Game theory is clearly the dominant theoretical paradigm in economics, and hugely important in political science as well, but does not appear to have made much of an impression on sociology. There is something odd about this. Swedberg quotes Max Weber, father of both our traditions, in an essay written just after 1900:
“The historical agent, to the extent that he is acting, as we are here assuming, in a strictly “rational” way, takes into account those “conditions” of the future course of events which interest him, which are “external” to him and, as far as he knows, given in reality. He then, in his mind, fits into the causal nexus various “possible” courses of action for himself, together with the consequences to be anticipated from them in combination with those “external” conditions, in order to decide on one or another of the courses of action appropriate to his “goal” in accordance with the “possible” outcomes which he has worked out in his mind.”
Weber here gives a very nice definition of the type of methodogically individualist decision theory which we economists use today. Yet 100 years later, game theory is not accepted in the mainstream of sociology. Why?
Richard Swedberg, in an essay for Theory and Society, attempts to answer that question. Tom Schelling, he of the social dilemma and the tipping point, unsurprisingly gained some traction with sociologists in the 1950s and 1960s. Both von Neumann and Morganstern, as well as Luce and Raiffa, were reviewed in the American Sociological Review, though the reviewer in both cases was an economist. Only a handful of models caught on, however. From my reading of Swedberg’s analysis, it seems four reasons were predominant.
First, the mathematical ability of sociologists (in that era, and to a lesser extent now) was too low to follow frontier developments in game theory. Second, many schools of sociology were, and are, uncomfortable with using such an individualist theory to analyze the outcome of social forces. Third, the use of game theory to make empirical predictions was less than successful – as Swedberg notes, game theory is better at explaning “why” than “how much?” Such connection with empirical reality was, and is, considered far more important by sociologists than economists. And fourth, some sociologists felt the axiomatics of game theory were far too demanding, and rather than expand the theory to incorporate incomplete information, or limits on reasoning power, or other factors that economists later studies, sociology simply left the technique behind. Swedberg argues that game theory in sociology is nonetheless a powerful tool for examining counterfactuals (something difficult to examine empirically, of course), and further that sociologists can contribute to game theory by discussing what the action spaces and payoffs look like in certain games, the ex-ante step that many economists do not take seriously enough. I would love to see precisely this sort of work by sociologists.
What is not made clear in the article, and perhaps is not well known to mathematical sociologists, are certain aspects of the history of game theory within economics. Sociologists were by no means alone in recognizing two big flaws in early game theory: the exact specification of the game form, including action spaces and payoffs, is very important, and the multiplicity of equilibria (or a nonunique core in cooperative games) makes analysis difficult. These two problems were to a large extent solved between the late 1970s and the late 1980s. The problem of specifying the game form in all its institutional detail was handled through the field of mechanism design, which roughly asks whether a planner or a principal can implement some outcome as the equilibrium of some game within a very large class. The robustness and refinement of equilibria led to a lot of work which helped us better understand what the Nash fixed point imposes in terms of decisionmaking, but ultimately led to something of a negative result: we will never have an equilibrium concept which is suitable for all types of games, and certainly not one which provides unique solutions.
Mechanism design and the robustness literature are interesting for two reasons. First, more or less 100 percent of the work in those areas was done by economists rather than by other social scientists – it is particularly interesting how little was done concerning the theory of games by practitioners in other fields. Any understanding of why applied game theory is most common in economics surely must be able to explain the absolute dominance of economists in pure game theory. Second, here is as good a place as any to give some dap to my home department, Northwestern MEDS. Some incredible amount of the important work in this game theory golden age was done there. To name only a few, the department at one time was home to Milgrom, Myerson, Stokey, Satterthwaite, Holmstrom, Baron, Ledyard, Kalai, Kamien, Sonnenschein, John Roberts, almost all of whom were young researchers at their productive peaks – ex-post, that must have been the best theoretical economics department of all time, right?
Final article from Theory and Society (No IDEAS link found). Tips of the hat to Richard Swedberg for posting full, final articles on his website, and to the post at orgtheory where I first came across this article.
A Fine Theorem 