘the histories of many key geopolitical events of the Cold War era … would be rewritten through this lens, to the point that post hoc analysis and history could become difficult to distinguish’.72 Among the first of RAND’s analysts to study the question of nuclear deterrence was Albert Wohlstetter, whose reputation for hard-nosed, fact-based analysis helped make him one of the most influential ‘defense intellectuals’ of the twentieth century.
From the first, Wohlstetter was an unlikely hawk. He was a logician, who as a teenager wrote an article for the journal Philosophy of Science that prompted Albert Einstein to invite him to tea. The physicist, who proclaimed Wohlstetter’s article to be ‘the most lucid extrapolation of mathematical logic he had ever read’, wanted to hash out the finer points of the piece with the seventeen-year-old.
At Columbia University, Wohlstetter joined a communist splinter group, the League for a Revolutionary Workers Party. Had the membership records of the group not been lost in a freak accident, Wohlstetter might never have made it into RAND at all. He joined the think tank in 1951 as a consultant to the maths division. His wife, Roberta, worked there too, first as a book reviewer in the Social Sciences Division, then as a highly respected analyst whose authoritative study on surprise attacks, published in 1962 as Pearl Harbor: Warning and Decision,73 would still be cited years later, including in 2004 by the 9-11 Commission.
Wohlstetter soon grew bored with the humdrum methodological work he had been assigned in the Mathematics Division. He was an aesthete with a taste for fine wine and haute cuisine, who would host classical music concerts at his modernist home nestled in the Hollywood Hills. He pined for more interesting challenges. One came his way when Charles Hitch, the head of RAND’s Economics Division, asked him to assess the best places to locate overseas bases for Strategic Air Command (SAC), America’s fleet of nuclear bombers. Fearing that the study would be every bit as dull as the assignments he was trying to escape from, Wohlstetter initially turned Hitch down. After turning the problem over in his mind that weekend, he changed his mind.
Wohlstetter had been disgusted by the US decision to drop atom bombs on Hiroshima and Nagasaki, an act he regarded as cruel and unnecessary. Here was a chance to reshape American nuclear strategy in a way that might spare cities in a future conflagration. He had detected a simple but serious conundrum at the heart of the basing question that piqued his interest: if your bases were sited close to the enemy, the enemy would also be close to you. It was not the first time someone had noticed this dilemma, but two intellectual influences led Wohlstetter to give the issue more serious thought: the first was game theory, the second was his wife.
Not only was game theory impossible to avoid in the Mathematics Division by 1951 but J. C. C. McKinsey, a good friend from his Columbia days who was also employed by RAND, was busy writing on the subject. Wohlstetter was not so interested in the mathematical intricacies of the theory but he did note the central premise: that in formulating a strategy, one had always to account fully for the actions of a rational enemy. His wife, Roberta, on the other hand, was investigating why the United States was completely unprepared for the Japanese attack on its ships. So Wohlstetter was acutely aware that no study of overseas American bases would be complete if it did not account for the possibility of a Soviet attack. He began digging deeply into the numbers and assembled a group of mathematically minded analysts to help. Known as ‘systems analysis’, their method, developed at RAND, was related to operations research but with a different emphasis. Operations research was a science of the possible: what can be achieved with the equipment and supplies available? Systems analysis, by contrast, was goal-orientated – what future weapons and strategies would be necessary to a specified mission? With its tacit commitment to considering every ‘rational’ eventuality, systems analysis is almost megalomaniac in its ambition.
The team considered numerous scenarios from basing the bombers in the US to the SAC’s preferred option of deploying them abroad. After exhaustive study, what they found was that under Strategic Air Command’s plan, the US bombers stationed in Europe were sitting ducks. A Soviet pre-emptive strike, they calculated, would wipe out nearly 85 per cent of the bomber force stationed in Europe. Worse, the near-elimination of US nuclear forces could be accomplished with just 120 bombs of 40 kilotons each – about twice that of Fat Man – leaving the Soviet Union free to invade Western Europe with impunity or hold America to ransom. The option that came out on top was to use the overseas bases to refuel the planes but not to station them permanently. Refuelling in-flight, an idea favoured by some Air Force leaders, was far too costly.
