Das Werk des Mathematikers John von Neumann hat in der Wirtschafts- und Politikwissenschaft tiefe Spuren hinterlassen. von Neumann war im Sommersemester 1929 als Dozent an der Universität Hamburg tätig. Noch im selben Jahr nahm er eine Einladung nach Princeton an, wo er die folgenden Jahre lehrte und gemeinsam mit Oskar Morgenstern das Buch *The Theory of Games and Economic Behavior* (1944) verfasste. Unser Beitrag bietet einen Crash-Kurs in Spieltheorie und führt in ihre militärischen und politischen Rahmenbedingungen ein.

Matthew Braham ist seit 2017 Professor für praktische Philosophie an der Universität Hamburg. Seine Publikationen sind in *Erkenntnis, Mind* und dem *Journal of Philosophy* erschienen. Bevor er in Groningen und später Bayreuth Professuren übernahm, arbeitete er als Wissenschaftlicher Assistent im Fachbereich Volkswirtschaftslehre der Universität Hamburg. Dort war Matthew Braham (zusammen mit Manfred J. Holler) einer der Erfinder und Wegbereiter des Hamburger Masterstudiengangs in *Politics, Economics and Philosophy* (PEP).

John von Neumann was one of the twentieth century’s intellectual giants. He was born in Budapest on 28 December 1903 as the eldest of three sons in a well-off Jewish family. He became a naturalized US citizen in 1937. His “nobility” – the “von” in his name – was because his banker father received a minor title from the Emperor Franz Josef. His brilliance stood out at a young age, and his life was characterized by a legend of a very colourful personality. Story has it that at the age of eight he was familiar with calculus and knew Ancient Greek. Later he was notorious for his occasional binge drinking and reckless driving – a piece of road in Princeton was nicknamed “von Neumann Corner” for all the incidents that he had there while at the wheel. The source of the accidents was not, however, drinking, but singing which led to a wayward way of navigating corners – or so they say. John von Neumann’s life was cut short on 8 February 1957 by bone cancer, which was probably a result of his exposure to radiation at the Bikini Atoll nuclear tests which he took part in.

During his lifetime, von Neumann published over 150 papers in pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer design, and economics. He was not only a scientific genius, but also extremely engaged in academic management and politics. He served in government commissions and advisory committees that affected US government policy during and after World War II. In 1943, von Neumann joined the Manhattan Project that developed US nuclear bombs that were dropped on Japan in 1945. His role was crucial: he did the calculations for the implosion device of the atomic bombs, allowing for a more efficient and destructive explosion. His models were also used to select the targets and plan out the path of the bombers in order to reduce the chances of their being intercepted.

John von Neumann’s stint at the Universität Hamburg came 1929. It was a step between his *Privatdozentur* in Berlin and his permanent move to Princeton in 1930. He arrived in Princeton first on a visiting lectureship and then became a founding faculty member of what became a world famous School of Mathematics at the Institute of Advanced Studies when it opened its doors on October 2 1933 – and where he spent the rest of his career. During his short Hamburg period he worked on set theory, quantum physics, and operator theory.

It is outright impossible to write a pocket-sized review of von Neumann’s intellectual contributions and significance – just think, he was even instrumental in designing the first computer for detecting a nuclear attack on the US. What we can do, however, is focus on one area that is significant for the Politik 100 x 100 Blog. This is his undisputable relevance for political science and political theory. John von Neumann is considered the father of game theory. His *Economic Behavior and the Theory of Games*, a 600-page tome written together with Oskar Morgenstern and published in 1944 by Princeton University Press opened up a whole new methodological world for the study of political phenomena. It must be noted that he proved what can be considered as the cornerstone of his theory of strategic behaviour in an article he published the year before he came to Hamburg, although it was not a line of research he pursued here. That cornerstone is known as the “Minimax Theorem”. The title of that article was “Zur Theorie der Gesellschaftsspiele ” published in *Mathematische Annalen* in 1928.[1]

The MiniMax theorem says that for many two-person strategic interactions it is simply pointless to try to “play” the game in the sense of trying to strategically outwit others. If each player considers for each possible strategy available to them the maximum that they can expect to lose if they choose that strategy, and then decides to choose the strategy that minimizes the maximum loss, then each can be certain that they are minimizing their losses. If, and crucially, each player thinks this way, then each can make sure that what they get from an interaction is completely determined by the structure of that interaction itself (“the rules of the game”).

