I was wondering when someone would ask that! It comes from the Wikipedia article on alpha-beta pruning in game theory, which is about strategizing (in a CDT fashion) in a game where your move and your opponent’s move alternate. So it’s not directly connected to the post, but I felt it imparts the right intuitive flavor to the notion of a decision theory.
Cool, thank you. It does impart the right flavor. I really like what Luke has started with putting pictures in main posts. Something about it makes it easier to read.
It was clear to me that the tree represents a two-player zero sum game with alternative moves, where Square is trying to maximize some quantity and Circle minimize it. It wasn’t clear from the picture what algorithm caused the “pruning” though.
A decision tree (the entirety of my game theory experience has been a few online videos, so I likely have the terminology wrong), with decision 1 at the top and the end outcomes at the bottom. The sections marked ‘max’ have the decider trying to pick the highest-value end outcome, and the sections marked ‘min’ have the decider trying to pick the lowest-value end outcome. The numbers in every line except the bottom propagate up depending on which solution will be picked by whoever is currently doing the picking, so if Max and Min maximize and minimize properly the tree’s value is 6. I don’t quite remember how the three branches being pruned off work.
I spent the first several seconds trying to figure out the tree diagram at the top. What does it represent?
I was wondering when someone would ask that! It comes from the Wikipedia article on alpha-beta pruning in game theory, which is about strategizing (in a CDT fashion) in a game where your move and your opponent’s move alternate. So it’s not directly connected to the post, but I felt it imparts the right intuitive flavor to the notion of a decision theory.
Cool, thank you. It does impart the right flavor. I really like what Luke has started with putting pictures in main posts. Something about it makes it easier to read.
It was clear to me that the tree represents a two-player zero sum game with alternative moves, where Square is trying to maximize some quantity and Circle minimize it. It wasn’t clear from the picture what algorithm caused the “pruning” though.
A decision tree (the entirety of my game theory experience has been a few online videos, so I likely have the terminology wrong), with decision 1 at the top and the end outcomes at the bottom. The sections marked ‘max’ have the decider trying to pick the highest-value end outcome, and the sections marked ‘min’ have the decider trying to pick the lowest-value end outcome. The numbers in every line except the bottom propagate up depending on which solution will be picked by whoever is currently doing the picking, so if Max and Min maximize and minimize properly the tree’s value is 6. I don’t quite remember how the three branches being pruned off work.