Reception and Impact of the Book
Notwithstanding the ambitious quest for a new social mathematics embodied by the book, the concrete influence of the Theory of Games was initially felt, not in social theory, but in the domain of military strategy.
During the early 1940s, when the book was being written, through von Neumann’s influence at the Princeton branch of the Statistical Research Group and at the Boston-based Anti-submarine Warfare Operations Research Group, game theory became an element in mathematical models of military engagements, such as submarine-search and bombing strategy. For example, a submarine navigating a channel is pursued by an overhead spotter-plane, the former trying to minimize the probability of contact, while the latter strives to maximize it. Such models involved the application of a very small part of the mathematics - usually centred on the minimax theorem - to specific, confined problems. Concerned with facilitating interventions in the world, game theory qua operations research was far-removed from the broad abstract representation of the social order that von Neumann had sought in the Theory of Games. Nonetheless, it was the perceived success of operations research during World War II that provided the impetus for the Army Air Corps’ creation of the RAND Corporation in the late 1940s, where models of this kind continued to be developed and game theory was given strong institutional support. While there is little evidence that these game-theoretic models were of anything other than very limited influence in quantitatively shaping particular strategic decisions, it is incontestable that the language, terminology and “thought framework” of game theory became important to the strategic mind-set that dominated the Cold War, helping shape such books as Herman Kahn’s (1962) Thinking about the Unthinkable and Thomas Schelling’s (1960) The Strategy of Conflict.The Theory of Games also set new standards for mathematical rigour in the field of economic theory. For example, before leaving France to move to the US, mathematical economist, Gerard Debreu, read the book in Salzburg, Austria, at a summer school run by Harvard University. Though Debreu would never work on game theory, the book shaped his thinking. His pathbreaking Theory of Value (1959), an axiomatic treatment of Walrasian general equilibrium theory, refers to the outstanding influence of von Neumann and Morgenstern (1944 [1947]: x) “which freed mathematical economics from its traditions of differential calculus and compromises with logic”. Debreu’s Hilbertian stance, too, on the relationship between the mathematics of general equilibrium and the empirical economic substrate went even further than that of von Neumann on games: “the theory, in the strict sense, is logically entirely disconnected from its interpretations” (Debreu 1959: x). This austerity shaped the views of an entire generation of economists from the 1950s till the 1980s, during which general equilibrium theory represented the pinnacle of intellectual achievement in the discipline. The irony, of course, is that it was precisely their dissatisfaction with Walrasian general equilibrium theory that provoked von Neumann and Morgenstern in the first place.
It was in the post-war military-academic milieu that a new generation of game theorists came of age. Whether at Princeton or the RAND Corporation, or alternating between the two, young mathematicians such as Harold Kuhn, Lloyd Shapley and John Nash developed new lines of analysis. Shapley, a towering influence in the game theory community from the 1950s onwards, produced, among other things, the Shapley Value, which described the solution to a coalitional game in terms of the amount brought by each player to an average, randomly formed coalition. For his PhD thesis, Nash sought to provide for n-person games a solution that was as restricted as von Neumann’s minimax for the two-person game.
Introducing the conceptual division of games into co-operative, in which coalitions are permitted, and non-cooperative, in which players act in isolation, he proved the existence for the latter, under specific conditions, of what he called an “equilibrium point”, later known as the Nash Equilibrium (see Nash 1950a, 1950b; 1951; Leonard 1994). That von Neumann found this non-cooperative approach to be rather trivial is understandable in the light of his own aims for the theory. Subsequent work on non-cooperative game theory by Harsanyi, Selten, Aumann, Kreps and others has contributed to the transformation of the microeconomic canon and shaped modelling in industrial organization, international trade and a range of areas. The field of behavioural economics, which has recently enjoyed great expansion, owes its existence in part to the appearance of game theory. Although von Neumann replied sceptically to Kuhn concerning the ability of laboratory experimentation to shed light on the stable set, game theory did provide a structured basis for empirically testing the theory of individual decision, via its utility axioms, and various solution concepts, both cooperative and non-cooperative. This experimentation, too, began at the RAND Corporation (see Kalisch et al. 1954). Under the influence of John Maynard Smith, the theory of games has had a significant impact on the field of evolutionary biology (see Maynard Smith 1988).In short, although it quickly attained the status of a classic, which is to say that it was cited by many but read by few, the Theory of Games and Economic Behavior set in motion developments that deeply affected the economics discipline. From the recasting of the economic agent as a strategic player to the reshaping of entire fields of economic analysis; from the introduction of axiomatics into general equilibrium and social welfare theory to the rise of experimental economics, the direct and indirect influence of von Neumann and Morgenstern’s wartime book has been profound and long lasting.
Robert Leonard