Game theory, for all of its hype, isn’t all that great at telling us what to do in real life. When Morgenstern and von Neumann originally published the magnus opus of game theory, Theory of Games and Economic Behavior, one buyer falsely got his hopes up in believing that it might help him manipulate the stock market. Others expressed scorn at the field’s shortcomings and distance from application – game theory could conveniently prove already intuitive results, but it couldn’t tell us how to win at chess.
Despite the fact that game theory is not a panacea for the world’s economic problems, it can still be extremely useful. The telecom auction in the 1990’s, designed by game theorists, saved the US and UK public billions of dollars (a cumulated 35 billion, to be exact). The powerful notion of a Nash equilibrium in multiplayer-games helps break out of the self-referential “I think that-my opponent thinks that-I think that-my opponent thinks that …” infinite loop and identify natural strategies in non-cooperative games.
However, there are many two-player games in which the Nash equilibrium is not a useful concept, because a particular game might have two of them. The famous example is prisoner’s dilemma (read more here: http://plato.stanford.edu/entries/prisoner-dilemma/). Another example is highway chicken: