I finally got around to reading chapter 3 in Games of Strategy by Dixit, Skeath, and Reiley. I've fallen way behind Messrs. Aaron, Austin, and Paul. They recorded their discussion of the chapter and Paul followed up with some written notes as well.
The decision tree is a method put forward by the authors for how to create a strategy for a sequential move game -- a game where each player takes a turn in sequence as opposed to simultaneously.
These trees or flow charts start with a list of the choices the first player has -- each option being a different branch of the tree. The second player's options branch off of each possible play by the first player, etc. So If my choices are A or B and the second player's choices are Y or Z then the tree would look like this:
The four boxes on the right side are the 4 possible end results of this two-turn game. From here, you can analyze the value of each of those 4 results, then predict the 2nd player's best actions after either A or B, then decide what the first player's best choice is.
Multiple sequential turns can be added on and further branch from here to model the entire game.
Tragedy of the Game Commons
One specific example in the book immediately reminded me of a classic awkward gaming moment. In the example a handful of neighbors decide, in turn, if they will pitch in to fund the upkeep of a common area. Although they all want the area maintained, only a certain number of them have to pitch in to make it happen. After building the decision tree, the game theory "correct" play for the first person is to never fund the upkeep because the other people will.
In economics there is a similar concept called the tragedy of the commons. Which describes how in real life no one ends up paying to maintain the common area described in the books example.
I think we've all seen this behavior in board games. One player is winning and something must be done to stop that person. But stopping the leader does not help the person doing the stopping -- it only hurts the leader. So no one wants to.
Eventually, everyone teams up to stop the leader or one player is forced to do so and this never feels fun. In fact, sometimes it feels so un-fun that no one ends up prevents the leader from winning.
Obviously, Tragedies of the Game Commons are something games should strive to avoid. Can decision trees help us designers see them coming?