Lynne Kiesling
To answer my own question, I'd say it depends on the model, and the stringency of the assumptions, and whether or not the model's (and the economist's) focus is on understanding human action, or on constructing an elegant, self-contained model.
I agree with Tyler Cowen's list of ways that economics research can derive testable predictions from game-theoretic models. I think a lot of the interesting and valuable thinking is in the institutions (there's a surprise!), because game-theoretic models that are most likely to have some explanatory teeth are likely to have multiple equilibria. Institutions are a way to explain how we end up at one equilibrium instead of another. Behavioral, evolutionary, and experimental research all deal with institutions and can shed light on this.
But I do have a snarky follow-up question for Tyler: to what extent do you think that our colleagues are interested in understanding human action? What about the extent to which we economists are enamored with our tools, and engage in "math for math's sake" work? Just asking ...
Look at it from a practical point of view and take Peter Small's "the Ultimate Game of Strategy" where he states: "Establishing a successful niche in the lucrative world of e-business is not about competing to win money or rewards - it is about winning co-operation. Mutual benefit holds the key to becoming a winner - this game is about getting and keeping attention and co-operation both from other players and from customers. It is a game that is 99% about communication and only 1% about technology."
The game theory should not be in one person's direction but should be a bottom-up evolutionary stigmergic approach. Or even better, look at Charles Handy's request for democratic corporations where power will swift from an artistocratic top-down to a democratic bottom-up approach, where steps are modelled by collectivities and not by all too often much too ignorant and arrogant leaders. Game theory is an important issue in solving conflicts and in mitigating operational risks!
Public Choice taught us to remember that the political class may be primarily out for itself. Perhaps we should remember something similar about the economics profession?
Institutions are multi-equilibria brokers