Common Ground: EGT and CGT?

I took a Game Theory course as an undergrad in the fall of 2000. In this course, we studied a smattering of standard game theory as well as some voting theory. Now, I don't know exactly what is considered "game theory" but there are often some keywords that clue me in when someone is asking whether I know something about the economic side of game theory. I'm not ignorant of these terms, especially having taken a class, but I'm not a pro either! I have not tried to come up with utility functions as a model for different market outcomes. Nor am I familiar with different scenarios where a Nash Equilibrium exists and can be found quickly.

Still, as I mentioned recently, I dug into economic game theory definitions and used the term "symmetric game" to describe a game equal to its negative ("reflection"?). In both arenas, we still have players who make decisions and the game state they are looking at has a value. In both arenas, we talk about making a move and how to remove suboptimal choices.

How well do these different fields actually intersect, then? If a course were "team taught" covering aspects of both topics, would students be totally lost, or would there actually be some cohesion there?