The World the Game Theorists Made

Paul Erickson

• Publisher: University of Chicago Press
• Year: 2015
• ISBN:
  9780226097206
• Topic: Biowissenschaften
• Subtopic: Wissenschaft Allgemein

In recent decades game theory—the mathematics of rational decision-making by interacting individuals—has assumed a central place in our understanding of capitalist markets, the evolution of social behavior in animals, and even the ethics of altruism and fairness in human beings. With game theory's ubiquity, however, has come a great deal of misunderstanding. Critics of the contemporary social sciences view it as part of an unwelcome trend toward the marginalization of historicist and interpretive styles of inquiry, and many accuse its proponents of presenting a thin and empirically dubious view of human choice.
           
The World the Game Theorists Made seeks to explain the ascendency of game theory, focusing on the poorly understood period between the publication of John von Neumann and Oscar Morgenstern's seminal Theory of Games and Economic Behavior in 1944 and the theory's revival in economics in the 1980s. Drawing on a diverse collection of institutional archives, personal correspondence and papers, and interviews, Paul Erickson shows how game theory offered social scientists, biologists, military strategists, and others a common, flexible language that could facilitate wide-ranging thought and debate on some of the most critical issues of the day.

CHAPTER ONE

The Game Theory Phenomenon

This book is about one of the great intellectual conversations to unfold in the latter half of the twentieth century: a great sequence of debates, now lingering into their seventh decade, about the prospects for building a mathematical theory of rational decision-making that might not only revolutionize the study of human behavior and social interaction, but that had the potential to rationalize decision-making in every area of human affairs, from business to foreign policy. At the heart of these debates lay game theory—a theory of strategic interaction between rational individuals—which was launched in 1944 by the publication of mathematician John von Neumann and economist Oskar Morgenstern’s Theory of Games and Economic Behavior. In the years that followed, buoyed by postwar military funding and the grand ambitions of the game theorists themselves, the theory (and its close intellectual relatives, from mathematical programming to social choice theory) established footholds in an array of fields from mathematics and operations research to social psychology, political science, economics, philosophy, and evolutionary biology. Game theory also found itself at the heart of discussions of some of the crucial problems of the Cold War era, from the design of effective weapons systems to the resolution of the nuclear arms race. Indeed, many familiar problems and concepts—from “mutual assured destruction” to “the tragedy of the commons”—have become difficult to conceptualize except in game-theoretic language.

Certainly, the ambitions of game theory’s proponents have at times been sweeping. Von Neumann and Morgenstern introduced their ideas by placing them next to the great triumphs of mathematical science in ages past, and envisioned a future in which their work might bring the study of society out of its present dark age into a truly scientific future. And toward the end of his career, Morgenstern would seek to write a history of game theory that located its roots in enlightenment debates over the calculus of probabilities—thereby tying game theory’s distinctively modern formulation of rational behavior to the philosophical luminaries of the age of reason.1 Yet quite apart from the size of the historical stage upon which game theory’s creators imagined themselves, it is hard not to be struck by the sense of glamor, power, and prestige that has attached itself to game theory during the high years of the Cold War and beyond. Echoing von Neumann and Morgenstern’s aspirations, game theory rapidly became the province of a new fraternity of intellectuals—men like von Neumann and Morgenstern, Thomas Schelling, or John Harsanyi, to name a few—who blended old and new, classical and midcentury modern. They imagined themselves in part as revivers of the great enlightenment tradition of moral philosophy, diving with flair into the great problems of ethics and philosophy of science, into the study of how one ought to think and act that existed well before modern “social science” took form in the nineteenth century. Yet they typically were also imbued with the ethos of an era that glorified science, sporting an ultramodern mathematical idiom, fluent in the language of computers, man-machine systems, ICBMs, and other manifestations of Cold War high technology. They moved at will from the traditional settings of academia—the ivied walls of Princeton or Harvard—to the new corridors of power in midcentury America: the Pentagon, military-funded think tanks like the RAND Corporation (resplendent in its modernist glass and steel Santa Monica headquarters), or the research campuses of Bell Labs and IBM.