The idea was generalised later by John Nash – whose name is given to the so-called “Nash Equilibrium” solution concept. It is very much worth a mention here that the two Johns were not of one mind about Nash’s contribution. For von Neumann, Nash’s solution concept was in a sense “artificial” because it was too “individualistic”. At an informal conference on game theory in 1955, he criticized Nash’s approach for ignoring “the enormous variety of observed stable social structures; many differing conventions can endure, existing today for no better reason that they were here yesterday”.[2] It is certainly disputed that this criticism is sound. Nash’s equilibrium concept is more general than von Neumann’s own version because it accounts for both games of pure conflict *and* coordination, while von Neumann attention was confined to games of pure conflict. The artificiality charge cuts both ways.

In *Games and Economic Behaviour*, von Neumann (together with his co-author) laid the foundations of modern utility theory and hence what we now call “Rational Choice Theory”. This is none other than an account of how instrumentally rational agents (agents pursuing their own goals, be it good, bad, or ugly) should or do choose. Whether or not game theory is a descriptive or normative account of behaviour really depends on the problem we are interested in. The descriptive account asks, how can we model the decisions of such agents? The normative account asks, what should such agents do? Both are exercises in practical rationality. In both cases the same set of phenomena is studied: selection of states of the world with respect to the preferences (call this “utility”) of a type of agent (an instrumentally rational one).

Game theory is simply the extension of this idea of rational choice from decisions about what to do when faced with non-purposive and non-intentional events – “nature” – to decisions involving purposive events – the decisions of other instrumentally rational actors. And this is where the importance for Political Science kicks in. Game theory is a natural way of analysing that aspect of politics that concerns conflicts of interest – something that politics is really all about (although not exclusively so). And it is often revealing, because it studies the selection of states of affairs that might not even be intended or desired by any of the agents involved.

Game theory has had a wide set of applications in political science: from explanations of the social contract and the emergence of states to international relations, arms races, political competition, coalition formation, voting, and theories of justice and fairness. It has even found its way into Marxist scholarship. The branch known as analytical Marxism employs game theory to understand class relations and exploitation as well as revolutionary strategies. It is notable that since its inception in 1969, eleven game theorists have been awarded the Nobel Prize for Economics. All this and more, including developments in theoretical biology, is the result of the creative genius and endeavours of von Neumann – or, “Johnny” as he would happily answer to in America, while always insisting on the use of his nobility of his “von” (and never capitalized at the beginning of a sentence, an infelicity that would annoy him).

If there is one game that it is now impossible not to think about when reflecting on political phenomena it is the so-called Prisoner’s Dilemma. This is a simple model of the dilemmas of social interaction between two or more rational individuals pursuing their own interests (although it was not the product of von Neumann’s imagination, nor even of his interest). The “game” is in the following story:

Two gangsters, Row and Col, have been arrested for a serious crime. The district attorney gives them one hour to either confess or deny the charges. The district attorney, who took a course in game theory at university, explains that if both prisoners confess, each will be sentenced to ten years in prison. However, if one confesses and the other denies the charges, then the prisoner who confesses will be rewarded and get away with serving just one year. The other prisoner will get twenty years. Finally, if both prisoners deny the charges, each will be sentenced to two years. The prisoners are kept in separate rooms and are not allowed to communicate with each other.[3]

As is well-known, rationality á la von Neumann and Morgenstern dictates that each will confess the charges even though it will make both worse off given that they both want to minimize their term in jail. Descriptively and normatively (not necessarily morally) this can be questioned as the “correct” solution. One may ask, what use is such a framework of analysis if it can be shown to be false or implausible because the underlying assumptions about the capacity for rational behaviour can be disputed?

