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# Oskar Morgenstern's Transformation (1925-38)

### The austrian economist who fell in love with mathematics

Unlike his collaborator John von Neumann (1903-57), economist Oskar Morgenstern (1902-77)’s name today remains synonymous with more-or-less a single work: the book *Theory of Games and Economic Behavior** which the two co-authored in the war years from 1940-44. An economist by training, Morgenstern had prior to the 1944 work never before published any mathematical papers or written even a single mathematical proof. Then in 1944, seemingly out of nowhere, comes a highly technical brick of a book at 625 pages co-authored by Morgenstern in his and von Neumann’s first (and only) collaborative effort.

This week’s newsletter is about Oskar Morgenstern’s transformation from an Austrian political economist in the 1920s to the co-inventor of game theory in the 1940s.

## Morgernstern’s Early Life (1902-25)

Oskar Morgenstern was one year von Neumann’s senior, born in 1902 about 500 miles from Budapest in the provincial town of Görlitz in the Kingdom of Prussia, which by then was part of the German Empire. His father Wilhelm is described by historian Robert Leonard as a businessman and merchant* *(Leonard, 2004), although Oskar described him as more of a “ne'er-do-well” who at times seemed unable to hold a job.

“On my father’s side, my family gos back to about 1530 in Saxony, my Lutheran forebears having been farmers, church wardens, judges, and businessmen”—Oskar Morgenstern

Oskar’s mother Margarete (born Teichler) was one of several illegitimate daughters of the Prussian Emperor Frederick III, a member of the Hohenzollern Dynasty (Sigmund, 2017). There seems to have been *“some sort of settlement from the Emperor to acknowledge her (Margarete’s) status”*, but her husband Wilhelm, “Willy”, apears to have squandered the money. This left the Morgenstern family to* *nearly starve to death following the Austro-Hungarian Empire’s defeat in World War I.

“There was no food. His [Oskar’s] mother would have a tiny little bit of food and portion it out to the kids, and I guess her husband, eating very little for herself”—Carl Morgenstern

By that point, the family had moved to Vienna where Oskar’s father Wilhelm secured a job for the coffee and tea importer Julius Meinl and Co., eventually leaving the family modestly comfortable (Leonard, 2004).

Beyond this, not much is known for certain about the early years of Oskar’s life. As he later described, his memories of the tumultuous period were fragmented. We don’t know why the Morgensterns decided to leave Görlitz in 1914, although the mobilization of German troops for war may have played a part.

In Vienna, Morgenstern attended *gymnasium* (“high school”)* *which seems to have been a *“real, no bullshit education”, *according to his son Carl.* “Strong and strict. He learned a tremendous amount of things in the gymnasium.” *including* “Latin and Greek, to some unknown proficiency”*. Oskar also picked up Swedish, having been sent to Sweden with his sister Hannah during the summers of 1921-22, likely due to an outbreak of tuberculosis in Vienna.

### In University (1922-25)

Although having done poorly in mathematics—supposedly having to repeat one class—Morgenstern was nonetheless accepted to the University of Vienna to pursue a *Dr. rer. pol*. degree in 1922. Nominally a degree in political science, this allowed him to do work in economics (Sigmund, 2017) which, as a field of study, in Europe at the time was a field closely intertwined with politics. A very social and extroverted student, Morgenstern in the 1920s become acquainted with many of his fellow economics students, faculty members and other figures of Viennese culture. He attended meetings of the logical-empiricist discussion group the Vienna Circle during the Moritz Schlick (1882-1936) “phase” from 1924-28, where he met both Felix Kaufmann (1895-1949) and Karl Menger (1902-85). He also came to know Joseph Schumpeter (1883-1950), after meeting him in a coffeehouse. As retold by Allen (1991): “*After conversing amiably for some time, Schumpeter invited Morgenstern to his mother’s apartment at Doblhofgasse 3. Frau von Kéler greeted the young men and served tea and cakes, as would be expected. But when the conversation lulled, Frau von Kéler turned off all the lights and played the polonaise and other Chopin pieces on her piano in the dark”. *

## Austrian Economics

A Ph.D. student of Ludwig von Mises (1881-1973), Morgenstern more-or-less by default joined the economic circles of the Austrian School (of economics) as a fourth generation member. His advisor, von Mises (third generation) was also the Ph.D. advisor of Friedrich Hayek (1899-1992), who was three years Oskar’s senior. Known for his arrogance and big-headedness, von Mises claimed that he had personally saved Austria from Bolshevism, writing in his memoir *“This event was all to my credit, and mine alone”*. He also claimed to have delayed the Great Depression by ten years. The older brother of mathematician and a founding member of the Vienna Circle Richard von Mises (1883-1953), the two von Mises brothers supposedly couldn’t stand one another (Sigmund, 2017).

