The von Neumann-Morgenstern Collaboration (1938-43)
“It will be a strange essay for economists, but it can be important. Very.”
By 1926, mathematician John von Neumann (1903-57) was a professional researcher in two disparate fields: set theory and quantum mechanics. That year, he took it upon himself to write a paper on a completely different topic entirely: mathematical modelling of strategic interactions. von Neumann’s result, what is now referred to as the von Neumann’s minimax theorem, was published two years later under the title Zur Theorie der Gesellschaftsspiele, “On the Theory of Games of Strategy” (see essay below).
Despite the (later) significance of this work, following its publication the man himself returned to his research on set theory and quantum mechanics, as well as his developing interests in ergodic theory, rings of operators, the Haar measure and theoretical computer science. Indeed, von Neumann did not publish on the topic of ‘strategic interactions’ again for another ten years, until 19371. Then, seven years after that, seemingly out of nowhere von Neumann (with Oskar Morgenstern) produces what has since been called the “groundbreaking text that created the interdisciplinary research field of game theory”, Theory of Games and Economic Behavior* (TGEB).
The book has been cited more than 50,000 times as of 2024. This despite the fact that it (at least for economists) is a famously overwhelmingly complex mathematical text. Since its release in 1944, the work of 18 Nobel laureates has been in game theory, including John F. Nash Jr. (1928-2015), Kenneth Arrow (1921-2017), Gérard Debreu (1921-2004) and Jean Tirole (1953-).
This is the fifth in my series of essays on the von Neumann-Morgenstern collaboration (see the 1st, 2nd, 3rd and 4th here), and their work on TGEB in the period 1938 to 1943.
Their First Meeting (1938)
Although they would later be close friends, neither Morgenstern or von Neumann remembered the first time they met. This is odd, because Morgenstern would later write that von Neumann’s presence at the Institute for Advanced Study was one of the mai reasons why he pursued a position at the nearby Princeton University when he emigrated from Austria:
“The principal reason for my wanting to go to Princeton was the possibility that I might become acquainted with von Neumann and the hope that this would be a great stimulus for my future work.”
According to Morgenstern’s later recollections, the two mens’ first meeting must have been “soon after the university opened” in the fall of 1938 (Morgenstern, 1976). The circumstances of their second meeting are known in more detail. It happened after a lecture Morgenstern gave during a luncheon at the Nassau Club in Princeton on February 1st, 1939. As he later wrote, von Neumann and Niels Bohr (1885-1962) invited him for tea in Fine Hall. There, the three conversed for several hours about games and experiments:
“This was the first time that we had a talk on games. The occasion was heightened by Bohr's presence.”
Although Morgenstern later wrote that these talks “were taken up again with both at Weyl’s house”, the first entry in his diaries2 that mentions von Neumann is actually dated March 9th, 1940, when Morgenstern writes: “Yesterday at the Neumanns; alone. Very pleasant. There they both said that I should come to the institute after all”.
Regardless, according to Rellstab (1992), around this time Morgenstern was writing a short paper on the theory of games meant for economists, and so was actively pursuing von Neumann for help in explaining his 1928 minimax result. Their third meeting occurred in October 1939 as Morgenstern was making progress with the paper, which he at this point referred to as a paper on ‘maxims of behavior’. Following an (intense) discussion, Morgenstern later writes economist Frank Knight (1885-1972) at the University of Chicago about his dissillusionment with the Princeton economics department, commenting that he is much more inspired from working with mathematicians. Prior to von Neumann, Morgenstern had worked with both Abraham Wald (1902-50) and Karl Menger (1902-85), as early as in the early 1930s:
“Those with whom to discuss such problems are principally the mathematicians, of which we have some excellent ones in town. I have now been stimulated by these talks and proceeded to jot down notes on a further paper of what I called maxims of behavior. In this paper I shall endeavor to investigate a very curious relationship between the quantitative limits which maxims have.”
