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Split or Steal? : An Interesting Take on the Prisoner’s Dilemma

The British game show Golden Balls is similar to any other game show in that contestants compete against one another to maximize their own payoffs. The show consists of three rounds in which contestants pick golden balls with various amounts of money on them (anywhere from £10 to £75,000). In the final round only two contestants and five balls remain. This final round determines how the remaining money (the sum of the five balls) should be distributed between the two remaining contestants. This final round is actually just a modified version of the prisoner’s dilemma with the following payoff matrix:

table

The two contestants are presented with two balls, one with split on the inside and another with steal on the inside. If they both split then they each receive 50% of the money. If one steals while the other splits then the stealing one receives all the money while the other receives nothing. If they both steal than they each receive nothing. The dominant strategy in this game is to always pick steal, since this maximizes profit if the other picks split and doesn’t matter if they steal. The Nash Equilibrium in this game is for both players to walk home with nothing. However, contrary to the classic prisoner’s dilemma where the two prisoners are isolated; the two contestants are allowed to discuss with each other how they should pick. This can change the game quite a bit. After watching several episodes of the show I found that the most common outcome is actually for one person to pick split and the other to steal the money. The pre-decision discussion will usually consist of both players promising each other that they will split. One of the two will trust the other and pick split while the other, counting on the trustworthiness of the other, will choose steal.

In this short video clip we meet Ibrahim and Nick, who must decide how £13,600 (~$22,000) will be split.  This game has a unique outcome from all of the others, especially in the strategy that is used. During the discussion Nick tells Ibrahim that he is going to steal. Nick also says that if Ibrahim chooses split then he will give him half of the money after the show. This makes it much more likely for Ibrahim to choose the split because choosing steal gains him nothing while he at least has a chance of getting money if he chooses split. Nick now knows that Ibrahim will probably not choose steal so he chooses split also. They both end up choosing split and walking out with half of the money.

Link: http://www.npr.org/blogs/money/2012/04/25/151378032/game-theory-explained-with-golden-balls

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