The RAND study, entitled Selection and Use of Strategic Bases, proved completely unpalatable to the Air Force.74 Wohlstetter’s team briefed officials on over ninety occasions but met near-uniform intransigence. ‘I hope none of you are taken in by all this slide-rule razzmatazz,’ one colonel scoffed after hearing their presentation. A major obstacle proved to be SAC’s chief, the cigar-chomping Curtis LeMay, who would serve as a model for a couple of the bellicose generals in Dr Strangelove.
Even more uncompromising than Arnold, LeMay had led the Twentieth Air Force’s campaign of carpet-bombing Japanese cities. ‘All war is immoral,’ he once declared. ‘If you let that bother you, you’re not a good soldier.’ LeMay’s preferred nuclear strategy, the ‘Sunday Punch’, was ‘Massive Retaliation’ by another name: a no-holds-barred attack on the Soviet Union with every atom bomb at SAC’s disposal in response to any aggression. If there was, as RAND now claimed, a risk of a Soviet surprise attack then, why, that was sufficient reason to hit them first. It was not so much a war plan, Kahn told SAC officers, as a ‘war orgasm’.
Eventually, RAND engineered a meeting with General Thomas White, then acting Air Force chief of staff. A worried Wohlstetter, convinced that he had decisively demonstrated America was on the brink of a war that it would lose, presented his team’s analysis one more time and convinced White of its importance. In October 1953, two months after the RAND presentation, the Air Force agreed to harden bases to atomic attack and reduce the number of aircraft stationed overseas to the bare minimum. Wohlstetter’s recommendations were never fully acted upon. Instead, SAC adopted the plan the RAND team had rejected as too expensive: refuel US-based bombers in mid-air and reduce SAC’s dependency on foreign bases. Still, RAND had forced a major rethink of Air Force strategy on the basis of theoretical mathematical projections.
Wohlstetter continued thinking about America’s nuclear defences. At the end of the 1950s, he laid out his ideas in ‘The Delicate Balance of Terror’, an article that helped to shape strategic thought in America for decades.75 Wohlstetter attacked the widely held belief that the existence of two nuclear powers eliminated the risk of an all-out global war. There was no atomic stalemate, he argued. The West had been lulled into a false sense of security by imagining that Soviet leaders favoured attacking in ways that would result in plenty of warning for the US. ‘However attractive it may be for us to narrow Soviet alternatives to these, they would be low in the order of preference of any reasonable Russian planning war,’ he argued and, echoing game theory’s minimax principle, he added that ‘In treating Soviet strategies it is important to consider Soviet rather than Western advantage and to consider the strategy of both sides quantitatively. The effectiveness of our own choices will depend on a most complex numerical interaction of Soviet and Western plans.’
His conclusion was that there could be no atomic stalemate and no let-up in vigilance. Any American vulnerability was both an invitation for the Russians to launch an immediate attack and reason for the US to pre-empt them by launching first. But as Wohlstetter was busily briefing commanders in Washington, von Neumann brought news of a weapon that threatened to make bombers obsolete altogether.
In 1950, RAND had produced a number of studies concluding that the development of long-range ballistic missiles should be an Air Force priority.76 Partly in response, the Defense Department initiated the Atlas Missile Project in 1951 to determine whether a rocket armed with a 3,000-pound warhead could be sent to destroy cities more than 5,000 miles away. But the bombs dropped on Hiroshima and Nagasaki were many times too heavy for Atlas, and the first US thermonuclear test, codenamed ‘Ivy Mike’, on 1 November the previous year had used a 74 metric-ton device, too heavy to be loaded on a plane, never mind a missile. Atlas was consequently a rather lower-priority project – a moonshot for the future. But in 1953, von Neumann, accompanied by Teller, told RAND’s physicists that the weaponeers at Los Alamos were on the verge of being able to make hydrogen bombs light enough to fit on rockets, and Hap Arnold’s vision of city-destroying projectiles that ‘come streaking out of somewhere’ could quickly be realized.
