Philosophy and Logic of Games

(3 Credit Hours) · Undergraduate

Shall we have a game? The course will explore the philosophy and logic of games, exploring all things games. We shall begin with some elementary game theory and decision theory, including elementary probability theory, covering mixed strategies, Nash equilibria, the prisoner's dilemma, and Tit-for-Tat, and then eventually the fundamental theorem of finite games, game trees, the hypergame paradox, and many examples of finite games and their strategies, such as Nim and other games. The latter part of the course will delve into infinitary issues, including determinacy and nondeterminacy, connections with the philosophy of mathematics, Conway games, and the surreal numbers as games. It will be a highlight of the class to cover the analysis of various infinite games, including infinite chess, infinite draughts, infinite Hex, infinite Wordle, infinite Sudoku, and more.