The Aumann/Schelling Nobel has inspired much discussion over the intellectual usefulness of game theory. In response to Michael Mandel's worry that game theory does us no good, Tyler offers a number of responses, and Mandel reiterates his concern. Over at Crooked Timber, John Quiggin discusses problems of indeterminacy in the absence of the common knowledge assumption. Drezner defends Schelling against Slate's Fred Kaplan. Mark Kleiman notes that Todd Gitlin is a moron for claiming that Schelling doesn't understand non-zero-sum games!
Unless we understand game theory to simply be the Aummann-ish formalism, with its ridiculous epistemic and behavioral assumptions, then it is probably not very useful. But it is better to see Aummann style game theory as a stylized limiting case of the logic of interdependent action, which is what game theory is the theory of. We can contrast between formal and substantive game theory, the latter being the very heart of social science and social and political philosophy. Thomas Schelling is the greatest living substantive game theorist, in the tradition of Hobbes and David Hume, but with the benefit of the discipline Nash, von Neumann, and Morgenstern (and others, including Aumann,) imposed upon game theory through formalization.
To move the subject toward my domain, let me assert that the reason contractarian political theories are superior to the alternatives is not due to the idea of a fictive contract, but because of the recognition of the centrality of patterns of interdependent action to social order. You can't understand the good society until you understand society. And you can't understand society without understanding interdependent behavior. But you can't understand interdependent behavior unless you understand behavior. And to do that, you need to understand (1) how people represent their alternatives, and (2) how they order them, for which you need the cognitive sciences.
(Esoteric aside: Regarding Tyler's five options for making game theory predictive, my sense is that (1) and (5) actually are one. The indeterminacy of the social world is a function of the indeterminacy of representation. Sooner or later the behavioralists will get around to discovering basic philosophy of language. This also bears on Quiggin's worries. For Kripkenstein reasons, previous behavior underdetermines the "rule" upon which one behaves, even if the rule is "maximize expected utility." If my strategy is a conditional rule sensitive to my representation of your strategy, which is a conditional rule sensitive to your representation of my strategy, etc., then an equilibrium, being a set of strategies, will be a slippery creature indeed. Thankfully, the in-principle indeterminacy of rules and representation need not worry us too much if there is stable regularity in the way we in fact tend to ascribe belief and motivation to others.)
Let me quote my abandoned dissertation proposal by way of saying why I think substantive game theory is about the most important thing there is:
Central to the contractarian framework is a clear grasp of the interdependence of reasons for action in certain kinds of social settings. The idea of mutual advantage implies that we can often do better jointly than we can individually. There are gains to be had from cooperation. However, as Hume put it, “the actions of each of us have a reference to those of the other, and are performed on the supposition that something is to be performed on the part of the other.” It follows that the kinds of social cooperation we will be able to achieve and sustain depends on our expectations of the behavior of others. Our reasons to act to bring about the goods of cooperation, and to enter into agreements and comply with principles designed to facilitate them, therefore depend on the nature of the psychological capacities that enable agreement, assurance, and compliance. If we cannot sufficiently trust ourselves and others to keep agreements, or to adhere to conventions that are like agreements, or if we by nature severely discount future value, or are unwilling to tolerate more than a little risk, then we may find ourselves able to conceive of a social order that each of us would prefer, but which none of us may enjoy.