Such was the promise. Yet looking beyond the glamor, the assumed lineage, and the breathtaking ambitions, game theory’s allure was (and remains) enigmatic and contested. Its widespread use in the social and behavioral sciences might be understandable if it received high marks according to some commonly cited standards for assessing the usefulness of a “theory”—for example, its predictive power or its ability to describe the way individuals make decisions. But many of the same scholars who have most raised the profile of game theory in the social and behavioral sciences have simultaneously served as the strongest critics of the theory’s empirical adequacy. This is true, for example, whether we look to Herbert Simon’s notion of “bounded rationality,” which explicitly assumes that humans lack the computational power to be true rational actors in the sense of game theory; or to the extensive literature, following the lead of experimental psychologists Amos Tversky and Daniel Kahneman, which claims that in many plausible situations humans routinely violate the principles of probability theory and decision theory that underlie the larger theory of games. Moreover, to this day, there remains little agreement among game theorists as to what constitutes a “solution” for many games: as a recent textbook of game theory for economists notes, “One of the intriguing and frustrating aspects of game theory is that there does not yet exist a universally accepted solution concept that can be applied to every game.”2 Indeed, when it comes to many of the particular “games” we care the most about—nations trying to abide by an arms control agreement, corporations deciding whether or not to enter a market, or children deciding how to share a slice of cake—we are typically left not with one predicted outcome or a definite set of rules of rationality to follow, but many.

From those standing at a greater distance from the brand of rational choice theorizing embodied in game theory, the criticisms have been still more vocal. New Left intellectuals of the 1960s—not to mention their more activist allies in the streets—assailed game theory for its ties to military funding agencies, for its presumed complicity in rationalizing an aggressive national security policy, and for its ethical inadequacy. In their eyes, the game theorists’ pretensions to scientific neutrality coexisted uneasily with the notion that game theory might somehow tell us how we should make decisions in social situations, not to mention in the realm of nuclear policy. Such critiques on ethical grounds have often been accompanied by disciplinary struggles: from political science to economics to philosophy, rational choice modeling has coincided with significant transformations of these fields that saw the displacement of historicist or interpretive styles of inquiry across a broad swath of their former terrain. Corresponding to this intellectual shift has been a remaking of the academic disciplines and working practices in ways that many commentators have found malign: the rise of “economic imperialism,” and a shift in power toward mathematically trained experts who hold sway in policy debates.3

This book seeks to make sense of what one might call the “game theory phenomenon”—the broad if contested spread of a mathematical tradition—between the publication of von Neumann and Morgenstern’s seminal 1944 book and the theory’s firm establishment in economics during the 1980s. It does so not by rendering a magisterial history of ideas. The intellectual corpus that has grown out of von Neumann and Morgenstern’s work, it is safe to say, is by now far too varied and diverse to imagine that any single narrative of development or growth over time could capture all its intricacies. Rather, this book explores the contours of the world that the game theorists made during this period: the kinds of intellectual and institutional connections that they catalyzed, the sheer variety of research programs their theory enabled and inspired, and the conversations and controversies that the new mathematics of rational choice facilitated. In light of the critical assessments of the theory outlined above, this kind of world-building has arguably been game theory’s most impressive contribution to our intellectual culture over the past seven decades. But at the least, examining the game theory phenomenon sheds much light on a number of key features of the Cold War sciences: the vogue for mathematical techniques, especially models of rational choice; the connection between these new techniques and disciplinary alliances and patterns of collaboration spurred by new forms of patronage during this period; and, above all, the significance of a far-flung set of debates over the nature of rationality and choice in an age of scientific and technological enthusiasm.

Outlining a History

If there is a canonical history of game theory extant today, it reflects the theory’s high-profile appearances in economics since the 1980s and a resulting growth of interest in its history among practitioners and historians of economics. Ostensibly pitched at economists, von Neumann and Morgenstern’s Theory of Games and Economic Behavior continues to be cited as a founding work of the game-theoretic tradition in economics, even if the research programs it inspired subsequently came to overshadow the original work and even substantially subvert its message. In particular, the award of a Nobel Prize in economics to a trio of game theorists in 1994—John Nash, John Harsanyi, and Reinhard Selten—focused attention on the history of a particular approach to solving games that was not present in von Neumann and Morgenstern’s work—the “Nash program” of reducing all games to noncooperative games (in which players could not form binding agreements) and identifying their “Nash equilibrium” points. Nash—working against a colorful if only vaguely relevant backdrop of US military support for research in game theory, as depicted in the 2001 film A Beautiful Mind—proved the fundamental theorems about such games in his papers of the early 1950s. Harsanyi subsequently generalized Nash’s analysis to situations involving incomplete information, and Selten provided powerful economic applications of the theory, especially in the field of industrial organization.4

