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Paul Erickson. The World the Game Theorists Made . Chicago: University of Chicago Press, 2015. Pp. 384. $35.00 (paper).

2017; University of Chicago Press; Volume: 7; Issue: 1 Linguagem: Inglês

10.1086/691132

2152-5188

Philip Mirowski,

History and Theory of Mathematics

Previous articleNext article FreeBook ReviewsPaul Erickson. The World the Game Theorists Made. Chicago: University of Chicago Press, 2015. Pp. 384. $35.00 (paper).Philip MirowskiPhilip MirowskiUniversity of Notre Dame Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreAll self-aware intellectual historians must eventually ask themselves how they will set out to delimit the complex of ideas/phenomena they seek to explicate. Sometimes they may concede their principles of selection seem a bit arbitrary, and the resulting object of their narrative a bit elusive. (Is there really such a thing as an “Age of Fracture” or a defensible history of salt?) Yet when it comes to something like game theory, you might think such problems could be safely ignored; after all, aren’t there three entries in the Stanford Encyclopedia of Philosophy devoted solely to game theory? It appears to be a form of mathematics; how much more precise can you get?In practice, this imprecision is the advantage of history as opposed to a textbook or encyclopedia entry: one is permitted to entertain the notion that there is rather less of substance than first meets the eye from a more Olympian perspective. Paul Erickson hesitantly coquettes with this perspective in the book under review, primarily because it is impossible to overlook the fact that game theory has overpromised to be all things to all people. Erickson struggles with this checkered past, where some intellectual programs have embraced, and then rejected, the contributions of game theory—which, of course, has itself not remained invariant over the last 70 years. This could have been the occasion for a rich philosophical meditation on how a mathematical tradition could become entrenched over a substantial stretch of time, often by jumping disciplines, even though its actual logical contributions may have been vanishingly small. And when it comes to context, I challenge anyone to desist in thinking “Cold War” when hearing the term “game theory.”Nevertheless, almost ruefully, Erickson draws back from this prospect, to retreat to the banal platitude that game theory constituted a set of “tools” that seemed useful to various people. Having spent substantial time around economists, I know how this perfunctory appeal to “tools” tends to be the last refuge of the intellectual scoundrel, especially talking about mathematics. When it comes to a real tool like a Swiss army knife, the can opener does not neutralize the awl, nor does it force you to “imagine” a corkscrew when confronting a bottle of wine.So if the designation “tool” is misleading, what then is game theory? Erickson solves his problem by mostly close reading of a very few texts—and of those, he tends to favor textbooks. I do not mean to suggest that he has not done substantial archival work or digested the secondary historical literature. He knows where many of the bodies are buried; it is just that when one begins to catch the whiff of corruption, his writerly demeanor turns very pedantic, as though it is all so very technical that mere prudence dictates that we must hurry on by. Moreover, in what I consider one of the main weaknesses of the volume, Erickson omits to treat the histories of operations research and neoclassical economics in any detail, even though they were the two main citadels where game theory was incubated and then sent out to conquer the world. And it is curious that so little of that technical content is examined or explained. Let me try to indicate what I mean by this in a quick flyover of the contents of individual chapters.Chapter 2 consists of a close reading of John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behavior (1944). This is the rankest body when disinterred. The beginning of wisdom is to note the book was not really about “games” in the vernacular sense, but rather a set of moves made as interventions in a number of disciplines simultaneously, with orthodox economics as one prime suspect. Yet, Erickson elides the important fact that it mounted a frontal attack on neoclassical economic orthodoxy, a fact that had dire consequences for its acceptance down the road. Erickson proceeds to tick the other boxes: it was also about Hilbert’s metamathematics, about quantum mechanics and the search for an ontological justification for stochastic ontology in various disciplines, the use of fixed-point theorems and the conjuration of different notions of “solutions” in the form of minimax and stable sets, the appendix on measurable “utility” added as afterthought, and so on. Yet because Erickson is narrowly focused on the text, none of this will be understood adequately by someone not already steeped in the history of the multiple contexts. After all, von Neumann really was a genius, and there were wheels within wheels within wheels of what he was trying to achieve. One must concede there were indeed flaws in the project, but Erickson’s verdict that the book “in 1944 was less a secure achievement than a promissory note” (73) really just parrots the dismissive modern line on von Neumann (especially in economics) that he should stay well and truly buried: hurry