- Excerpt, letter from Oskar Morgenstern to Frank Knight, 14th of October 1939.
Following three dinners at von Neumann’s house in January, March and April of 1940, Morgenstern’s excitement about a future collaboration is indeed quite apparent in his diaries. As he would later write of the period:
“von Neumann and I had many […] very animated and wide-ranging discussions. There was an instantaneous meeting of minds and a spontaneous empathy between us. I mentioned to him that I was greatly interested in studying both his papers, the one on game theory and the one he had delivered in Vienna on the expanding economy. We quickly exchanged reprints, I giving him in particular my work on perfect foresight.”
The latter, Morgenstern’s work on perfect foresight, is the paper “Das Zeitmoment in der Wertlehre” (“The Time Element in Value Theory”), which von Neumann praised and recommended that he (Morgenstern) extend into a book on risk, foresight and revenue. The two papers by von Neumann he is referencing is the 1928 paper on minimax (“A Theory of Games”) and the 1937 paper “On a System of Economic Equations and A Generalization of Brouwer’s Fixed Point Theorem” first presented in 1936 at Menger’s Vienna colloquium (see essay below) and later published in its proceedings.
By April 4th, Morgenstern is noting in his diary that:
“In the evening John von Neumann came and we had a discussion for nearly four hours: Maxims of behavior (he sees completely what it is about and how difficult it is), about games, about basics questions of mathematics, he talked about Gödel and general philosophy of science. It has been a long time since I spent such an interesting evening. He stuck totally to the point and we may continue tomorrow. It is a pity that we have not discussed more often together; but I did not think I could contribute to his problems.”
At this point, there is a meeting of minds between the two men. Morgenstern is seemingly able to capture von Neumann’s attention and interest on topics related to economics and is growing more confident that his own contributions are worthwhile.
“Some people tell me, that they have never seen me in such a good form and good mood. This is due to Johnny who completely woke me up. Suddenly wishes are being fulfilled” — Morgenstern
European Émigrés
From Morgenstern’s diaries, later writings and the work of historians of mathematical economics (in particular Andrew Schotter and Urs Rellstab), it seems clear that it was Morgenstern, not von Neumann, who was the impetus for the writing of Theory of Games and Economic Behavior. Morgenstern first introduced the idea of a possible co-authored book with von Neumann in his diary as early as May the 3rd, 1940. As he writes,
“Neumann has left. We spent a few more evenings & discussed many hours. Especially mathematical economics. It would be wonderful if we could write a book together. It should be possible to do that over time”.
That time would indeed come, albeit not for another few years. Famously, von Neumann was a very productive man who in the period they worked on the book (1940-44) also published 17 other papers in addition to his involvement in the Manhattan Project and various consultancies in Washington. In the summer of 1940, he found time to travel to Seattle where he (among other engagements) gave lectures on games. As he communicated via letter to Morgenstern, he was also making progress with four-and-more-person games involving strategies and equilibria in the context of the formation and breaking of coalitions (Rellstab, 1992).
At this point in time, eleven months had passed since Germany invaded Poland, prompting the United Kingdom and France to declare war. Following the invasion, the Soviet Union responded by threatening war on Estonia, Latvia, Lithuania and Finland unless these countries signed a pact ceding parts of their territories. Finland refused, prompting the Soviet Union to invade in November of 1939.
In April of 1940, Germany invaded Denmark and Norway. In June, the Soviet Union broke its pact with Estonia, Latvia and Lithuania, occupying their territories entirely. In May, Germany launched an offensive against France, Belgium and the Netherlands. In June, Italy followed by declaring war on the United Kingdom and France, invading the latter. In November, Hungary joined forces with Gemarny, Italy and Japan.