The first to hear at RAND were Ernst Plesset, head of the Physics Division, and David Griggs, the former US Air Force chief scientist who had held Plesset’s job in RAND’s early days and was now a consultant for the think tank. They passed on what they knew about the Los Alamos work to another RAND physicist, Bruno Augenstein, who began working through the implications of the news. The first Soviet hydrogen bomb test on 12 August 1953 gave his work added urgency. The ‘Mike’ device had been housed in a gigantic vacuum flask to keep its liquid deuterium fuel cool. Analysis of fallout from the Soviet test had revealed the presence of lithium, an indication that lithium deuteride, a solid at room temperature, might have served as a fuel for their device. If the Soviets had managed to make lithium deuteride in quantity, they could probably make weapons small enough to be loaded onto a bomber – or perhaps even launched on a rocket.
The Atlas programme’s managers had asked for missiles to be built to demanding specifications. They wanted a rocket that would fly halfway around the world at six times the speed of sound and land within a half-mile of the target. Augenstein realized that a lightweight hydrogen bomb rendered those requirements unnecessary. Using figures he got from Los Alamos, he calculated that a bomb weighing less than 1,500 pounds would produce a blast of several megatons. His research also suggested that the Russians would have trouble shooting down missiles travelling much slower than the speeds envisioned by those in charge of the project. Augenstein’s most significant discovery, however, was that the destructive power of the new warhead meant that a missile that landed between 3 and 5 miles away from the target would be sufficient – and within the capabilities of contemporary missile guidance technology. The US could develop ICBMs years earlier than the Atlas programme envisaged, perhaps as soon as 1960. And Augenstein knew that if he had reached these conclusions, the Russians had too – only earlier.
Augenstein’s report landed on Collbohm’s desk on 11 December 1953. Much impressed, Collbohm took it to Washington the next day to try to convince senior Air Force officers of the urgency of the situation. They wanted to wait. In October, the Air Force had itself assigned eleven of the country’s leading scientists and engineers to examine the feasibility of ICBMs – with von Neumann as their chairman. Codenamed the ‘Teapot Committee’, the panel had started their deliberations the previous month. Augenstein returned to RAND to prepare a formal report that would flesh out the technical details of the missiles and estimate how many missiles of lesser accuracy would be needed to destroy Soviet cities.
The Air Force received Augenstein’s final analysis, entitled A Revised Development Program for Ballistic Missiles of Intercontinental Range, on 8 February, 1954 – two days ahead of von Neumann’s committee. Their conclusions and recommendations were almost identical. Within a couple of months of the two reports, the US had relaxed the tight strictures imposed on the Atlas project and started a fast-track programme to develop missiles tipped with H-bombs.
On 21 August 1957, the USSR sent the R-7 Semyorka streaking nearly 4,000 miles through the air from Baikonur Cosmodrome in Kazakhstan. A few weeks later, essentially the same rocket put Sputnik into Earth orbit. The first successful flight of an Atlas rocket, a direct result of the programme that von Neumann helped to accelerate, took place on 28 November 1958. The armed Atlas D entered service in September 1959, within the timescale that Augenstein had envisaged in his report. The ICBM’s threat of raining death from the skies at the lunatic push of a button has hung over the world ever since.
