Joho the Blog » The semi-transparent Prisoner’s Dilemma

The semi-transparent Prisoner’s Dilemma

A British game show that I never heard offers a version of the Prisoner’s Dilemma. As the host explains at the beginning, if both contestants agree to split the pot, they split it. If one chooses to split and the other to steal, the stealer gets the whole thing. If they both choose to steal, they get nothing. So, here’s the clip in which one of the players injects a new variable. [SPOILERS IN THE REST OF THIS POST]

SPOILERS SPOILERS SPOILERS

Why does the guy on the right (Mr. Right) finally choose the way he does?

If Mr. Left believes that Mr. Right will Steal, then Mr. Left will Split, so Mr Right might as well Split. If Mr. Left thinks that Mr. Right will Split, then Mr. Left will Steal, so Mr. Right can either Split (so Mr. Left gets the pot) or Steal (so neither gets anything); might as well Split. If Mr. Left believes that Mr. Right will steal and will break his promise to split the pot afterwards, then Mr. Left might Steal just to screw Mr. Right, in which case Mr. Left might as well let Mr. Left get the money rather than foregoing it for both of them, so Mr. Right should Split. No matter how you slice it, Mr. Left should Split.

If that’s right, and if Mr. Left were given time to work it through, then Mr. Left should have Stolen (assuming his aim is to maximize his share). But I’m pretty sure that I’m wrong about that.

2 Responses to “The semi-transparent Prisoner’s Dilemma”

  1. That was genius.

    What Mr Right had to do was convince Mr Left that if he chose “Steal” then he would absolutely, positively, not get any cash.
    And therefore his choices were “Choose to believe that Mr Right would not split afterwards, and to spite him.” and choose “Steal”, or “Choose to believe that Mr Right would split, and go along with it.”

    That makes it a much better bet to choose to split, because that’s now the _only_ way Mr Left can make any cash. So he chooses to do that, and Mr Right, knowing that, chooses to Split too.

    Very, very, clever thinking by Mr Right there.

  2. Absolutely fascinating. Mr Right was soooo smart.

    The paradox: he persuades Mr Left to split based on him saying he’s going to steal and that he’s A MAN OF HIS WORD. Then he goes against his word to Mr Left’s benefit.

    O’Henry would have loved this.

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