With such monumental geopolitical unrest underway, no doubt war was on both mens’ minds throughout their collaboration. Both European men in their late 30s in 1940 they had lived through the First World War, in all its horror, as teenagers in Austria and Hungary. They had both left Nazi Germany in the 1930s (von Neumann in 1930 due to the persecution of Jews and Morgenstern in 1938 following the Anschluss). In other words, they had both been living with the consequences of war since they were children. This fact is bound to have had an impact on both mens’ outlook. Indeed, as von Neumann’s daughter has described in several places, including to me personally, “this very gregarious, fun, personality covered up a deeply cynical and pessimistic view of the world underneath”. Morgenstern too, in his own diary, at times reveals similar views, such as on March 4th 1940, when he wrote “Myrdal is a brilliant head […] How shocking from the mouth of such a person to hear the words ‘it makes me sad to live in this world; I don’t feel like doing it anymore’. How many times have I not literally said the same thing to myself”.
Overlapping Interests
In addition to sharing similar personal histories and personality traits, the two men also shared common interests. Biographies of von Neumann (of which there are multiple, but I recommend this* for novices) mention his passions for mathematics above all, but also his love of languages and history. As legend has it, the man conversed in Ancient Greek at age six and, in addition to his native Hungarian, was tutored in English, French, German and Italian. In an obituary that appeared in Life Magazine a friend of von Neumann also described his deep interest in European royal families and Byzantine history (Blair, 1957):
“He is a major expert on all the royal family trees in Europe. He can tell you who fell in love with whom, and why, what obscure cousin this or that czar married, how many illegitimate children they had and so on”
The most well known (potentially apocryphal) story about von Neumann’s interest in the latter goes as follows:
“One night during the Princeton days a world-famous expert on Byzantine history came to the von Neumann house for a party. ‘Johnny and the professor got into a corner and began discussing some obscure facet,’ recalls a friend who was there. ‘Then an argument arose over a date, Johnny insisted it was this, the professor that. So Johnny said, ‘Let’s get the book!’. They looked it up and Johnny was right. A few weeks later the professor was invited to the von Neumann house again. He called Mrs. von Neumann and said jokingly, ‘I’ll come over if Johnny promises not to discuss Byzantine history. Everybody things I am the world’s greatest expert in it and I want them to keep thinking that’.”
Although there are no comprehensive biographies of Morgenstern’s life, similarly as von Neumann, he seems to have shared his interests in language and history. As his former colleague Michael D. Godfrey recounted to me in 2021, upon meeting Oskar he had the impression of a man “Informed about everything. […] What ever I asked him, he knew—not only all about it—but who did what, why they did it. The point came where I tried to find something he would say he didn’t know anything about, and I never achieved that”. In many ways, the contents of Oskar’s diaries (which he kept from 1917 to his death in 1977) largely support this impression, as they are filled with commentaries of world events, history, politics, scientific observations—in addition to gossip, rumors and other minutia. Like von Neumann, he mastered several languages, including French, English and, at least superficially, Swedish, in addition to his native Austrian German.
Complementary Expertise
Although Morgenstern and von Neumann shared similar histories, traits and interests, their academic and professional disciplines could hardly be farther removed. von Neumann had worked on Hilbert’s program (with Hilbert himself and was there when Gödel ended it) while simultaneously helping to develop the mathematical foundations of quantum theory. He was about as accomplished a professional mathematician, both pure and applied, that had or has ever lived.
Morgenstern, on the other hand, appears to have been mathematically illiterate prior to his involvement in Menger’s Vienna Colloquium. He received private turing lessons in high school and pre-calculus mathematics from Wald as late as in 1935. As Morgenstern wrote in his diary on the 8th of November of that year:
“A lot of work in the office today, as usual. But, home in the evening. Mathematics again. One hour. Now, we are already differentiating. Wald thinks that in a year I will be ready to understand almost everything in mathematics.”
