The Nobel laureates for 2005 in Economics are Thomas Schelling and Robert Aumann for their work in game theory, which is basically the theory of strategic interactions between individuals or groups. Marginal Revolution has a good summary of the work of both Schelling and Aumann on their blog. I am not familiar with Aumann's work, but just last week, we discussed some of Schelling's racial segregation work in my graduate Urban Economics course.
The most interesting aspects of Schelling's work in my opinion:
1. His analysis of how people racially segregate into neighborhoods. He starts from a fairly realistic assumption that most people do not want to be a significant minority in their neighborhood. From that innocent assumption, he shows that people will start to move to neighborhoods where they are a majority, and you end up with neighborhoods that are totally segregated even when most people do not prefer a totally segregated neighborhood.
2.He also did very interesting work on using game theory to explain the nuclear conflict of the Cold War in his book The Strategy of Conflict. Schelling showed that countries can make their bargaining position better by giving themselves less options (giving yourself less options make your likelihood of retaliation greater). He also showed that uncertain retaliation is more credible in nuclear war than guaranteed retaliation (why would you retaliate after you have already been destroyed?). As pointed out by Marginal Revolution, you can see pretty good illustrations of his ideas in the movie Dr. Strangelove.
No questions here, just illustrating more interesting, non-mainstream applications of the field of economics...