1Paul Erickson’s fascinating history of game theory begins by describing its subject matter not as an idea, paradigm, institution, nor even as a ‘theory,’ but as a “great sequence of debates … about the prospects for building a mathematical theory of rational decision-making.” (1) This series of debates is given coherence, both in the minds of the historical actors and in the construction of this book, by the mathematical tradition associated with “rational choice modeling,” a tradition that ultimately was more of a common way of talking about rational choice than a coherent, shared theory of choice. In Erickson’s analysis, “game theory” is a diverse set of tools that share a “common genealogy”: an analogy might be to a genome, in which a great variety of genes have traveled together over the generations, some because they are functionally linked, necessary to each other, and some because the accidents of history brought them together in more or less workable relationships.

2This book is organized by an understanding of postwar science as being a thing of ‘interdisciplines’ oriented around problem areas of interest both to patrons and theorists, of historically contingent sets of theoretical tools and associated practices (especially those associated with mathematical modeling and, later, computer simulation), and of longstanding, perhaps insoluble, debates about fundamental questions: the nature of rationality and its actual role in human thought and action; the tension between the *is *and the *ought* in the scientific study of human behavior; the role and validity of theoretical abstractions, especially mathematical abstractions, versus empirical or experimental evidence in the study of human behavior; the possibility of reconstructing human science on ‘positive’ foundations similar to those in the physical sciences. These old debates were expressed in new languages in the postwar era, and these new languages, especially game theory, shaped the content of these intersecting discourses. This history of game theory, therefore, is a history of an imagined intellectual community’s discursive self-construction (and fragmentation) over time.

3The core narrative Erickson presents begins in Chapter 2 with a discussion of von Neumann and Morgenstern’s 1944 landmark *Theory of Games and Economic Behavior. *Erickson’s emphasis on the heterogeneity of game theory pays dividends right up front, as he interprets *Theory of Games *less as a point where a brand new, whole thing was created than as a brilliant but incomplete assemblage. In Erickson’s words,

game theory as it stood in 1944 proved less a unified axiomatic approach to the study of rational behavior and more a diverse collection of terminology, notational representations of games, and results, coupled with more completely fleshed-out theories of utility and of the two-person zero-sum game. (18)

4This characterization is not intended by Erickson to diminish von Neumann and Morgenstern’s accomplishment but rather to indicate that “game theory” could mean quite different things to the readers of this vital text. While these ideas, tools, solutions, goals, and practices ‘went together’ in *The Theory of Games*, they were distinct and potentially separable; much of the story told by Erickson in later chapters is the story of how these elements, plus a few crucial later additions, were separated, combined, and recombined in different ways at different times to address different problems.

5Probably the two most essential additions to the assemblage created by von Neumann and Morgenstern were the ideas of Nash equilibrium and of the evolutionarily stable strategy. Chapter 3, “From ‘Military Worth’ to Mathematical Programming,” establishes military-sponsored mathematical work at RAND and at Princeton (especially in Albert Tucker’s seminar on game theory) on problems of logistics and programming as vital to the embrace of game theory among mathematicians, who were at the time very nearly the only constituency interested in the concepts and tools of game theory. Nash’s concept of equilibrium solutions in noncooperative games, he shows, was a fitting product of this context and the interests of key patrons, such as the Office of Naval Research, and, he argues, it marked a significant shift in the problems and tools that constituted game theory.

6Chapter 4 tells the story behind another important remix of these ideas, tools, practices, and concerns, Duncan Luce and Howard Raiffa’s 1957 *Games and Decisions*, the book that probably did the most to introduce game theory to the social and behavioral sciences. After a decade in which game theory had been almost exclusively the province of mathematicians supported by military agencies interested in optimization problems, *Games and Decisions* opened the game theory conversation to an audience that was not only broader, but also substantively different in its disciplinary backgrounds and goals. The title *Games and Decisions* is a telling clue revealing Luce and Raiffa’s reframing of game theory as a theory of decision-making, which was related to, but distinct from, a theory of economic behavior connected to a particular understanding of utility or a set of tools for solving optimization problems. As Chapter 5, “The Brain and the Bomb,” shows, once it was reframed as a theory of decision-making, game theory had something to offer to people interested in *The Strategy of Conflict* (the title of Thomas Schelling’s famous 1960 book) and so was taken up by strategists trying to understand the ultimate two-player zero sum game (the Cold War) and by the burgeoning new field of conflict resolution.

7Significantly, “debates over arms control and conflict resolution had placed game theory at the center of discussions on the problem of how to rationalize cooperative behavior in a world of rational egoists.” (24) As Chapter 6, “Game Theory Without Rationality,” reveals, cooperation amidst competitive struggle was a topic of great interest in evolutionary biology in the 1960s. Game theory first appeared in the work of evolutionary biologists who “found the theory’s parsimonious explanations of social life in terms of the actions of self-interested individuals more convincing than the collectivism they associated with Wynne-Edwards’s theory of group selection, and who favored a set of working practices involving mathematical models and computer simulations.” (23) This was a profoundly ironic development, as Erickson notes, for “the end result of game theory’s foray into biology thus was a theory of rational choice stripped of anything resembling ‘rationality’ or ‘choice’.” (238) The subsequent re-spread of game theory back into the social sciences in the 1980s brought the “evolutionarily stable strategy” of Maynard Smith back in as a refinement of the noncooperative Nash equilibrium solution concept. “The result,” Erickson states, is that “over the past three decades [there] has been a refocusing of game theory, away from the analysis of rational behavior and toward the examination of evolutionary dynamics, from the analysis of optimization to the analysis of equilibrium in human and natural economies alike.” (239)