During the development of Theory of Games and Economic Behavior, Morgenstern’s proficiency appear to have been at the level of an undergraduate, as he in late August of 1941 wrote in his diary that “With set theory I get on quite well. Now I am calculating with cardinal numbers (transfiniter). Johnny gave me Hausdorff's book, which I will do after Fraenkel”.
Mathematics aside, Morgenstern certainly had expertises of his own. He was after all, a former Ph.D. student of Ludwig von Mises (1881-1973), co-founder (with Hayek) and former director of the Austrian Institute of Economic Research (WIFO), a university professor of economics and chief editor of the Zeitschrift für Nationalökonomie. Clearly fascinated and admiring of mathematics, Morgenstern also appears to have been an important cheerleader for the development of more advanced mathematics in economics (which, by the way, appears to have put him permanently at odds with the economics department at Princeton).
“One other major theme of his [Morgenstern’s] intellectual life was his spectator's fascination with the role and uses of mathematical formalisms. This rather set him apart from his Viennese colleagues in economics, who were under the sway of Mises's hostility to mathematics.” — Mirowski (1992)
Their critical view of economics too, thus, appears to have been common ground for the two men. As Morgenstern later in his life noted that “von Neumann was always amazed at the primitive state of mathematics in economics; he commented in the 1940s that if all economics texts were buried and dug up one hundred years later, people would think that the economics they were reading was written in the time of Newton” (Schotter, 1992 p. 104; Morgenstern, 1976).
Shared Acquaintences
By 1940, two also shared a common close acquaintance in fellow Princetonian Kurt Gödel (1906-78). As Morgenstern noted in his diary in March of 1940, “Gödel arrived from Vienna. Via Siberia. This time with wife. When asked about Vienna: 'The coffee is wretched.'“ (Sigmund, 2017). The two first met in Vienna in the early 1930s, as both attended meetings of the Vienna Circle. Later participants in Menger’s colloquium (Gödel starting in 1929, Morgenstern in the early 1930s), the two kept in touch throughout the decade and indeed, for the rest of their lives (see essay below).
von Neumann famously first met Gödel during the latter’s presentation of his incompleteness result at a mathematics conference in Köningsberg in September of 1930. He (von Neumann) took an immediate liking to Gödel, whom he would correspond with throughout the 1930s. von Neumann greatly admired Gödel and on several occasions lobbied to bring onto the IAS faculty.
Among other shared acquantances mentioned in Morgenstern’s diary are Menger, Einstein, Bohr, Oppenheimer, Weyl, Siegel, Milnor, Kakutani and others.
Their Collaboration (1940-44)
It is apparent from Morgenstern’s diaries that the two men developed a friendship, perhaps more so than anything else, in the years 1939-42. During Christmas of 1940, for instance, Morgenstern (still a bachelor) went on vacation in Louisiana and Mississippi with von Neumann and his wife Klára (“Klári”) after presenting a paper on unemployment at a session of the American Economic Association in New Orleans (Morgenstern, 1976). As Morgenstern later wrote, the majority of their work on The Theory (as their work is sometimes called) took place during these years “either at my apartment over the bank at 12 Nassau Street or at 26 Westcott Road where Johnny lived with his wife Klára and daughter Marina”. In intense periods, they would meet for breakfast at the Nassau Club “almost every day […] consuming quantities of coffee”.
Men in Opposition (1940-41)
We know that von Neumann never familiarized himself with the fundamentals of modern economics. Thus, in the early stages of their work, Morgenstern’s role was to supply von Neumann with criticism about established economic thinking (Rellstab, 1992). As Morgenstern wrote in his diary in October of 1940, “Recently lunch with Johnny. I told him about some criticisms of the theory of indifference curves and he agreed totally with me. He is also convinced that marginal utility is not eliminated.” As argued by historian Andrew Schotter and others, Morgenstern was by this point quite in opposition to the established neoclassical theory of the day. As his former colleague at Princeton Michael D. Godfrey told me:
“As I'm sure you know Oscar did not get along with the economics department at Princeton. Like at all. […] Most people who are classified as economists […] participate in the accepted methodology and content of economics. They just don't think about things the way Oscar did. They have beliefs that they adhere to that Oscar could point out were just obvious nonsense. And he tended to do that. People like Friedman who invented the consumption function. It's a great piece of work. Oscar would just say: that's bullshit.”