At RAND, the melding of von Neumann’s game theory with defence policy continued apace and found a vocal advocate in the corpulent form of Herman Kahn. To the chagrin of his colleagues, Kahn toured the US cheerfully recasting their theories as provocatively as possible, rapidly becoming the most infamous of RAND’s ‘defence intellectuals’. ‘Thinking about the Unthinkable’, an idea virtually synonymous with the RAND ethos, was the title of one of Kahn’s books and reflected game theory’s rational, at times pathological, precept of imagining the worst possible response to any policy. A true ‘jester of death’,77 Kahn played deterrence theory for laughs, delivering his lines with relentless deadpan humour while he reasoned his way through the apocalypse, always willing to go a step further than anyone else. Beneath all his shtick, Kahn was deadly serious. When his fellow strategist Bernard Brodie worried during a RAND meeting that even a nuclear strike solely on Russian military targets located outside cities would still kill two million, Kahn piped up that a strategy that left ‘only’ two million dead could not be dismissed out of hand.78
Kahn was a physicist by training – during his early days at RAND, he had run Monte Carlo hydrogen-bomb-related simulations on the dozen or so high-speed computers then operating in the US.79 He was one of about seventy researchers at RAND given the high-level security clearances necessary to work on bomb design and he worked in the Physics Division, separated from the rest of the building by an electronic door. But Kahn was not content to skulk behind a closed door, calculating. He ambled along the corridors of RAND, sniffing the air for stimulating problems that would help make his name. Game theory piqued his interest for a while and, inspired, he began (but never finished) a book on its application to military planning.80 Then he found Wohlstetter and quickly realized that the new field of nuclear deterrence theory matched his unique talents. Formal game theory was too constraining for Kahn, but its assumptions often hover below the surface of his work.
Kahn eventually compiled his early lectures on deterrence into a massive tome of more than 600 pages and gave a copy to Wohlstetter, who advised him to burn it.81 Instead, he published it, and ‘On Thermonuclear War’ went on to sell a remarkable 30,000 copies in hardback.82 In it, Kahn asserted that nuclear war with the Soviet Union might be survivable and ‘would not preclude normal and happy lives for the majority of survivors and their descendants’. ‘Will the survivors envy the dead?’ Kahn asked at the foot of one table before concluding that they would not. The table, headed ‘Tragic but Distinguishable Postwar States’, listed numbers of dead (from 2 to 160 million) against the time Kahn thought that the economy would take to recover (up to 100 years).
It was the sort of blithe strategizing that Stanley Kubrick, who read Kahn’s book closely, would satirize so brilliantly in Dr Strangelove.83 ‘Now, the truth is not always a pleasant thing,’ says the film’s ultra-hawkish general, Buck Turgidson, as he makes the case for a massive strike on the Soviet Union,
but it is necessary now to make a choice, to choose between two admittedly regrettable, but nevertheless distinguishable postwar environments: one where you got twenty million people killed, and the other where you got a hundred and fifty million people killed … Mr President, I’m not saying we wouldn’t get our hair mussed. But I do say no more than ten to twenty million killed, tops.84
It was also the type of strategizing that sickened many of Kahn’s critics. Pacifists, including Russell, felt Kahn had inadvertently made the case for universal disarmament. One of the most notorious reviews of Kahn’s book, by mathematician James Newman, appeared in Scientific American.85 ‘Is there really a Herman Kahn? It is hard to believe … No one could write like this; no one could think like this,’ wrote Newman. ‘Perhaps the whole thing is a staff hoax in bad taste.’86 ‘This is a moral tract on mass murder,’ Newman continued, ‘how to plan it, how to commit it, how to get away with it, how to justify it.’
Kahn was appalled by Newman’s review – so appalled, in fact, that he soon started writing a sequel. The success of On Thermonuclear War helped Kahn win a million-dollar grant from the Rockefeller Foundation, and with it he set up his own think tank, the Hudson Institute in New York, which he called a ‘high-class RAND’.
RAND’s zeal for game theory research had largely fizzled out by the early 1960s, though its tenets and approach were embedded in the think tank’s culture from the systems analysis it pioneered to the prescriptions of its defence policy experts. One of the last at RAND to turn game theory to the question of nuclear deterrence was Harvard University economist Thomas Schelling. He conceived of war as bargaining by other means and he set out his new approach to conflict in a 1958 paper.87 ‘On the strategy of pure conflict – the zero-sum games – game theory has yielded important insight and advice,’ he says. ‘But on the strategy of action where conflict is mixed with mutual dependence – the non-zero-sum games involved in wars and threats of war, strikes, negotiations, criminal deterrence, class war, race war, price war, and blackmail; maneuvering in a bureaucracy or a social hierarchy or in a traffic jam; and the coercion of one’s own children – traditional game theory has not yielded comparable insight or advice.’ Much of Schelling’s career would be spent addressing this lacuna.
