What unites prisoners, hockey goalies, and piles of stones? The answer is Game Theory! Game Theory is a branch of math that tells us the best way to make decisions in situations with other players with their own preferences and interests. It also allows us to compute how to win in any deterministic game. Game Theory is incredibly useful in everyday life and has incredibly deep research questions.
In this class, we will cover everything from how to avoid getting poisoned by chocolate, what binary numbers have to do with the stone-taking game of Nim, what you and your friend should do if you get in trouble together, why some surreal numbers are fuzzy, and the not-so-secret strategy tip that every single coach in professional hockey is getting wrong.
More specifically, we will discuss decision-making contexts, ranging from naturally occurring ones such as team plays in sports, all the way to contrived ones such as the prisoner’s dilemma. We will talk about how probability theory affects decisions in these games and will also discuss games where there is no randomness. We will show how to fully solve any game with no randomness or hidden information, regardless of whether the players have the same set of moves available to them.
Prerequisites: Understanding of the rules of chess. Basic familiarity with binary, modular arithmetic, remainders, and rational and irrational numbers. Some experience and comfort with probability theory, on the level of being able to find the probability that at least one of the top two cards of a shuffled deck is an Ace.