The von Neumann-Morgenstern Collaboration (1938-43)

“It will be a strange essay for economists, but it can be important. Very.”

Left: Morgenstern and von Neumann at the beach wearing suits (Photo: unknown). Right: Colorized photograph of Morgenstern and von Neumann at the beaching eating lunch (Photo: Courtesy of Karin Papp)

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).

John von Neumann’s Minimax Theorem (1928)

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.

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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.”