Everybody is reacting to the Golden Balls video that I and others have posted. They are saying that the Split or Steal game has been solved.  I am not so sure.

  1. First of all I would like to point out that this solution was suggested here in the comments the first time I (or anybody else I believe) linked to Golden Balls in April 2009.  Florian Herold and Mike Hunter wrote:   “Perhaps a better strategy would be to tell your opponent that you are going to pick steal no matter what, and then offer to split the money after the show. Pointing out that your offer constitutes a legally binding oral contract, which has been taped, and viewed by hundreds of thousands of witnesses.  That way your opponent can opt to pick split, and half the money with you. Or defect in which case you both get nothing.”
  2. Also, Greg Taylor has a good analysis in the comments to Friday’s post.
  3. But the successful application of the idea in the most recent video ironically shows the flaw in their reasoning.  Consider the player who receives the proposal and is suggested to play split.  This is the player on the left in the video.  He should ask himself whether he believes that the proposing player will actually play Steal.  Florian, Mike, and the rest of the Internet make the observation that Steal is a dominant strategy and therefore a promise to play Steal is credible.  But Steal is a dominant strategy for a player with the standard payoffs and the guy who makes this proposal has revealed that he does not have the standard payoffs.
  4. Now you may respond by saying that the proposal to play (Split, Steal) and divide the winnings at the end is in fact a selfish proposal as it avoids the inevitable (Steal, Steal) outcome. So, you say that the proposer is in fact confirming that he has the standard payoffs and therefore that Steal is a dominant strategy and his promise is credible.
  5. But let’s look more closely. If he intends to carry out his proposal then he expects to end up with half of the winnings. Indeed he expects to have the full check given to him and either because of altruism, fairness, or reputational incentives to prefer to hand over half of it to the opponent. As he sits there with the balls in his hand and the expectation of this eventual outcome, he can’t avoid concluding that the cheapest way to bring about that outcome is to instead just play Split right now and allow the producers of the show to enforce the agreement.
  6. Given this the player who is considering this proposal should not believe it.  He should believe that the proposer is too nice to carry out his nice proposal.  A selfish player faced with this proposal should play Steal because he should expect the proposer to play Split.
  7. Having dispensed with this try, my personal favorite solution is the one proposed by Evan and elaborated by Emil in which the two men commit to randomize by picking each others’ balls.
  8. In any case, this video is an essential companion to the original for any undergraduate game theory course.
  9. Finally, does this Golden Balls show actually exist?  In the present?  How long ago did this happen?  Or is this just some kind of Truman Show like experiment you are all subjecting me to?