Both von Mises and his star pupil Hayek (a remote cousin of Ludwig Wittgenstein) were die-hard liberals in the classical sense, advocating for economic freedom above anything else. In 1927, the two founded the Austrian Institute of Economic Research (WIFO) which Hayek and Morgenstern co-directed until the former left for the London School of Economics (LSE) in 1931 (Leonard, 2010).

Despite being surrounded by people who were, Morgenstern was never a free marketeer in the vain of von Mises, Hayek and most of other members of the Austrian School. Founded during the Austrian Empire of the late 19th century, credit is often given to economist Carl Menger (1840-1921), especially for his work *Principles of Economics* (1871) which to this day serves as one of the bibles of Austrian economics. The book is considered the first modern treatise to advance the theory of marginal utility. Unlike Karl Marx (1818-1883) and others, Menger advanced the idea that the marginal utility of goods (benefit derived from consumption), not labour inputs, was the source of their value. This perspective allowed for a plausible theoretical answer to the so-called diamond-water paradox which asks why diamonds are more highly valued than water, when the latter is on the whole more useful than the former. Unlike neoclassical economists, Menger emphasized uncertainty rather than perfect rationality in the making of economic descisions. Thus, he agreed with economist/sociologist Thorstein Veblen (1857-1929)’s critique of the neoclassical “economic man”, *homo economicus*, described by the latter as:

“A lightning calculator of pleasures and pains, who oscillates like a homogeneous globule of desire and happiness under the impulse of stimuli that shift him about the area but leave him intact. He is an isolated, definitive human datum, in stable equilibrium except for the buffets of the impinging forces that displace him in one direction or another”— Veblen (1898)

### Wirtschaftsprognose (1926-28)

Morgenstern’s dissertation, simply entitled *Wirtschaftsprognose* (“Economic Forecasting”), presented a mixture of two schools of thought. The central claim of the dissertation is that economic forecasts are fundamentally impossible. His circular argument goes as follows (simplified):

Any intelligent economic agent will react to a forecast. That reaction will have to be anticipated when the forecast is made. The agent would take this into account, which would also have to be anticipated, and so on.

On the one hand, Morgenstern’s argument stresses uncertainty. On the other, the source of the uncertainty in his argument is a result of the actions of rational agents. The conclusion of his argument may thus be said to be inspired by Menger and the Austrian school, but the argument itself is very much not. Indeed, both in its content and phrasing, Morgenstern even in 1926 appears to have been sympathetic to classicism, perhaps even neoclassicism.

In 1928, Morgenstern turned his dissertation into a book entitled *Wirtschaftsprognose, eine Untersuchung ueber ihre Voraussetzungen und Moeglichkeiten *(“Economic Forecasting, An Examination of its Requirements and Possibilities”). It was published by Springer in Vienna. He had written it in 1926-27 while spending a year at Harvard University as an Honorary Research Fellow supported by a luxurious three-year travel grant provided by the Laura Spelman Rockefeller Memorial (Universität Wien, 2021). In the book, Morgenstern again employs his circular argument for the impossibility of economic forecasting using what has later been called the “Morgenstern Paradox”. In it, he uses the plot and characters from Doyle’s* The Memoirs of Sherlock Holmes: The Final Problem *(1893) as a narrative device:

The Morgenstern Paradox (1928)

“Sherlock Holmes, pursued by his opponent, Moriarty, leaves London for Dover. The train stops at a station on the way, and he alights there rather than traveling on to Dover. He has seen Moriarty at the railway station, recognizes that he is very clever and expects that Moriarty will take a faster special train in order to catch him in Dover. Holmes' anticipation turns out to be correct.

But what if Moriarty had been still more clever, had estimated Holmes' mental abilities better and had foreseen his actions accordingly? Then, obviously, he would have travelled to the intermediate station. Holmes, again, would have had to calculate that, and he himself would have decided to go on to Dover. Whereupon, Moriarty would again have "reacted" differently.

Because of so much thinking they might not have been able to act at all or the intellectually weaker of the two would have surrendered to the other in the Victoria Station, since the whole fight would have become unnecessary.”

