Hacking the Golden Balls

Via Bruce Schneier, a refreshing exploitation of the (modified) Prisoner's Dilemma round on the split-or-steal game show Golden Balls.

Last 5 posts by David Byron


  1. says

    The "modification" is that the prisoners are permitted to talk and therefore plan (and, in this game, launch a meta-game).

  2. says

    (a) Nobody said it was research.
    (b) Nobody said it was Nobel-level*
    (c) The fact that you stumbled over, or rhetorically postulated, both (a) and (b) while failing to discern anything more than "one outcome among many" puts your comment, if not your discernment, at risk of lapsing into the "what's the fuss about?" category.

    The Kobyashi Maru was the unwinnable scenario, and Kirk rendered it winnable by breaking the test's implementation. Here, the total loss scenario is only one of four (namely, {lose-lose, lose-win, win-lose, win-win} since the payoff matrix is identical to the classic PD), and non-Kirk forces the most extensively favorable outcome through psychological manipulation.

    So it appears that even your hashtag fails in relevance.

    * Nash did score for game theory, though not in a simplified game-show form.

  3. Mercury says

    The modification is that the other balls actually contain German Shepard pie.

    Seriously, what's this video doing on a dog fancier blog?

    The brown shirt guy upped the drama but he almost shot himself in the foot for no reason by riling up the other guy to "steal".

  4. says

    In the classical PD defecting (here, "stealing") is unambiguously a player's best move regardless of what the other player does. In this game, Nick's gambit has a chance because in this variant Abraham gets zero regardless of what he plays if Nick follows through on his (credible) threat to play steal. Stealing is only a weakly dominant strategy here, unlike the classical PD.

    I would interpret the communication period as also changing the game fundamentally, even though players cannot write binding contracts. Nick's promise to split his winnings with Abraham in effect changes the payoffs, because there's more than money at stake here.

    Given Nick has made a promise on national TV to share, his payoff if he wins the whole pot and doesn't follow through on his promise is not 13,600, it's rather: [ 13,600, breaks his word, revealed to be a liar on national TV ]. If Abraham thinks that Nick would prefer [ 6,800, keeps his word, and is revealed to be a good guy to national audience ] to that outcome, then Nick's promise to share is credible and Abraham should play split.

  5. Crissa says

    I'd say Nick's promise – in the US at least – is not something you can bank on. Verbal contracts mean nothing.

  6. Joe says

    My understanding is that generally, oral or verbal contracts are indeed legally enforceable in the US, but the fundamental challenge is obviously proving what was agreed upon. But if a verbal contract was captured on video – as this one was, or backed up via subsequent emails and text messages after the fact, I'd say they are enforceable.

  7. David Schwartz says

    Chris Auld: That's not true. Whatever move is best for one player is necessarily best for the other player as well, since the game is symmetric. So if both players play their optimal strategy, they will both choose the same thing. Clearly, "split/split" is better than "steal/steal". You cannot assume the two player's choices are independent and then figure out what strategy is best. That's like figuring out the best chess move by assuming your opponent chooses his move randomly. When you choose what move is best for you, you should assume your opponent makes the move that is best for him, not that he might make either move.

  8. says

    Joe is correct. This would be an enforceable contract in the United States. The statute of frauds, or the requirement that a contact be in writing, most commonly applies to the sale of land or a surety obligation. It would not apply to this case.

  9. says

    … or sale of goods valued at $500 or more, a contract which cannot be completed within one year by its terms … and the one that frightens Patrick the most: a contract for marriage.

  10. says

    David: If all that matters to the players is their monetary payoffs, then (steal, steal) is the only Nash equilibrium.

    What I am noting is that money's not all that's at stake here. The communication here is not cheap talk because it took place on national TV! Suppose Nick had played steal, taken the entire pot, and broke his word to share with Abraham. This would be news; much of the country would conclude that Nick is an unreliable, lying jerk.

    Suppose Nick would be willing to pay more than 6,800 pounds not to be widely considered an unreliable, lying jerk. Then (steal, steal) is no longer a Nash equilibrium, because Abraham's best response to Nick playing steal is strictly to play split, as he realizes that Nick will keep his word and share the winnings. (Nick steals and shares, Abraham splits) is a subgame-perfect Nash equilibrium to this game.

  11. says

    I can't see a court enforcing the contract, not because it's verbal (obviously they have met all the legal grounds for a contract), but because the whole point of the game show is that the other person is expected to lie. Obviously every betrayal on this show doesn't end up in court.

    It's like suing the guy who punched you in the breadbox while you were in a boxing match.

  12. PLW says

    Chris, that's incorrect. This is a modified prisoner's dilemma, where there are 3 pure strategy equilibria steal/split and split/steal and steal/steal. In all three of those arrangements, neither player can improve by changing his strategy. Of course in the steal/split and split/steal equilibrium the person choosing split can screw the other guy by switching to steal, but from a strict monetary perspective he is indifferent so it is an equilibrium.

  13. Paul Baxter says

    If the host reveals what's inside ball number three, can we turn this into the Monty Hall paradox?

  14. says

    PLW: You're right, thanks for the correction, I left out the word "symmetric" before "equilibrium" (see the post to which I was responding). That doesn't alter the remainder of the argument.

  15. PLW says

    No probablo. It's also the unique trembling-hand perfect NE, which is probably more salient than symmetry. I showed the first half of the video in my intermediate micro class today and stopped the video before the reveal. We found the equilibria and talked about these issues. Then I asked them to vote on what the players would reveal. Although all off them claimed to have not seen this, the modal answer was split/split.