At other times, Morgenstern provided von Neumann with parallels between economic theories and his developing theory of games, such as the non-zero nature of most economic problems. From his diary: “Yesterday I showed him the contact curve; it stands in relation to his games because it makes a difference who goes first. He will think about all of this. Moreover, I showed him the causal relationships in Böhm-Bawerk’s price theory where, as one can easily see, one obtains different results, depending on the assumed knowledge of the other person’s position. It differs from a game because a profit is possible.”
From this perspective, Morgenstern’s contributions to The Theory are considerable, as he was the one suggesting topics and perspectives to von Neumann, rather than the other way around. As argued by Schotter (and supported by Godfrey in our conversations) “Morgenstern was a visionary, and his vision can be seen most clearly in the introduction to The Theory. […] The problem for economic science is shifted from a neoclassical world composed of myriad individual Robinson Crusoes existing in isolation and facing fixed parameters against which to maximize, to one of a society of many individuals, each of whose decisions matter. The problem is not how Robinson Crusoe acts when he is shipwrecked, but rather how he acts once Friday arrives. This change of metaphor was a totally new departure for economics, one not appreciated for many years.”
The period of ideation and intense discussions between the two men arguably lasted for about a year, from April 1940 until May 1941. In this period, von Neumann lectured on games both in Seattle (Summer ‘40) and Princeton (October ‘40) and wrote two related paper, entitled ‘General Foundations’ (October) and ‘Decomposition Theory’ (January ‘41).
By May of 1941, von Neumann was advising Morgenstern to (finally) write his paper on the ‘maxims of behavior’. A month later, von Neumann follows up by suggesting that they instead write a paper on games together. Morgenstern begins the work by writing an introduction to von Neumann’s papers for an audience of economists. This must have been a somewhat familiar task for him, as he in 1936 (as editor of the prestigious Zeitschrift für Nationalökonomie) had helped Abraham Wald with a similar task (of contextualizing mathematical findings to economics), see essay below.
The result of Morgenstern’s efforts was likely the paper
Morgenstern, O., 1941. Professor Hicks on value and capital. Journal of Political Economy, 49(3), pp. 361-393.
wherein Morgenstern lists his issues with marginal utility theory, citing the works of both von Neumann and Wald, the failures of the established “so-called ‘mathematical economists’ […] Walras, Pareto, Fisher, Cassel and hosts of later ones” and argues that “In economics we should strive to proceed, wherever we can, exactly according to the standards of the other, more advanced, sciences”.
The Paper Becomes a Pamphlet (Fall of 1941)
By August of 1941 Morgenstern describes working “a lot” and that “Johnny” “works very hard. All operation theory; he looks ailing sometimes. And the speed with which it goes; it's really scary. And he's so nice about it". Their intense collaboration continues, and in September the first draft of the first chapter of (what would become) TGEB is completed. As later Morgenstern recounted:
“As our paper progressed, we thought—always sitting together and writing jointly—that perhaps the paper might have to be still a little longer. Johnny said it might have to be published in two parts, one piece being too long for a scientific journal. I said that wouldn't matter to me at all; on the contrary, we should be as detailed as the subject matter required. So we began to work and as our work progressed, Johnny said: "You know, this will hardly do as a paper, not even in two parts. Perhaps we should make a small pamphlet out of it”.
Morgenstern notes that they briefly considered a 100 page version for publication, before von Neumann suggested “why don’t we go to the Princton University Press and ask them whether they would be interested in such a pamphlet?”. According to Morgenstern, the then-director of “The Press” was accommodating and they quickly reached an agreement of delivering a manuscript for a pamphlet of “about 100 pages”. As the work progressed, however:
“We completely forgot about any restriction to 100 pages and worked, thought, and discussed endlessly”.
