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Review of:

Robert Leonard
Von Neumann, Morgenstern, and the Creation of Game Theory


By: Nicola Giocoli
Università di Pisa
[Review online on March 29th, 2011]

 

In this much-awaited volume, the historian of economic thought Robert Leonard presents the results of his two-decade-long research on the life and intellectual achievements of the two founders of modern game theory, the Hungarian mathematician John von Neumann and the Austrian economist Oskar Morgenstern. The end result was well worth the wait because Leonard has produced a fascinating book which should be recommended first and foremost to economists and game theoreticians, even more – for reasons that will be detailed at the end of this review – than to historians of economics.   

The central thesis of the book is straightforward: in order to explain the creation and initial character of game theory we have to look at its founders “as flesh-and-blood figures”, fully immersed and personally involved in “the cultural and political context of fin-de-siècle and interwar Europe.” (p.2); that is to say, a mere examination of the formal content and properties of their new theory, which would be typical of a pure rational-reconstruction-style approach to the history of economic thought, would fall very short of providing a correct characterization of the motivations and events leading to the publication of Theory of Games and Economic Behavior (TGEB thereafter), the 1944 classic which officially marked the beginning of modern strategic analysis. Only a “thicker” historical approach may do the trick, and this is a simple lesson that historians now know all too well after more than two decades of debates about “thin” versus “thick” historiography, but that very few economists keep in mind when they compare, or apply, alternative theories or models without considering the wider context and motivation within which those theories and models were developed and could only find their raison d’être.   

The book is made of three parts. The first two are dedicated to the European part of the life and academic career of, respectively, von Neumann (Part I, Chs.1-4) and Morgenstern (Part II, Chs.5-8). Yet, in these chapters Leonard goes much beyond a mere biographical account as he manages to draw a truly fascinating picture of the Hungarian and Viennese societies during the turbulent interwar years. In the case of Hungary the focus is in particular on its lively mathematical community, which played so big a role in the intellectual formation of the young von Neumann, and on the mathematicians’ special position within Hungarian society. Especially interesting —and a true novel contribution— is the first chapter, dedicated to the early 20th-century world of chess and chess players in Continental Europe and to the deep interactions of this world with the German and Hungarian mathematicians. Leonard’s goal in these pages is clear, and exemplary of his historical method: it was not just a matter of analytical convenience, but a direct consequence of the status and popularity of chess in high-brow mathematical circles, that the very first instances of game theoretic analysis by German-speaking mathematicians (like Zermelo’s famous 1913 paper) tackled a kind of mathematical problems (say, demonstrate the existence of a winning strategy) which were peculiar of chess, or chess-like, situations. Similarly, the chapters about Vienna focus on the ongoing academic struggles at the local University, which deeply affected Morgenstern’s formative years as a student and a would-be economist. Here, even more than in the case of Hungary, the narrative thread is provided by the social and political upheavals of the period, chiefly among them the spread of anti-Semitism and the rise of Nazism. Indeed, Leonard shows how politics was barely hidden behind the fierce rivalries among the various prima donnas of interwar Vienna economics (Spann, Mayer, Mises), all of whom exercised a major impact on Morgenstern.  

The book’s main thesis already comes to the surface in these first two parts, despite their dealing with events all preceding the TGEB. Both the interest of the young mathematical genius for applying formal methods to strategic analysis and the unease of the young economist with the various strands of economic theories he had been exposed to in Vienna can be traced back almost entirely to the powerful scientific, social and political stimuli to which von Neumann and Morgenstern had been exposed in those very years. Indeed, Leonard brilliantly reconstructs the, sometimes quite thin and not entirely intuitive, filiations of ideas that —as he claims— turned out to affect the two protagonists of his story. A couple of examples may be: i) the thread going from the various approaches to the playing of chess —is the game art or science?— up to the mathematics of von Neumann’s 1928 foundational paper and his polemics against the French mathematician Borel, or, ii) the sequence which starts from the debate over the foundations of mathematics, goes through Brouwer’s Intuitionism and Karl Menger’s social combinatorics, and culminates with the shaping of Morgenstern’s methodological dissatisfaction with equilibrium economics. But regardless of the main historiographic point, and leaving aside the high scholarship they contain, the chapters in the first two parts are simply great reading —a masterful example of historical novel. Indeed, when the reader gets to the dramatic eighth chapter (which ends with the 1938 Anschluss), she is really captured by Leonard’s ability to transmit the feeling of the imminent, yet unstoppable, tragedy.   

