Monday, May 7, 2012

Let's Play Golden Balls

Imagine the following situation:

Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal—if one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?

If you were one of the arrested men, would you betray your partner or remain silent? If you were just an observer, what do you think should the two arrested individuals do?

Golden Balls is a game show in the UK that places two contestants (after a couple of "elimination" rounds) in a similar situation. Given a jackpot amount that was determined in earlier rounds, contestants given two golden balls, one with the word SPLIT printed inside and the other with the word STEAL printed inside. They are then asked to secretly choose a ball. Each contestant's winnings are determined by the following rules:
  • If both contestants choose a SPLIT ball, the jackpot is split equally between them.
  • If one contestant chooses a SPLIT ball and the other chooses a STEAL ball, the "stealer" gets all the money and the "splitter" gets nothing.
  • If both contestants choose STEAL balls, they both get nothing.
The players have a chance to speak with each other face to face before making their choices.

If you were one of the contestants, how would you play the game? If you want to see one of the better ways to do it, watch this video.

The two situations above represent a problem called prisoner's dilemma, a classic example of game theory--which is a method of studying how people, businesses, and other entities make decisions. In a follow-up post, I will discuss a proposed solution to the prisoner's dilemma problem and we'll see how this solution agrees to or differs from how you and I will play the game.

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