Luckily, for CGT this has a simple solution: the game tree. Want to prove something about a specific position? Just draw out the game tree and label the options appropriately. Students should learn this as soon as possible; I broke the news to my freshmen class right away.
Bad news: I'm expecting rigorous proofs in this class.
Good news: these can be a proof by picture.
Unfortunately, I didn't do a great job teaching the basic requirements. We had problems with:
* Arrows to left/right options of a position. These were sometimes nearly vertical so it was impossible to discern whether they were for right or left arrows. Other times they pointed up, which is often very difficult to read.
* Not drawing all the options. We hadn't learned about dominated options yet, so all options should have been listed.I think that the next time I teach this sort of course, I will have to be far more explicit about what makes a game tree. Also, I've done a good job this semester of using examples to motivate, but perhaps I didn't do enough examples of game trees.
Tomorrow the students have their first exam. Dangerous! I've decided to include a question where the goal is to find errors in a given game tree. I really wish I'd included these sorts of questions in the first few homeworks! We'll see how it goes.
(Oops! I inadvertently took last week off from posting. Sorry!)