Schelling also demonstrated that even in many situations where no explicit communication was allowed or possible, players were able to coordinate their responses for mutual benefit far more often than game theory predicted. In one class experiment, Schelling asked his students to suppose they had to meet a stranger in New York City the next day but had no means of communicating with them. When and where should you meet? The most common answer was Grand Central Station at noon. Schelling called these unanticipated solutions to cooperative games ‘focal points’, and they showed the limits of theory. ‘One cannot,’ Schelling concluded, ‘without empirical evidence, deduce what understandings can be perceived in a non-zero sum game of maneuver any more than one can prove, by purely formal deduction, that a particular joke is bound to be funny.’88 But Schelling warned such tacit communication may not be enough to prevent a conflict escalating into a nuclear exchange.89 He recommended strengthening channels between the leaders of the US and Soviet Union several years before the Cuban Missile Crisis would expose how poor communication between the two might have disastrous consequences. Like his colleagues at RAND, Schelling thought the threat of ‘massive retaliation’ was not credible when the other side had the capacity to strike back equally massively. The Soviet Union would never be deterred by a policy that would mean national suicide for the US if it was ever acted upon.
Von Neumann’s last word on nuclear deterrence was published in 1955. Defense in Atomic War expresses the new bomb’s power in stark terms.90 ‘The increases of firepower which are now before us are considerably greater than any that have occurred before,’ he says.
The entire tonnage of TNT dropped on all battlefields during all of World War II by all belligerents was a few million tons. We delivered more explosive power than this in a single atomic blast.91 Consequently, we can pack in one airplane more firepower than the combined fleets of all the combatants during World War II.
Von Neumann explains that while historically the upper hand in a war might oscillate between combatants, this step-change in the destructiveness of weapons now available to the superpowers had changed the nature of war completely. ‘The difficulty with atomic weapons and especially missile-carried atomic weapons,’ he argues, ‘will be that they can decide a war, and do a good deal more in terms of destruction in less than a month or two weeks. Consequently, the nature of technical surprise will be different from what it was before.’ As a full-force nuclear attack from one side is impossible to defend against, ‘this will probably mean you will be forced not to ‘do your worst’ at all times, because then when the enemy does his worst you cannot defend against it … Hence, you may have to hold this trump card in reserve.’
A strategy of exercising restraint – rather than the reflexive ‘wargasm’ of massive retaliation – was by 1960 a popular position at RAND. 92 The patently hollow threat of going nuclear in response to the smallest attack with conventional forces was doing nothing to discourage Soviet aggression. Even as Dulles made his 1954 ‘massive retaliation’ speech, the US was becoming increasingly ensnared by a conventional conflict in Vietnam, and by the end of the same year the secretary of state himself was questioning the policy. In a letter to President Eisenhower in December, Dulles asked whether the US was ‘prepared to deal adequately with the possible “little wars” which might call for punishment related to the degree and locality of the offense, but which would not justify a massive retaliation against the Soviet Union itself’.
RAND’s response to the problem of fighting ‘little wars’ was the doctrine of ‘counterforce’. Pioneered by RAND’s Brodie, beefed up with game theory matrices by RAND analysts, then articulated most comprehensively by William Kaufmann, counterforce proposed sparing cities in the first instance. In response to Soviet aggression, the US would fire a small number of weapons at non-urban military targets, then use the threat of a well-protected nuclear reserve force as a bargaining lever to halt further escalation. Kaufmann hoped that if the Russians did retaliate, they too would avoid hitting cities. Civilian lives could be spared, and with time for negotiations to defuse the crisis perhaps an all-out nuclear exchange could be averted.
