Most of the econ blogs have lauded the Nobel Prize to Thomas Schelling and Robert Aumann, who won for their work on game theory and its applications. However Business Week's Mandel has called it a letdown; and the Austrian economists are in principle opposed to applying mathematical reasoning to human behavior - a critique particularly directed against the work of Aumann.
Mandel's though represents a more mainstream complaint - that the empirical accomplishments of game theory have been disappointing. And according to this article there are zero applications of game theory to practical business.
One wonders though whether this type of criticism is fair; after all the presumption is that the sub-discpline aims at generating practical techniques and empirically testable statements. Consider general equilibrium theory; nobody (least of all its theorists) pretend that an empirical test can be made about the existence of equilibrium. Rather the theory is intended to close a gaping hole in the internal logic of the partial equilibrium model (if other market prices determine how to draw a pair of supply and demand curves, where do those prices come from?) It provides an coherent, benchmark idealization for understanding how markets work. Of course, the idealization itself cannot represent how markets really work.
As I understand it, game theory offers another benchmark, this time of how strategic behavior works. Incidentally, later theorists may develop some practical techniques and applications (as was the case with the computable general equilibrium models). However this is not the standard by which to judge current work, which is predicated on formally working out the implications of complete rationality in game-like settings.
Chess and tic-tac-toe provide a good analogy. Tic-tac-toe is completely computable, because it is so simple. Chess on the other hand is extremely complex, and appears to be beyond a computational solution for a long time to come. Game theory basically analyzes tic-tac-toe type of games. I don't mean that to be disparaging - what I mean is that games are reduced to a set of rules and strategies as to be amenable to a computational solution.
Real world strategic behavior is more like chess than tic-tac-toe: moves are guided by intuition, rules-of-thumb ("seize the center", "don't bring out the Queen too early", "bishops of opposite color endgames are drawish"), subject to exceptions that only the experienced can detect in specific positions.
Game theory skeptics want models that tell us, in a manner of speaking, how chess is played. Unfortunately for that you don't need a mathematician or an economist - you need a chess expert! Similarly within practical business settings, the people you would ask about business games would be - well, the players themselves.
Here we see the benefit of the game theorist's approach: reducing games to a simple structure permits generalization to a wide variety of settings. The "Prisoner's Dilemma" for example arises over and over and over in many settings (war, business, resource maangement, and - law enforcement?). But as for not bringing out your queen to early - that principle makes sense only to chess (unless you happen to suffer an overdose of imagination.) The cost of course, is that one must be contented with analyzing tic-tac-toe types of games.
As in everything else, game theoretic approaches have a trade-off. My intuition is that within the hyper-complex endeavor which is the advancement of economic science, the Nobel prize has nudged us closer to the optimum.