Game theory, mathematics, and economics

In early 2000, the editors of an European journal on the history of economic thought solicited the separate views of prior Nobel laureates in economics. We were asked to list, and briee y to justify, what we considered to be the e ve major contributions to economics over the past century. I included game theory in my listing; I suspect that many of my peers did the same. We were not asked to provide a rank ordering, but, as I have thought more about such a possibleranking ofmy own entries, I cameincreasinglyto the judgment that game theory should perhaps be placed at the top. These notes are aimed to explain this judgment. An interesting feature of game theory’s contribution, as compared with others on my own or others’ listings, is the extreme lag in its eiective impact below its ultimate potential, which, as I shall argue, remainseven at century’s end. For many years after the publication of The Theory of Games and Economic Behavior (von Neumann and Morgenstern 1944), economists interpreted the theory largely as oiering possible insights into the behaviour of decision makers placed in small-number interactive settings, notably the strategies of duopolists and oligopolists. Only belatedly did economists who began to specialize as game theorists turn to analyses of solution concepts, to the relationships between rules and patterns of outcomes, and, e nally, to the applicability of game theory’s appropriate mind-set to all areas of social interaction, up to and including political philosophy itself. My subsidiary thesis is that, even at the century’s turn, game theorists themselves, and certainly their peers in other areas of economic inquiry, do not yet fully appreciate the contribution that this research programme, properly understood and applied, can make to the science of economics. In part the ambiguity here stems from the generalized failure of economists, everywhere, to understand what their wholedisciplineisabout ‐a failurethat, in its turn, prompts game theorists to remain quite timid in advancing claims for the paradigm shift that their research programme embodies. But the ambiguity also ree ects both the origins and early emphases within game