Counterforce was quintessential RAND, epitomizing the think tank’s quest for, as Kahn put it, ‘more reasonable forms of using violence’. The problem was that avoiding bloodshed was not a universally popular idea within the US military. The Strategic Air Command (SAC), in charge of America’s bombers and ICBMs, was particularly hostile to the new strategy.
Counterforce would find more receptive ears in government after the 1960 election of President John F. Kennedy, whose campaign was covertly aided by some of RAND’s experts. Among them was Daniel Ellsberg, who would leak the top secret ‘Pentagon Papers’, with their damaging revelations about the Vietnam War, to the press in 1971. Kennedy’s defence secretary, Robert McNamara, would hustle a host of RAND analysts, including Kaufmann, into the White House. The young ‘Whizz Kids’, as they became known, earned the enmity of the Air Force, their one-time sponsors, as their systems analysis studies undermined prized bomber and rocket projects – but supported accelerating the Navy’s submarine-launched Polaris missiles and expanding the Army’s conventional forces. Tired of having their defeats rubbed in their faces by the new gang of Ivy Leaguers, the Air Force soon hired their own analysts, and the Navy and the Army followed suit. RAND’s methods were embedded in US military thinking, shaping the country’s approach to theoretical nuclear conflicts – and to the very real ‘little wars’ to come in Southeast Asia and elsewhere.
In June 2019, the Pentagon accidentally published to its website the US military’s guidelines for planning and executing small-scale nuclear warfare. The sixty-page document, JP 3-72 on Joint Nuclear Operations, was quickly removed – but not before it had been downloaded by the Federation of American Scientists (FAS), a charity founded by Manhattan Project researchers in 1945 that is devoted to peaceful uses of atomic energy.93 The report’s focus is worst-case scenarios, and its emphasis is on fighting wars, rather than deterrence. Critics aver that such talk of limited nuclear war helps convince America’s enemies that the US would be prepared to use the bomb – increasing the chances that someone will. By imagining the worst, the worst is brought a step closer to being realized.
The dilemma is one that RAND’s analysts would have recognized. Seventy years after they began applying the tools of game theory to nuclear strategy, the stakes are higher than ever, the bombs dropped on Hiroshima and Nagasaki mere firecrackers compared to some of the bombs in the American and Russian arsenals. More countries now possess the weapons, and others are threatening to produce them. The expertise required to build a device is now widespread enough that it is not unfeasible that a well-organized terrorist group could build one. So a strategy document from the world’s most powerful bearer of nuclear arms might be expected to be unrecognizable in its scope compared with the stuff produced by the Cold-War-hardened strategists of the 1950s. Much of the report, however, is strikingly familiar – not least the epigraph that begins the third chapter on ‘Planning and Targeting’: ‘My guess is that nuclear weapons will be used sometime in the next hundred years, but that their use is much more likely to be small and limited than widespread and unconstrained.’ It comes from the 1962 book Thinking About the Unthinkable. Its source is Herman Kahn.
‘The most spectacular event of the past half century is one that did not occur,’ said Schelling in 2005, a couple of days before collecting his Nobel Prize. ‘We have enjoyed sixty years without nuclear weapons exploded in anger.’ Schelling attributed our ‘stunning good fortune’ to an unspoken taboo against the use of even the ‘smallest’ bomb. Should the horror of Hiroshima and Nagasaki fade from the public consciousness, he warned, should more nations or even terrorist groups acquire nuclear weapons, there is no guarantee they will share this ‘nearly universal revulsion’ against their use. We are on borrowed time.
By the mid-1950s, von Neumann too was on borrowed time. Perhaps it was all the nuclear weapons tests he had attended, or his unhealthy diet or simply bad luck, but cancer was slowly metastasizing through his body. Unaware of the illness, he spent his last years in frenzied activity. While mathematicians tend to produce their best work in their twenties and view middle age as the twilight of their productive years, von Neumann would produce his most original work yet. He began a quest to understand the phenomenal powers of sophisticated machines from the ground up; in particular the high-speed computers he had helped build and the most complex and mysterious of them all, the human brain.