Active learning with Monty Hall in a game theory class

The authors describe a game that students can play on the first day of a game theory class. The game introduces the 4 essential elements of any game and is designed so that its sequel, also played on the first day of class, has students playing the well-known Monty Hall game, which raises the question: Should you switch doors. By implementing a procedure proposed some 45 years ago, students not only quickly grasp the correct answer, but also become keenly aware of the importance of the assumption that players have common knowledge of the essential elements of a game.