A Wonderful Discovery (1941)
“At the time when we were about to write down a new proof for Johnny’s famous minimax theorem, originally developed in 1928, I went out for a walk on a brilliant, snowy cold winter day. I went towards the Institute for Advanced Study and since I was cold, I walked into the library, looking around idly. I picked up E. Borel’s Traité du Calcul des Probabilités, and there I saw in it suddenly a paper by Jean Ville dealing wih Johnny’s 1928 paper. Here, in restating Johnny’s minimax theory, insead of using Brouwer’s fixed point theorem, he gave a more elemenary proof.” — Oskar Morgenstern (1976)
If we take Morgenstern at his word, given the later reception of The Theory, this chance encounter was indeed quite important. As he later wrote: “From this date on (i.e., from 1944 on) stems the introduction of methods of convex bodies into the modern literature of economics“. Had it not been for their discovery of Jean Ville (1910-89)’s extension of von Neumann’s minimax theorem, in other words, the first expansive mathematical treatment of game theory (TGEB) would not include methods of convex optimization, and
“Many writings in other fields would have been retarded” — Morgenstern (1976)
By 1942, von Neumann had moved to Washington to work in a research office for the Navy. Their “pamhplet” was by this point quite well developed. Morgenstern visited him there frequently, while von Neumann would only occasionally travel back to Princeton. As they were quite busy (von Neumann was at this point working on what would become the Theory of Detonation Waves*, while Morgenstern was busy teaching “something like twelve to fourteen hours per week”). That being so, the two still managed to find time to converse about “Cambridge Ancient History” and “Thucydides”, “books we discussed extensively when not working on ‘the next chapter’".
As Morgenstern has described, they wrote together for the duration of their collaboration, by longhand, and he would spend the next day typing up two copies of everything they had written, putting in formulas, giving one copy to von Neumann and keeping one for himself. The work was done without financial or secreterial aid. Following a brief trip by von Neumann to England, on the 28th of December 1942, the two completed the final pages of their first draft:
“At Christmas we put the last touches to the manuscript and also wrote the preface dated January 1943, and it was in the very first days of January that we made the work final.”
Morgenstern’s later Ph.D. student Martin Shubik (1926-2018) in 1992 described the contents of the final book as:
“Four important separate pieces of work. They were (1) the theory of measurable utility; (2) the language and description of decision-making encompassing the extensive form and game tree with information sets, and then the reduction of the game tree to the strategic form of the game; (3) the theory of the two- person zero-sum game; (4) the coalitional (or characteristic function) form of a game and the stable-set solution. “
The Pamphlet Becomes a Book (1943)
“The people at The Press were quite overwhelmed seeing a manuscript of about 1200 typed pages full of graphs and uninhabited mathematical notations.” — Morgenstern (1976)
I believe I once read that J.R.R. Tolkiens’ Lord of the Rings was divided into three volumes to minimize financial losses due to the high cost of typesetting and printing in the 1950s. That work, at 1077 pages, indeed seems quite modest in comparison with the manuscript Morgenstern sent over the Princeton University Press in April of 1943. As he later described, “they were generous and said they would try very hard to publish the book (during World War II!)”. In order to do so, an edited “clean” version of the manuscript would have to be produced. The two were able to obtain “an enormous grant of $500 each” (about $9,000 in 2024) from their employers (Princeton and IAS) to cover costs associated with retyping and readying of the manuscript (including drawing of all diagrams by a draftsman at the National Bureau of Economic Research). “This was done and then a Japanese “enemy alien”, a young mathematician put in all the formulas from the original manuscript”.
