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Friend or Foe: Game Theory on TV

This article is about a game show that I used to watch when I was a kid. The show was called “Friend or Foe” and aired on Game Show Network from 2002-2003 and then briefly again in 2008. Contestants on the show worked in teams of two with someone they didn’t know and answered questions to earn money. At the end of the game the team that had accumulated the most money was sent to the “trust box.” This is the part of the game that relates to this course. The interactions in the trust box can be analyzed using Game Theory as a two player game similar to the Prisoner’s Dilemma.

In the trust box each player had the option to choose “friend” or “foe” without seeing what the other player was choosing. If both players chose friend the players split their total earnings 50-50. However if one of the players chose “foe” while the other chose “friend” the player who chose “foe” received all of the earnings  while the player who chose “friend” received nothing. If both players chose “foe,” neither player received any money. This game could be modeled in a game theory matrix as follows where X represents the total earnings that the players have accumulated:





X/2 , X/2

0 , X


X , 0

0 , 0

Looking at this matrix, we can see that that (Player 1, Player 2) = (Foe, Friend) and (Friend, Foe) are Nash Equilibria because neither player can gain from changing their strategy for the given strategy of the other player. We can also see that choosing “Foe” is a dominant strategy for either player because it is a best response or at least an equal response to either strategy of the other player.

Looking at the game this way, however, makes it seem simple and uninteresting. What makes it interesting and what drives people away from the dominant strategy is the participants’ idea of not wanting to “cheat” the other person out of the money that they have earned together. Because people want to be nice, they don’t always chose “foe.” The tendencies of players when taking into account this type of behavior could still be modeled and explained with game theory if we added a sort of “emotional payoff” from doing the right thing. This emotional payoff, however, is hard to quantify and varies from player to player. In the end it is what makes the game interesting and what made it work for TV.


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September 2011