In Golden Balls, a British television show in the mid-2000’s, the
players face the prisoner’s dilemma. They have two choices on
their way to winning a jackpot: split or steal. If they both steal, neither
gets the money. If they both split, they split the money. If one steals and the
other splits, the ‘stealer’ takes the entire jackpot. The dominant strategy,
then, is to steal.
In this episode, Nick
achieves the Pareto optimal state despite the dominant strategy of stealing. He
claims that he will steal regardless of the discussion, and offers to
split the winnings informally after the show if Abraham chooses split. Otherwise, they both walk away with nothing, he claims. In the
end, Nick persuades Abraham to split, and secretly splits to achieve the Pareto optimal state
despite the dilemma.
Nick can avoid the trap of the dominant
strategy because of the circumstances of this game. For one, the prisoners are
allowed to discuss their choice before making it. However, conversation doesn’t always work: in many other episodes, discussion still
leads to Pareto un-optimal states (steal-splits, or steal-steals). The second aspect is that the prize is
splittable. Abraham trusts Nick enough to attribute some non-immaterial
probability to actually splitting after the show. That version of the ultimatum game is something for another blog post.
1 comment:
Hi Sam, I think you're right that the circumstances of the game (that the players can discuss their choice before making it) definitely changes the scenario, because the players can try to figure out the other person's strategy. However, in this TV show, the players do not face a prisoner's dilemma to begin with because there is no dominant strategy. If we are looking at Nick's decision, he will definitely steal if Abraham splits. If Abraham steals, however, Nick is indifferent between splitting and stealing (his payoff for each one is zero). His strategy depends on Abraham's decision, and he won't end up coming to the same strategy each time. We can only have a prisoner's dilemma if there is a dominant strategy that is Pareto-inefficient. There is no dominant strategy, therefore there is no true prisoner's dilemma.
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