on; nothing to see here.Chapter 3 seems set up to deal with the obvious role of the military in the early life support of game theory, but following recent trends in intellectual history, it more or less rejects the notion that military patronage had substantial effect on the intellectual content and formal development of game theory (9). First, while operations research is mentioned, it is treated as though it were coextensive with the rather limited concept of “military worth,” as though nothing more than a bean counter technology of budgeting and allocation. Although the central role of RAND gets acknowledged, at no point does Erickson really explain why game theory initially was treated there favorably, only in the space of a decade to be jettisoned like yesterday’s newspapers. Yet transience left its legacy: RAND also served as the incubator for the premier anti–von Neumann solution concept, the Nash equilibrium. Erickson cannot be bothered to explain this concept and its weaknesses in any detail, even though it subsequently became the solution concept of choice in many disciplines post-1970. The fact that such a solution concept, postulating a hostile war of all against all, was rendered temporarily plausible by the Cold War is something Erickson does not entertain. Neither does he attempt to counter the baleful influence of the best seller and movie A Beautiful Mind on popular understanding.Chapter 4 wants to suggest that game theory then jumped to the so-called behavioral sciences; but in fact, mostly it documents the brief romance of some narrow segments of psychology with game theory, only to divorce soon thereafter. Primarily it consists of a close reading of Duncan Luce and Howard Raiffa’s textbook Games and Decisions (1957). Although Erickson hints that this was all bound up with 1950s enthusiasms such as cybernetics, information theory, and computational metaphors, he neglects some important work by Hunter Heyck on the role of “decision theory” in the 1950s in the effective separation of “the decision” from the decider. A serious historical epistemology would regard this strange reification of the “decision” as something inhuman as unprecedented, and thus a fruitful entry point into numerous questions of how “rationality” grew to become so weirdly unrecognizable in this period, particularly in game theory. It also had some relation to the surreptitious importation of German thought (Carl Schmitt’s decisionism, realism in international relations, neoliberalism) into American social science. But Erickson appears impervious to larger intellectual trends in the relevant disciplines.Chapter 5 finally confronts the usual linkage of game theory to nuclear war but downplays the direct military funding in favor of the treatment of game theory in the fleeting quasi discipline of “peace research.” The stalking horse in this chapter is the work of Anatol Rapoport and his textbooks N-Person Game Theory (1970) and Prisoner’s Dilemma (1965). There is something unbalanced in his focus on this critic of game theory, since the more orthodox choices would have scrutinized John Harsanyi and Robert Aumann, heroes of a more conventional Whig history, and inventors of some of its more important modern technical manifestations. But of course, shifting attention to the latter would have documented the rather more belligerent influence of war (and economics) on game theory instead of the counterintuitive narrative of “peace studies.” It would also have better contemplated the reasons that the military more or less abandoned its dalliance with formal game theory by the 1970s in favor of more free-form war gaming, just as the economists began to warm to it.Chapter 6 recounts the migration of game theory to mathematical biology in the guise of “evolutionary game theory.” John Maynard Smith and William Hamilton are the chosen protagonists; Erickson seeks to portray their work as “a relatively indigenous tradition with weak ties to Cold War patronage” (205); but he conveniently tends to overlook the ways in which it was a direct expropriation of models from economics and operations research, a fact often attested by some of the protagonists. Erickson seems intrigued by the notion that rational choice theory could be stripped of “rationality”; but this ignores the fact that the evanescence of agency is the hallmark of more modern rational choice theory in general.In my view, we still lack the insightful history of game theory that would comprehensively tackle the really interesting issues. First would be the question, How can a mathematical tradition end up saying so very little of any precision and specificity, while composed of bits and bobs borrowed from statistics, linear optimization, and topology, lacking any substantial agreement on solution concepts, and yet stand as the pinnacle of technical proficiency for so many different disciplines? Maybe someone willing to plumb the details of the mathematics, but also grounded in a more capacious sociology of knowledge and history of the natural and social sciences, could take up the challenge. Previous articleNext article DetailsFiguresReferencesCited by HOPOS Volume 7, Number 1Spring 2017 Sponsored by The International Society for the History of Philosophy of Science Article DOIhttps://doi.org/10.1086/691132HistoryPublished online February 22, 2017 For permission to reuse, please contact [email protected]PDF download Crossref reports no articles citing this article.