8Erickson’s last chapter, “Dreams of a Final Theory,” explores this ‘Nashification’ of game theory in the late 1980s. As he shows, by the mid-1980s, game-theoretic concepts, tools, and practices, particularly those associated with the ‘Nash program’ of describing all games as noncooperative games and of seeking equilibrium solutions to those games, had become central parts of many fields, especially economics and political science. The central role of Nash equilibrium came roughly 30 years after Nash’s original papers on the subject, which, of course, begs the questions, why Nash, and why then? Erickson does not have a single answer to these questions, but he suggests that Nash’s noncooperative game theory, as refined and reformulated by John Harsanyi and Reinhard Selten (among others), was seen by many as a theory of social interaction that could “reduce the study of all forms of social organization, from markets to governments, to the finding of equilibrium solutions to the relevant games” (24)—an expansive vision of a final theory that had great appeal at a time when general equilibrium theory and many other grand theories of the 50s-60s had crumbled under the weight of the crises of the 70s.

9In Erickson’s account, these hopes for a “final theory” ran aground in the mid-1990s, with the ambitious, unifying program of Harsanyi being followed by another fracturing or fragmentation of game theory. So, by the end of the book, we have a story of disparate mathematical strands being brought together in *The Theory of Games*, only to be broken apart and reformed time and again, first as a set of tools for solving optimization problems, then as a language for discussing rational decision-making, then as a framework for analyzing strategy and conflict, then as a way to analyze evolutionary competition, then as a set of tools for describing behaviors in relation to incentive structures. It is a fascinating story, and it is well told.

10Erickson’s framework does beg a few questions, however: If the various mathematical tools, practices, and applications to questions related to rational choices that were brought together by von Neumann and Morgenstern were so dis-aggregable and re-interpretable, then why were they so consistently recognized as being part of a thing called “game theory”? In some cases, it appears that certain notational forms, such as the payoff matrix, were the key signals that “this is game theory”. While those are not the only key signals, they clearly played an important role, and I would have liked to see a deeper exploration of those notational forms and the conceptual freight they carried, similar in approach (though not necessarily in scale) to what David Kaiser did with Feynman diagrams in *Drawing Theories Apart *(2005). In addition, if the story-line for game theory from the mid-90s on is a story of simultaneous growth and fragmentation, as it is in so many areas of the human sciences, then how does one differentiate between heterogeneity in a nevertheless common pursuit (game theory in the 1950s-mid 1970s), and fragmentation into substantively different enterprises (game theory in the 21st Century)?

11There is no one answer to this question, but Erickson’s approach works very well in this book. Even though I am by temperament more a ‘lumper’ than a ‘splitter,’ I found his account persuasive and insightful.

12The only things that I found missing from this account were a deeper exploration of the significance of specific notational forms (as noted above), and a more sustained examination of game theory’s history in relation to the history of mathematical modeling in the human sciences. To be fair, Erickson does discuss the rise of modeling, but I personally would have liked more on the topic, as one could argue that perhaps the most significant intellectual transformation in the human sciences over this period, and one in which game theory played a major part, is the advent of mathematical modeling as *the* mode of analysis across many fields.

13*The World the Game Theorists Made* is an admirable complement to existing work on the history of game theory. Where Robert Leonard’s fine *Von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science, 1900-1960* (2010), is a study of the intellectual, political-cultural, and personal contexts in which Von Neumann and Morgenstern (and a generation of mathematicians fascinated by chess) worked and lived and how these contexts, through these individuals, shaped the creation of game theory, Erickson’s book is very much about the evolution of game theory as it moved into different niches in the academic ecology of postwar science. Read together, the two enrich each other. From another perspective, Nicola Giocoli’s 2003 work on “modeling rational agents”, Philip Mirowski’s *Machine Dreams* (2002), Lorraine Daston, et al.’s *How Reason Almost Lost its Mindi *(2013), and Sonja Amadae’s *Prisoners of Reason* (2016) form an interesting set of complements as well, for, while they differ in significant ways, all four of these works are explorations of the history of rationality, as constructed in the social sciences (especially economics), with game theory being seen as an epitome of the mid-century attempt to turn reason into a thin thing of rules and mechanisms (rather than judgment, ethics, or experience). *The World the Game Theorists Made* intersects these histories less directly, but it does speak to them: for instance, its careful study of the transformation of game theory into something that did not presuppose reason (and sometimes, not even much choice) appears to strengthen the argument that there was a powerful drive to redefine reason in terms of a stripped down, mechanical kind of rationality. At the same time, Erickson’s emphasis upon the tools and practices of game theory as constituting game theory raises questions as to whether “game theory” had an inherent (as opposed to a contingent) politics, and if so, where that politics is to be found.

14In sum, this is a compelling story, insightful and well-grounded in a careful reading of an impressive variety of primary sources across a number of fields and subfields. Few historians could follow this complex technical discourse across fields, let alone do so over time. The result is a book that tells us much about game theory, and even more about how “theoretical tools” were used, imported, and adapted in postwar human science.