The third part (Chs.9-13) reconstructs the interaction between von Neumann & Morgenstern after their migration in the US, the process that led to the publication of the TGEB, as well as the wartime and early postwar applications of the new discipline (the latter taking place within the Cold War context).  In the first block of chapters (Chs.9-11), Leonard’s narrative reaches its climax. These pages aim at persuading the reader that von Neumann’s somehow surprising return to game theory following the outbreak of WWII ­—a return that, independently of his encounter with Morgenstern, would lead him to the drafting of the two 1940-41 manuscripts which contained the gist of the TGEB— was justified by his sense of despair about the falling apart of the world in which he had been nurtured (a sense well documented by the touching personal correspondences quoted in the book), as well as by the moral imperative to apply his exceptional analytical power to try devise a rational recipe which a society made up of selfish individuals could apply in order to avoid self-destruction and reach an acceptable degree of stability.

Leonard builds quite a lot upon the sociological interpretation of the main solution concept proposed in the TGEB, the stable set, and upon the related idea that this interpretation (the stable set as a paradigm for social resilience to inner and outer attacks) might in some sense satisfy von Neumann’s urge to “do something” in the wake of the European catastrophe. However, sometimes Leonard seems to build too much on that. For example, he hardly mentions that, important as it may be in the TGEB, the stable set notion is founded on an even more basic concept of rational behaviour, namely, the minimax criterion, which dates back to the 1928 paper and which embodies a very peculiar notion of rationality-as-prudence, or rationality-as-autonomy, whose origin and justification in von Neumann’s thought is left unexplained. Moreover, it is odd that the locus magnum of the sociological interpretation of the stable set is the TGEB’s first chapter, which, as confirmed by Leonard, is the only one in the book that may be substantially credited to Morgenstern.

A few other questions are left unanswered in these chapters. Given that von Neumann stopped publishing original mathematical research after his migration to Princeton, would it be too malicious to suspect that his sudden return to game theory was at least in part motivated by the desire to “produce something” to uphold his well-deserved fame and status? What was the actual impulse behind the crucial 1940-41 manuscripts? Did he conceive of them just for the occasion of his Spring 1940 trip to the West (see Chapter 9), a trip culminating in a series of seminars on game theory in Seattle? Why, in a very unusual detour from strict rigor, did von Neumann offer in the book two different proofs for the central minimax theorem upon which the whole theory is built? Why did the axiomatic foundations of EUT appear only in the second edition of the volume? However, though the list might go on, questions like these should not diminish Leonard’s achievement. As already demonstrated by his 1992 HOPE Supplement and 1995 JEL papers, these pages confirms that he is undoubtedly the leading expert on the history of the collaboration between von Neumann and Morgenstern and on the genesis of their 1944 masterpiece. Hence, this portion of the book, though providing no real new facts to the knowledgeable reader, is the most proper culmination of a long and fruitful research program.

After all these praises, I regret to say that the final two chapters (Chs.12-13) represent the weakest part of the book. There are two main reasons of dissatisfaction. First, the analysis of the post-1944 diffusion and early applications of game theory would have required a much deeper investigation of the analytical features of the new discipline. This drawback —which somehow also affects the other chapters where Leonard deals with game theory proper, but which is felt here more severely than elsewhere— risks undermining, or at least leaving unsubstantiated, some of the author’s claims. For example, Leonard recognizes that game theory was quickly considered of little practical use by the US military establishment and that its main contribution to postwar social science has been as a toolbox for operations research and neoclassical economics. I agree with that claim, but, exactly, why was it so? Which kind of game theory is Leonard talking about here, the TGEB’s cooperative approach or Nash’s noncooperative version? Or take Leonard’s overemphasis on the circumstance that game theory set the stage for the development of (a certain strand of) experimental economics. That’s once again a correct remark, but it is incomplete and not so relevant. It is incomplete because the TGEB also provided the seeds of at least another strand of economic experiments, namely, those about expected utility theory and its later variants, about which Leonard is silent; it is hardly relevant because a book whose narrative ends around 1955, i.e., at least two decades before the first serious wave of experimental economics, should have rather covered other research paths which were immediately opened by the newly born discipline (say, information economics), and possibly also those which, sometimes unexpectedly, were not (say, industrial organization, where the direct impact of early game theory was nil).