More recent Nobel prizes in economics for individuals known for their contributions to game theory—Thomas Schelling and Robert Aumann in 2005, and Leonid Hurwicz, Eric Maskin, and Roger Myerson two years later—added additional datapoints to the history, either by honoring applications of the theory to problems of “mechanism design,” or to the game-theoretic analysis of “bargaining” in economics and elsewhere. As a result, historians and practitioners of economics have tended to outline a history of game theory that starts with von Neumann and Morgenstern, but that rapidly moves away from their problematic “cooperative” theory of multiplayer games and gravitates toward Nash’s program, which proved to be a much more natural fit with economics’ interest in the effect of incentives on rational individuals. Indeed, some have gone so far as to suggest that von Neumann and Morgenstern’s book retarded the development of game theory in the social sciences by overshadowing the work of the young John Nash and those who took inspiration from it.5

The history I relate here certainly features some of these high-profile individuals and their celebrated achievements, and to an extent their work structures the narrative arc of the book. Some of the dramatis personae will be familiar (in name at least) to modern practitioners of game theory: von Neumann and Morgenstern, Nash, Harsanyi, Schelling, Selten, and Aumann, among others. But these figures will often be overshadowed by others whose careers and research programs wielded significant influence on game theory’s earlier development, even if the resulting account will seem to a contemporary practitioner of game theory to dwell rather far from the action “at the front.” As we shall see, this relative shift in emphasis reflects two realities of game theory’s history prior to the 1980s, the decade in which noncooperative game theory celebrated its ascendancy within economics. First, it was not clear that Nash’s “noncooperative” theory of multiplayer games might attain primacy among the many alternative “solution concepts” that gained attention in the first years after 1944 (including von Neumann and Morgenstern’s own “cooperative” solution concept). Nor was it clear that the most important constituency for game theory would prove to be economists, even if an economist (Morgenstern) played a key role in producing Theory of Games and Economic Behavior, and even if some individual economists were from the start deeply engaged in the conversations that flowed from the publication of von Neumann and Morgenstern’s book.

Decentering the rise of noncooperative game theory within economics since the 1980s brings with it both historiographical promise and peril. This earlier period in game theory’s history was marked by the emergence of a wide variety of research programs representing tantalizing possible futures for what the theory might have—and might yet—become. Consequently it is difficult to hang the story of game theory between the 1940s and the 1980s on any of the traditional objects of analysis in the history of the sciences: an individual life, or even a manageable collection of individuals with common life stories and intellectual pedigrees; a well-defined discipline, research program, or “paradigm” with well-developed borders or trajectory; or a particular institution. While there were a number of particular patrons who supported research involving game theory, there were no readily identified “departments of game theory” on university campuses during this period; aside from a relatively small number of research centers identified with particular prominent scholars, it is equally difficult to identify any today. The first regular academic journals specifically devoted to game theory (most notably, the International Journal of Game Theory) only began to appear in the 1970s. And while there was a small cadre of individuals who might have self-identified as “game theorists” working during this period, they often lived wandering lives, moving between departments of economics, the social and behavioral sciences, mathematics, industry, various regions of the defense establishment, and fields like operations research, industrial organization, and others that remain relatively difficult to classify.6