Morgenstern later wrote that he in the book “*showed in some detail in particular that the pursuit developing between these two could never be resolved on the basis of one of them out-thinking the other (‘I think he thinks that I think …’), but that a resolution could only be achieved by an ‘arbitrary decision’ and that it was a problem of strategy” *(Morgenstern, 1976). However loosely, Morgenstern thus appears to—even as early as in 1926—have made attempts to present his argument in a formal statement which might be amenable to proof by someone with formal training in mathematics. He himself, was not that person. As Leonard (1992) writes, *“Morgenstern remained personally incapable of taking the theoretical steps that he himself envisioned .. in his continuous agitation for mathematical rigor, he was ultimately calling for a theoretical approach in which thinkers of his own kind would have increasingly little place”.*

## A Fascination with Mathematics (1925-38)

Morgenstern’s philosophical disagreements with the Austrian School (including his advisor von Mises and friend Hayek) grew as he completed his Ph.D. dissertation and left for Harvard via England in 1925. As Leonard (2010) writes, by the time he returned to Austria in 1927, Morgenstern had *“read the works of Edgeworth, Bowley and Whitehead, even meeting with several of them during his travels”*. He went to see Francis Y. Edgeworth (1845-1926) in Oxford, having read his *Mathematical Psychics* (1881) and discovered Edgeworth’s notion of a contract curve representing the points at which final allocation of two goods between two people can occur as a result of trade from an initial allocation. Edgeworth was even at that point considered a highly influential figure in the development of neoclassical economics, and the first to apply formal mathematical techniques to model individual decision making. He is most known now for his contributions to the development of utility theory, the indifference curve and his famous Edgeworth box. Upon their meeting, Morgenstern is said to have *“expressed great pleasure at the publication of his collected papers, urg[ing] him repeatedly to republish Mathematical Psychics, then totally out of print”. *Edgeworth died shortly after their meeting, in 1926. While at Harvard, Morgenstern also frequented private seminars held by Alfred North Whitehead (1861-1947). Whitehead, of course, was the Ph.D. supervisor and co-author of Bertrand Russell (1872-1970) and his famous *Principia Mathematica*.

Although both influential in the history of economics, Whitehead and Edgeworth would not have been the most obvious candidates for the admiration of a student of Ludwig von Mises. However, by that time Morgenstern had grown quite disenchanted with many of his fellow economists, especially those identifying strongly with the Austrian school—which more or less disavowed the use of mathematics in economics. As he wrote in 1976, *“When I became a Rockefeller Fellow, I was a product of the Austrian School of Economics […] But I was constantly troubled by the fact that Böhm-Bawerk’s theory of bargaining and the “marginal pars”, while dealing with fundamentals, could not be considered completed”*. As Leonard (2010) writes, Morgenstern was “*an outlier. Even as a young economist, he was keen to emphasize his differences with the central figures of the Austrian community, including Mises, Mayer and Hayek, as a result of which he sought alliances with others”.*

During a stay in Italy in 1928, Morgenstern wrote in his diary about going to a mathematical conference attended by David Hilbert (1862-1943), Hermann Weyl (1885-1955), Emile Borel (1871-1956) and Oswald Veblen (1880-1960), son of Thorstein. Given that he had never had any formal training in mathematics, it is unclear what benefit the discussions at the conference could have been to him. He did write about the experience in his diary more than 40 years later, reminiscing that *“Hilbert was a great mathematician but not a pleasant person. I remember the Congress in Bologna in 1928 & how he, his wife & I happened to drive from Milan to Zurich, ate together in the dining car etc. I was of course “overawed” at the time (26!) But asked a few things about axioms & had just spent a few weeks beforehand, partly in Cannes, studying Hilbert-Ackermann’s logic, which was crucial for me.” *

Hilbert and Wilhelm Ackermann (1896-1962)’s 1928 book *Grundzüge der theoretischen Logik* (“Principles of Mathematical Logic”) is a highly technical book on elementary mathematical logic, grounded in first-order logic. As C. H. Langford wrote in his 1930 review, the book *“deals with mathematical logic very much after the fashion of the first volume of the Principia Mathematica”*. Again, Morgenstern’s benefit from reading the text is unclear. Russell’s *Principia Mathematica, *a similar text, is renowned for its rigor which, among other results, grounded the theory of addition to logic by proving—in no less than thirty pages—the validity of the proposition 1+1 = 2. As Langford writes:

“The authors begin with a treatment of the theory of elementary functions of propositions, and go on, in their second chapter, to a consideration of the logic of classes and its application to the traditional syllogism; they then take up a discussion of general propositions that involve a use of the notions "some" and "all" as applied to variables denoting individuals.“

What does seem clear, is that Oskar Morgenstern by 1928 was quite enchanted with mathematics. In particular, perhaps, he was enchanted with the idea of applying mathematical techniques to the understanding of economic and strategic phenomena ala his Sherlock Holmes scenario.