The answer is actually quite straightforward and easy to overlook. It is the framework – the methodology – and its generality that are important. When we get ourselves into thinking like “Johnny”, so cogently formulated in the opening lines of “Zur Theorie der Gessellschaftsspiele”:

*n* Spieler, *S*_{1}, *S _{2}*, . . . ,

*S*, spielen ein gegebenes Gesellschaftsspiel,

_{n}*G*. Wie muß einer dieser Spieler,

*S*, spielen, um dabei ein möglichst günstiges Resultat zu erzielen?[4]

_{m}This question is certainly reasonable and straightforward for the study of politics (this does not say all politics can be reduced to such questions, although clearly some may believe so). It seems true to say in von Neumann’s own words, that, “there is hardly a situation in daily life into which this problem does not enter”. Politics is no different. That is, social life emerges out of a mix of skill and chance. What von Neumann offered us with the development of game theory was to introduce a structured and simplified way to think about skill and chance and how they bring about worlds we live in. The starting point is the observation that our social world is a construction: made in part by individual agency. Game theory is a way of thinking about this construction to generate explanations and predictions of people’s choices in strategic situations. And, that is what much of the business of politics is all about (certainly much of its bluff and bluster). It is of note that none other than that foremost advocate of structuralism in anthropology, Claude Lévi-Strauss, referred to *Games and Economic Behavior* as a paradigmatic example of structuralist social science.

Whenever we read a game theoretic analysis – pure or applied – we should always keep in mind what the cultural and historical currents were that led to its emergence and development. John von Neumann belonged to a *Mitteleuropean* culture of mathematics and science that emerged in the early twentieth century and whose protagonists were enthralled by the idea of the unity of science. And that culture suffered through two great calamities. Game theory emerged in, and from, this milieu as one of the strands of thinking about how to understand what had happened. The belief was that a new mathematics of society might indeed provide practicable answers. As much as von Neumann was driven by his love of mathematics, he was also driven by practical concerns of the world around him. His development of the theory of games was motivated by both his desire to understand the practical rationality of abstract theoretical problems of bluff and bluster, for example in poker games, as well as the problem of finding a way in which we could steer the future away from havoc that the bluff and bluster of politics can wreak on the world. The destruction of this culture is recorded in his letters and is a vivid reminder of the human catastrophe that von Neumann lived through.

Despite this historical and cultural context, John von Neumann was certainly no angel. His thinking, directly, and indirectly was highly influential in the RAND Corporation, a strategic think-tank set up in 1948 to provide advice to the US Armed Forces. As part of his involvement in developing US Cold War strategy von Neumann became a proponent of a pre-emptive nuclear strike against the Soviet Union to prevent an even worse nuclear war. He was, so to speak a Cold War Warrior and later the author of the strategy of “mutually assured destruction” that carries the appropriate acronym that “Johnny” himself takes credit for: MAD. It is because of this that he has been engraved into popular culture. John von Neumann is apparently immortalized as Stanley Kubrick’s *Dr Strangelove* (von Neumann spent the last couple of years of his life in a wheelchair).

Game theory has been an enormously productive project in the science of society. We find political scientists, economists, and philosophers all applying his framework – and no less so than here at the Universität Hamburg. On the 8th November 2019, the Deutsche Forschungsgemeinschaft (DFG) approved a major interdepartmental (political science, economics, philosophy) application for a Research Training Group (Graduiertenkolleg) on Collective Decision-Making. One of the central methods? Game theory.[5]

[1] John von Neumann, Zur Theorie der Gesellschaftsspiele, *Mathematische Annalen* 1928, 100(1), pp. 295-320.

[2] Robert Leonard, *Neumann, Morgenstern and the Creation of Game Theory: From Chess to Social Science 1900–1960*, Cambridge University Press (2010), p. 245.

[3] Martin Peterson (ed), *The Prisoner’s Dilemma*, Cambridge University Press (2015), p. 1.

[4] *n* players *S*_{1}, *S _{2}*, . . . ,

*S*are playing a given game of strategy,

_{n}*G*. How must one of the participants,

*S*, play in order to achieve a most advantageous result?

_{m}[5] This essay draws its biographical information on John von Neumann from the following sources: Giorgio Isreal and Millán Gasca, *The World as a Mathematical Game*:* John von Neumann and Twentieth Century Science*, Birkhäuser (2009); Robert Leonard, *Neumann, Morgenstern and the Creation of Game Theory: From Chess to Social Science 1900–1960*, Cambridge University Press (2010); Norman Macrae*, John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. *Pantheon Press (1992); William Poundstone, *Prisoner’s Dilemma*, Anchor Books (1992). I would like to thank Manfred J. Holler for his insightful comments.