The Princess Bride

Common Knowledge and Rationality

In this classic film, one scene illustrates the humorous side of common knowledge and the limits of strategic reasoning in game theory.

The Man in Black (our hero) challenges Vizzini (bad) to a battle of wits. The Man in Black will poison one of two wine goblets, and Vizzini must choose which one to drink.

Before reading on, watch the scene.

Vizzini's reasoning demonstrates the infinite regress of common knowledge, "I know that you know that I know..." Perhaps more importantly, it highlights the fundamental notion of strategic moves that we will encounter. When the rules of the game are flexible, you can change them to your advantage! Changing the game beats playing the game.