“In a 1931 overview of the field of mathematical economics for the Encyclopaedia of the Social Sciences, Morgenstern wrote that there was no reason why mathematicians might not be applied to the social sciences and to economics in particular”—Leonard (2010)

Simultaneously, as time wore on he was growing increasingly disenchanted with Austrian economics. In early 1929, he was ranting in his diary about von Mises, writing that he was sick of his “*worn-out methodology” *and arrogance, finding his “*concluding talk especially […] just impossible”.*

#### Karl Menger’s Influence

Some time in the 1920s, Morgenstern was introduced to Carl Menger’s son, whose somewhat uninspired name, Karl Menger (1902-85) is often a point of confusion. Karl (the son) was the same age as Morgenstern and also attended the University of Vienna in the early 1920s. He had entered the university intending to study physics, however switching his focus to mathematics after attending a lecture of Hans Hahn (1879-1934)’s on *Neueres Über den Kurvenbegriff *(“What is New Concerning the Concept of a Curve”). A Ph.D. student of Vienna Circle co-founder Hahn, Karl received his doctorate in 1924 with a dissertation on the topic of *Über die Dimensionalität von Punktmengen* (“On the Dimensionality of Point Sets“). *Simultaneously—*at 20 years old—following the passing of Carl, he completed his father’s unfinished manuscript for the second edition of the book* Principles of Economics*, which was published in 1922. Even by that point, he (Karl) had thus also gained a considerable expertise in economics.

After receiving his doctorate in 1924, Menger became a *dozent* at the University of Amsterdam, working with L.E.J. Brouwer (1881-1966), who had proved the important fixed-point theorem which would later be employed by von Neumann to provide a purely topological proof of the existence of general competitive equilibria in strategic games. Karl returned to the University of Vienna as a professor of mathematics two years later, in 1927. That same year, he also became a member of the Vienna Circle. The following year, in 1928, Menger started his own colloquium, on topics within mathematics. Often referred to as simply “Menger’s Colloquium” or the “Vienna Colloquium”, it ran for ten years until the *Anschluss* of 1938 forced its disbanding. The group’s bi-weekly meetings included “*a mixture of lectures, discussions of unsolved problems and reviews of recent work”. *Menger published proceedings of the colloquia in the years from 1929-37 through either Taubner or Deuticke, whose eight issues included many contributions by highly respected mathematicians but suffered from limited distribution (Abbott, 1999). Few complete copies thus remain. Included in the proceedings were contributions from, among others,* *Eduard* *Čech (1893-1960), Gödel, Karl Popper (1902-94), Alfred Tarski (1901-83), Olga Taussky-Todd (1906-95), von Neumann, Norbert Wiener (1894-1964) and Abraham Wald (1902-1950).

In the mid-1930s, Morgenstern was invited to a meeting of the Vienna Circle by Schlick to give a discussion on the “Morgenstern Paradox”, which he again had employed to illustrate the problems of economic foresight in his 1935 paper *Vollkommene Voraussicht und Wirtschaftliches Gleichgewicht* (“Perfect Foresight and Economic Balance“) in the prestigious *Zeitschrift für Nationalökonomie*, which Morgenstern also served as editor of from 1930-38:

“This I did in a rather lengthy session, and the matter was discussed by many of those present in great detail. To the Vienna Circle belonged, in one way or another, Carnap, Feigl, Frank, Gödel, Hahn, Menger, Popper, Waismann, etc. Not all of them were present on this occasion.” —OskarMorgenstern (1976)

Following the talk, Menger (who was present) asked Morgenstern to repeat his lecture at his (Menger’s) colloquium, which was attended primarily of mathematicians.

Morgenstern attended the colloquium, afterwards being approached by Čech who* “said that the questions I had raised were identical with those dealt with by John von Neumann in a paper on the theory of games in 1928. Čech, then already a promising mathematician, outlined to me its principal ideas and results and was very eager that I should study this particular work.” *The paper Čech was referring to was, of course, von Neumann’s 1928 paper *Zur Theorie der Gesellschaftsspiele* (“The Theory of Games”) containing von Neumann’s proof of the minimax theorem.

In 1929, Morgenstern was appointed *privatdozent* of political economics at the University of Vienna. Two years later, in 1931, despite their differences, he succeeded Hayek at the Austrian Institute of Economic Research (WIFO).

