## Game Theory in Movies – The Princess Bride

In order to make movies both complex and interesting many screenwriters employ game theory unknowingly within their plots.  One classic example of this is in the 1987 version of the movie “The Princess Bride.”  In this movie there is a scene known as the “Battle of Wits” in which the main character Wesley challenges a cunning man known as Vizzini in a game for a Princess’s life.  In this game Wesley takes two goblets of wine behind his back and tells Vizzini that he has put Iocane powder, a deadly poison, into only one of the goblets.  He then instructs Vizinni to pick the goblet he wishes to drink and the man left standing wins the Princess.  In this setup of the game, the payoff matrix is as follows where A is Wesley and B is Vizzini:

 Vizzini’s Situation – If Poison is in A’s Cup Player A A’s Cup B’s Cup Player B A’s Cup n/a (1,-1) B’s Cup (-1,1) n/a Vizzini’s Situation – If Poison is in B’s Cup Player A A’s Cup B’s Cup Player B A’s Cup n/a (-1,1) B’s Cup (1,-1) n/a

Vizzini does not know what goblet the poison is in, therefore there are two payoff matrices based on the possibility that the poison is in either cup.  In this scenario each player must play opposite strategies, meaning that both players cannot drink from the same cup.  This is why the “n/a” appears in blocks of the matrix in which both players must drink from the same cup.  However, one can see from these tables that there is no dominant strategy considering that Vizzini does not know where the poison is located.  He has an equal chance of living or dying regardless of what cup he picks therefore the game appears to be a game of chance rather than wits.

However, what Vizzini does not know is that Wesley has spent years developing immunity to Iocane powder and has placed the poison in both cups rather than just one.  In this case, from Wesley’s perspective, the payoff matrix is as follows:

 Actual Situation – Poison in both cups and A is immune Player A A’s Cup B’s Cup Player B A’s Cup n/a (1,-1) B’s Cup (1,-1) n/a

In this case, no matter what strategy B, or Vizzini, employs he will still end up with a negative payoff, meaning that he will die.

This game pertains to what we have learned in class with a few twists.  First, in class we learned about dominant strategies and Nash Equilibriums.  However, from Vizzini’s point of view, there is no dominant strategy or Nash Equilibriums because he will change his strategy depending on whether the poison is in his cup or Wesley’s cup. This almost creates a “matching pennies” situation of sorts.  However, this situation is slightly different then “matching pennies” because not all of the strategies are permitted (i.e. Player A and Player B cannot both play A).  In addition, in this version there are two matrices that need to be considered rather than one.  In addition, this game has a deceiving trick because both players are considering different payoff matrices since Wesley has deceived Vizzini.  This means that Vizzini is playing a losing game from the start, which is what makes the game both interesting and funny to the viewer.

In all, the game theory in the “Battle of Wits” proves that the battle is a losing game and truly involves no wits at all.