In particular, histories focused on the traditional academic disciplines couple only loosely with the rise of game theory during this period. The theory’s deepest intellectual roots lay in mathematics, and individuals trained in mathematics would prove game theory’s strongest constituency for much of its early history; yet there is evidence that, at least initially, the theory’s status in the mainstream of “pure” mathematical research was precarious. Even labeling game theory a branch of “applied mathematics” provides it with little disciplinary foundation, given the institutionally nebulous position of applied mathematics in early twentieth-century American academia. Instead, game theory—much like cybernetics and information theory, which appeared at roughly the same time—was closely associated with broader cross-disciplinary research agendas and patterns of funding that a growing body of literature on the postwar human sciences has identified as a key feature of the period between World War II and the 1970s. During this period, existing university departments, pedagogy, academic journals, scholarly societies, and patrons did not disappear, but they were increasingly complemented (and possibly dwarfed) by new networks of funding, connections, seminars, conferences, and research institutes bound together less by traditional disciplinary expertise than by common practical endeavors and problems, modeling idioms, and methodologies. New areas of inquiry and expertise like operations research, “management science,” “general systems,” or “behavioral science,” all associated with the circulation of game theory during this period, typified the postwar growth of what Peter Galison has termed the “interdisciplines.”7 Reflecting this fact, scholars interested in the postwar human sciences broadly speaking have increasingly crafted intellectual histories of this era that leave traditional disciplinary boundaries behind. Steve J. Heims and Paul N. Edwards have explored the impacts of cybernetics and computing in psychology and the social sciences; Philip Mirowski has called our attention to the legacy of “operations research” for postwar economic thought; S. M. Amadae has followed the trail of rational choice theory across the behavioral sciences, political science, and economics; Deborah Hammond has explored the legacy of general systems theory; and more recently, much work by Hunter Heyck, Jamie Cohen-Cole, and Joel Isaac has shed light on this kind of intellectual fusion in other areas of the postwar human sciences.8

So if game theory’s history between the 1940s and 1980s cannot be traced to a particular discipline or research program, or even a single “interdiscipline,” what then can explain the theory’s wide appeal during this period? To date, the Cold War context has loomed large in the historiography as a possible explanation. S. M. Amadae’s work has connected the vogue for theories of rational choice (including game theory) with a set of high-level Cold War ideological and intellectual struggles to “rationalize capitalist democracy,” to create a liberal vision of economics and politics that might neutralize the appeal of socialism and statist calls for a planned society to further the common good. Such an account elegantly explains the emergence of several key theoretical traditions in political theory and economics, but it is less readily adapted to explain other episodes in the history of Cold War–era rational choice mathematics—for example, game theory’s appearance in the work of Marxist evolutionary biologists in the 1960s. Another approach follows the lead of an extensive literature in the history of science that has examined the impact of Cold War military patronage on the conduct of the physical and biological sciences.9 Certainly, for much of its early history, game theory circulated in close association with military money, via organizations like the Air Force–funded RAND Corporation and the Office of Naval Research, among others. And although military patronage would become less central to the theory’s history over time, it is hard to deny that it helped the theory survive at a time when it might otherwise have disappeared into obscurity.

It is tempting to draw connections between military funding and imperatives on the one hand, and the intellectual content of game theory on the other. One possible historiographical approach thus focuses on tracing the emergence of theories, models, and metaphors, and associating their spread with the influence of dominant discursive frameworks or modeling idioms that were characteristic of the Cold War era, or the demands of powerful patrons (especially military patrons) of science. Information theory, cybernetics, and systems modeling thus spread across fields like psychology, ecology, and molecular biology in part through their resonance with military-promoted discourses of command-and-control, man-machine systems, and the like.10 In a similar vein, depending on which history you consult, game theory survived in the postwar era in part through its apparent ability to capture the “image of conflict,” the paranoid us-or-them mindset of the military establishment and strategic community; it provided a natural framework for thinking about “the problem of the bomb”; or it resonated with a Manichean “ontology of the enemy” that emerged out of World War II military operations.11

Such approaches to interpreting the history of game theory and related models, metaphors, and theoretical frameworks have great appeal. It is har...

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• chapter 1. The Game Theory Phenomenon
• chapter 2. Acts of Mathematical Creation
• chapter 3. From “Military Worth” to Mathematical Programming
• chapter 4. Game Theory and Practice in the Postwar Human Sciences
• chapter 5. The Brain and the Bomb
• chapter 6. Game Theory without Rationality
• chapter 7. Dreams of a Final Theory
• Acknowledgments
• Notes
• Works Cited
• Index