An item of information in a game is common knowledge if all of the players know it and all of the players know that all other players know it and all other players know that all other players know that all other players know it, and so on.In the battle of wits scene from the Princess Bride, the Dread Pirate Roberts has just put poison (iocane powder) into one of the wine cups in front of himself or in front of Vizzini:
Dread Pirate Roberts: Alright. Where is the poison? The battle of wits has begun. It ends when you decide and we both drink, and find out who is right. And who is dead.(transcript)
Vizzini: But it's so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me.
Dread Pirate Roberts: You've made your decision then?
Vizzini: Not remotely. Because iocane comes from Australia, as everyone knows, and Australia is entirely peopled with criminals, and criminals are used to having people not trust them, as you are not trusted by me, so I can clearly not choose the wine in front of you.
Dread Pirate Roberts: Truly, you have a dizzying intellect.
Vizzini: Yes, Australia. And you must have suspected I would have known the powder's origin, so I can clearly not choose the wine in front of me.
Dread Pirate Roberts: You're just stalling now.
Vizzini: You'd like to think that, wouldn't you? You've beaten my giant, which means you're exceptionally strong, so you could've put the poison in your own goblet, trusting on your strength to save you, so I can clearly not choose the wine in front of you. But, you've also bested my Spaniard, which means you must have studied, and in studying you must have learned that man is mortal, so you would have put the poison as far from yourself as possible, so I can clearly not choose the wine in front of me.
Dread Pirate Roberts: You're trying to trick me into giving away something. It won't work.
Vizzini: It has worked! You've given everything away! I know where the poison is!
Dread Pirate Roberts: Then make your choice.
Vizzini: I will, and I choose. What in the world can that be?
Dread Pirate Roberts: What? Where? I don't see anything.
(Dread Pirate Roberts looks around while Vizzini switches the cups)
Vizzini: Well, I, I could have sworn I saw something. No matter. First, let's drink. Me from my glass, and you from yours.
Dread Pirate Roberts: You guessed wrong.
Vizzini: You only think I guessed wrong! That's what's so funny! I switched glasses when your back was turned! Ha ha! You fool! You fell victim to one of the classic blunders! The most famous is never get involved in a land war in Asia, but only slightly less well-known is this: never go in against a Sicilian when death is on the line! Ha ha ha ha ha ha ha! Ha ha ha ha ha ha ha! Ha ha ha (Vizzini keels over dead in mid laugh)
Buttercup: And to think, all that time it was your cup that was poisoned.
Dread Pirate Roberts: They were both poisoned. I spent the last few years building up an immunity to iocane powder.
tags: game theory, movies