“Johnny remarked in his usual manner that it is the fate of enemy aliens who are mathematicians to be punished for being enemies by having to put other people’s formulas into manuscripts”
Princeton University Press accepted the retyped manuscript without objections without it ever going to a referee. For the book to be published, however, Morgenstern had to reach out to “a friend, a well-known American” (John D. Rockefeller III) for financial support to cover the risk involved. The book went to print in the latter half of 1943 and was published on the 18th of September 1944.
“It will be a strange essay for economists, but it can be important. Very.”
—O. Morgenstern, July 25th 1941
Epilogue
Unlike von Neumann, Morgenstern is today remembered primarily for his work on The Theory of Games and Economic Behavior, as his later efforts in economics (such as On the Accuracy of Economic Observations in 1950, Predictability of Stock Market Prices in 1970 and Mathematical Theory of Expanding and Contracting Economies in 1976) never quite lived up to the monumental work he did with von Neumann.
Morgenstern would outlive von Neumann by 23 years. In his diary entry for September 5th 1970, he wrote “Dreamed of Johnny (seldom, but always good & then it moves me the whole following day or more). I think of him often — hardly surprising. What a shame that Carl couldn’t see him; however, he remembers “Janczi Baczi”. — What kind of time it was in P: Johnny, Weyl, Einstein, Bohr, Pauli, Siegel, etc. Dirac, — It is no longer the same. Only Godel remains. […] Of course one thinks that it was better in the past, but somehow it seems to me that objectively here.”
Three Books
More about the history of game theory (prior to von Neumann and Morgenstern’s 1944 book) can be found in these works:
Weintraub, E. R. 1992. Toward a History of Game Theory*. Duke University Press.
Dimand, M.A. & Dimand, R.W. 1996. The History of Game Theory, Volume I: From the beginnings to 1945*. Routledge.
Leonard, R. 2010. von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science, 1900-1960*. Cambridge University Press.
Urs Rellstab’s chapter in Weintraub’s 1992 book, ‘New Insights into the Collaboration between John von Neumann and Oskar Morgenstern on the Theory of Games and Economic Behavior’, is a wonderful resource, as is Philip Mirowski’s chapter ‘What were Von Neumann and Morgenstern trying to accomplish?’ and Andrew Schotter’s chapter ‘Oskar Morgenstern's Contribution to the Development of the Theory of Games’.
In writing these essays (on the von Neumann-Morgsenstern collaboration), I am immensely grateful to Leonard D. Godfrey, Robert Leonard, Guillermo Owen, Juan Carvajalino, Marina von Neumann Whitman, Karin M. Papp and above all, Carl Morgenstern, for generously sharing their time and expertise.
Thank you for reading Privatdozent, Have a great week!
Sincerely,
Jørgen
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References
Blair, C. 1957. Passing of a Great Mind. Life Magazine.
Morgenstern, O. 1976. The collaboration between Oskar Morgenstern and John von Neumann on the theory of games. Journal of Economic Literature, 14(3), pp.805-816.
Mirowski, P. 1992. What were Von Neumann and Morgenstern trying to accomplish?. Toward a history of game theory, 24(supplement), pp.113-47.
Schotter, A., 1992. Oskar Morgenstern's Contribution to the Development of the Theory of Games. History of Political Economy, 24(Supplement), pp.95-112.
Rellstab, U., 1992. New insights into the collaboration between John von Neumann and Oskar Morgenstern on the Theory of Games and Economic Behavior. History of Political Economy, 24(Supplement), pp.77-93.
Sigmund, K., 2017. Exact Thinking in Demented Times. The Vienna Circle and the Epic Quest for the Foundations of Science. Basic Books. New York, NY. pp. 215.
Shubik, M., 1992. Game theory at Princeton, 1949–1955: a personal reminiscence. Toward a history of game theory, 152.
von Neumann’s 1937 paper is called Über ein Oikonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes (“On a System of Economic Equations and A Generalization of Brouwer’s Fixed Point Theorem“).
Wonderful!