Channeling Strength and Game Theory

OK, hold onto your hats for a minute while I discuss some mathematics before getting to the game portion of this post.

There is an area of mathematics called game theory that attempts to formalize what it means to play a game in an intelligent manner. When you apply this area to the study of competitive behavior you get some interesting things. For instance, it deals with solutions of games (how to win, no mater what the opponent does), optimal strategies in general, etc.

Where might you have seen this area of mathematics before?  Well, if you've ever seen the movie A Beautiful Mind, about the life of John Nash, then you've seen a movie about one of the most famous game theorists of all time. It is an area that is heavily applied in economics, which is how Nash won a nobel prize in economics...for doing some mathematics. (He developed the concept of a Nash Equilibrium, which is pretty nifty when looking for solutions in a lot of different cases. Even if, as John von Neumann said, it's "just a fixed-point theorem" after all.)

So, what area of game theory are we interested in here? It's one of the first things that a new student of the field will learn, the idea of domination where it applies to different strategies. Essentially, if one strategy is better than another in every situation, it dominates that other strategy, and no sane player would ever use that weaker strategy. Domination isn't necessarily the best concept to apply in all cases, but it will serve the purpose for this discussion.