#### Abraham Wald’s Influence

As director of WIFO, Morgenstern eventually came to hire Abraham Wald (1902-1950) as a statistician. Wald was a Hungarian mathematician who had been home-schooled by his parents until college. This because the Hungarian school system required that students attend school on Saturdays, which Wald couldn’t because he was a religious jew who observed *Shabbat*. In 1927, he became Menger’s student at the University of Vienna. As retold in Leonard (2010), *“Abraham Wald had first knocked on Karl Menger’s door at the University’s Mathematical Institute in the autumn of 1927. […] He was particularly interested in geometry, he told Menger, and had been reading Hilbert’s Grundlagen der Geometrie, in which he thought improvements could be made by dropping some postulates and relaxing others. […] Wald registered at the University, but was not seen for more than two years, as he did not attend classes, having to serve in the Romanian army. Early in 1930, he reappeared […] Within a month he had characterized “betweenness” in the ternary relations in a metric space, yielding four publishable papers”. *Despite his lack of both attendance and funding,* *Wald would graduate with a Ph.D. in mathematics from Vienna in 1931. His interests in mathematics—according to Morgenstern’s obituary of him published in *Econometrica* in 1951—were in *“metric spaces, set theory and differential geometry”*, and many of his papers in the period 1931-36 were published in the proceedings of Menger’s colloquium.

As Wald was unable to obtain a position in Viennese academia (on account of his religion and nationality), Menger eventually reached out to Morgenstern to hire him at WIFO as a statistician. He did so in 1933.

“Like everyone else, I was captivated by his great ability, his gentleness, and the extraordinary strength with which he attacked his problems”— Oskar Morgenstern, 1951

Under Morgenstern’s directorship, WIFO had sponsored a series of lectures on “Mathematics of Economists”, given by Menger with help from both Wald and Franz Alt (1910-2011) (Sigmund, 2017). Morgenstern likely attended these lectures, and would later be tutored by both Wald and Alt in basic mathematics such as algebra and differential calculus.

While working as a researcher at Morgenstern’s institute, in addition to continuing to publish work in pure mathematics, Wald also began working on papers dealing with systems of equations in mathematical economics, including production and exchange variants of the Walrasian general equilibrium equation systema and the Cournot duopoly model (Leonard, 2010). By early 1935, Morgenstern was writing the Rockefeller Foundation—which had provided a grant for Wald’s position—praising his statistical and mathematical work, noting that there was *“still very much purifying to be done”* within mathematical economics (Morgenstern, 1935):

“On the basis of the experiences of the last years I have worked out a program for research which I beg to outline briefly. […] I am absolutely convinced that abstract theoretical work, even making use of mathematical analysis or of the modern methods of Logic that have not yet been applied o Economics, are just as necessary as the systematic collection of facts.”

By the end of 1935, Wald was assuring Morgenstern in writing that he too would *“soon understand nearly everything in mathematical economics”* (Leonard, 2010).

When asked about Morgenstern’s contribution to mathematical economics, his former Ph.D. student, game theorist Martin Shubik (1926-2018) is said to have replied (Rellstab, 1992 p. 77):

“Abraham Wald and John von Neumann. […] If that had been Morgenstern’s only contribution to economics in my estimation that would have been enough and would have been a contribution considerably larger than many of his peers […] It was Morgenstern’s ability both to see the relevance of the work of these two great mathematicians and to persist in getting them to work on problems of economic significance.”— Martin Shubik

## A Missed Opportunity (1937)

In 1937, Menger again urged Morgenstern to attend his colloquium, when a special guest, John von Neumann, was set to speak on his theory of an expanding economy. “*Unfortunately*”, due to his responsibilities at WIFO, Morgenstern was away in Geneva to attend the League of Nations committee meetings, thus the two did not meet. Indeed, it would be more than a year until they finally did, in Princeton, New Jersey in 1938.

This is the first in a series of essays on the von Neumann—Morgenstern Collaboration and the invention of game theory, featuring exclusive interviews with Carl Morgenstern, Marina von Neumann Whitman, Robert Leonard, Michael D. Godfrey and others.

Those interested in learning more about the history of game theory are encouraged to acquire the following books:

**Weintraub, E.R. (1992).***Towards a History of Game Theory**. Duke University Press**Dimand, M.A. & Dimand, R.W. 1996**.*The History of Game Theory**, Volume I. Routledge.**Leonard, R. J. (2010).***Von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science**, 1900–1960. Cambridge University Press.

Thank you for reading Privatdozent. Have a great weekend!

Sincerely,

Jørgen

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The Unparalleled Genius of John von Neumann, May 19th 2021

Gödel’s Constitutional Quarrel, June 14th 2021

Kurt Gödel’s Brilliant Madness, June 21st 2021

The Duties of John von Neumann’s Assistant in the 1930s, July 11th 2021

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## References

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