Second, and rather mysteriously, the narrative in the last two chapters does in a sense without the two protagonists of the book. Yes, von Neumann’s involvement with war activities is the focus of Chapter 12, but it is a von Neumann who is depicted as almost totally detached from game theory, as if he had not just authored the TGEB. Yes, Morgenstern pops up here and there, especially in Chapter 13 (where on the contrary von Neumann is much less present), but his initial efforts to spread the new strategic gospel among fellow economists (as testified by his presentations in several seminars and AEA meetings) are almost entirely neglected. Note that I am not mainly arguing that Leonard has overlooked anything relevant as far as the two authors’ post-1944 contribution to game theory is concerned. Maybe he has, but that’s not the point. What I am really saying is that if Leonard, rightly or not, believes von Neumann and Morgenstern were distancing themselves from game theory proper in the postwar years, this is a crucial historiographical point which should have deserved the same in-depth analysis as that in the first two parts of the book.

Lest I sound too critical, I must add, to Leonard’s favour, that the interested reader may easily fill in the alleged gaps in his narrative by making recourse to the works of other historians. There is already a considerable literature dealing with the most analytical parts of the TGEB and of Nash’s game theory; other historians, like Phil Mirowski, have extensively examined the reception of game theory by the social scientists and the military establishment; finally, von Neumann’s multi-faceted postwar activities —as well as his pre-war ones— have been masterfully reconstructed by Giorgio Israel and Ana Millán Gasca, whose 2009 biography of the great Hungarian (The World as a Mathematical Game. John von Neumann and Twentieth Century Science, Birkhäuser) makes a proper complementary reading to Leonard’s book. Note that if we add to this list the huge amount of scholarship which already exists about the formalist school of mathematics and its influence on economics (think of the works by Leo Corry, E. Roy Weintraub and, again, Giorgio Israel), at the end of the day what seems to still be missing in the literature is just a comprehensive biography of Oskar Morgenstern alone, that is, for once detached by the towering figure of his friend and co-author and, above all, examined not only in his Austrian hey-days (about which Leonard’s book is probably insuperable), but also in his US postwar —and post-von Neumann— years, where his teaching and patronizing of the new discipline (which, until his death, largely betrayed his great expectations) should probably deserve more research.

The reference to the alternative sources about the history of game theory allows me to return to my earlier recommendation of Leonard’s book especially to economists and game theorists, more than to historians of economics. The reason for this advice is quite simple. Historians who have been acquainted with Leonard’s scholarship in the last 15 to 20 years would obviously still enjoy reading a volume where he summarizes his entire research, but would hardly find anything really new or unheard of which, more or less explicitly, the author hasn’t already published in prestigious journals (let me mention once again his 1995 contribution in the Journal of Economic Literature —a very rare achievement for an historian of economic thought!) or presented in several seminars and conferences around the world. Moreover, historians would probably have something to object here and there to Leonard’s assertions, including his main thesis. Not because, at least to this reviewer’s opinion, there is anything intrinsically wrong in them, but because, as historians, they are well accustomed to discuss “thick” reconstructions of the development of economic ideas and thus may well suggest alternative, even “thicker”, narratives or point at neglected connections which might further enrich Leonard’s picture. No, it is not historians of economics who should really read this book: it is economists and game theorists. If anything, for no better reason than as a blessed opportunity to cancel from their mind the groundless belief that the great advancements in economics may take place in a vacuum, i.e., totally detached from the context within which the people “in flesh-and-blood” behind those advancements live, work and think about their societies.