Besides being very useful, game theory is fun. A broad liberal education should include at least the basics of game theory, just as it should include the fundamentals of microeconomics. Indeed, game theory is one of the most important tools in the study of microeconomics and political science.
Wiki has an informative page on “Game Theory.” A great place to start is at the Stanford Encyclopedia of Philosophy page on Game Theory. Best of all, a free online course on game theory is being offered at Stanford. The course starts on 19th March and registration is open until March 25th. See the information about the course.