Winning With Game Theory

Wednesday, April 25th, 2012

This has been circulating around the Internet the last few days. Brilliant bit of strategizing.

 

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30 Responses to “Winning With Game Theory”

  1. #1 |  Alex | 

    No, it was mediocre strategizing!

    First of all, the bald guy was clearly one of those “split or I’ll feel bad about myself” dudes that can easily be manipulated into giving you all the money. The non-bald guy should have waited a second to come out with his strategy to see if it was even necessary. It wasn’t. The “my father told me…” nonsense was a clear indication that the bald guy was not going to steal under normal circumstances

    Second of all, why did the non-bald guy end up splitting? He gave up thousands of dollars. It’s a game show, he shouldn’t value not having to admit he lied to the guy after the show at thousands of dollars.

    Third, the bald guy should have responded to this strategy with “no, I’m going to steal, no matter what YOU say.” That would have reset things.

  2. #2 |  David | 

    I remember watching some Friend Or Foe? reruns on cable one day and wondering if such a strategy would work (complete, if necessary, with writing the other player a check as a show of good faith). I assumed that anybody who tried would get their episode canned, though.

  3. #3 |  Zargon | 

    A few thoughts about it.

    First, sure, it’s a substandard strategy if your goal is to walk away with all the money. But if your goal is to force a split, I’d say it worked out nicely.

    It was a pretty simple scheme, really. Precommit to taking steal, and now the other guy’s payoff matrix is simply steal – get nothing, split – get half if you trust the guy. Assuming that the precommitment was credible, the bald guy simply took the logical choice.

    The problem now, is now that the precommitter went back on his choice and took split as a show of his good faith, it probably won’t work in that format again. The next guy who tries is had to think about the other guy knowing about how it went this time around and taking steal. In that sense, while it made for a better youtube clip to go back on the precommittment and taking split, it broke the scheme. I’d predict with 90% certainty that the first imitatation of this scheme will end in tears for one or both.

    A possible modification to the scheme might be for the precommitter to add collateral. Something like “You can hold onto my wedding ring until I write you a check after the show”. Of course, the show will disallow out-of-game deals in their contract if anybody presents too polished of a scheme that gets the two people to split without having to trust each other. Other game shows already do that.

  4. #4 |  Chris in AL | 

    He acted to take the possibility of the other guy taking it all out of play. He wanted half and made a play to eliminate or at least greatly reduce the risk he would get nothing. I agree that it is unlikely to work again for anyone else. But this time it clearly worked.

  5. #5 |  Jamie | 

    Other potential reasons this is brilliant strategy (don’t know if these played into not-baldy’s payoff matrix or not):

    - He got to walk away looking like the smartest (or most successfully manipultive, or most skilled) guy in the room,
    - He is getting a ton of attention on YouTube,
    - He could have made side bets with people not on the show.

  6. #6 |  (B)oscoH | 

    They’re gonna have to rename this show Golden Bollocks when it comes to America.

  7. #7 |  EH | 

    Second of all, why did the non-bald guy end up splitting?

    God bless America. You are a credit to the human race.

  8. #8 |  Other Sean | 

    Elegantly made point about what life could be like if we were removed from the game of constantly guessing at other people’s intention.

    Who cares if it works only the once?

    I already know the world is full of fools like Alex (#1), but the existence of people like Nick – both shrewd and decent – is supposed to be impossible, according to conventional morality.

  9. #9 |  Alex | 

    Wait how am I a fool? I’m open to having my mind changed about this. Unless you’re going to make a moral argument against choosing steal.

  10. #10 |  Tim | 

    look up “Prisoner’s Dilemma” on Wikipedia

    “With the money I’ve won, I think I’ll respray my yacht” <– priceless

  11. #11 |  IGotBupkis, Legally Defined Cyberbully in All 57 States | 

    >> They’re gonna have to rename this show Golden Bollocks when it comes to America.

    LOL, and why is this? Us Yanks don’t use the term “bollocks” — 90% of us wouldn’t have a clue what it meant.

  12. #12 |  IGotBupkis, Legally Defined Cyberbully in All 57 States | 

    >>> I already know the world is full of fools like Alex (#1), but the existence of people like Nick – both shrewd and decent – is supposed to be impossible, according to conventional morality.

    Ah, no… in casual social situations, “where what goes around” is potentially able to “come back around”, the best policy is decency and charity. That’s why otherwise deadly single-encounter policies like forgiveness, charity, mercy, and magnanimity manage to survive as social behaviors.

    You need to look up the Iterated Prisoner’s Dilemma (IPD) on wikipedia or somewhere else.

    As it turns out, Gandhi was wrong — his exclamation, “an Eye for an Eye only makes the whole world blind!” is patently wrong, and this bit of Game Theory (IPD) applied to the real world shows it.

    “An Eye for an Eye, with forgiveness” is built into the way the universe works. So the original Jewish maxim, tempered with Christian charity, is in the design of the universe. That may not be a Sign from God, but it does say which religion is closest to “Truth” when it comes to human behavior…

    The biggest problem with this gameshow is that it’s a single-encounter situation… so the iterated aspect of the PD isn’t really applicable. So the pure, dismal, PD rules apply, and you should work to screw your opposition over.

  13. #13 |  CyniCAl | 

    On Jeopardy, if there is a tie after Final Jeopardy, the tied contestants each get the cash they won, and each gets to return the next day for a chance to win more cash.

    I’ve often thought that an enterprising contestant could propose to the other contestants, before the taping begins, that if there is an opportunity during Final Jeopardy to wager an amount that generates a tie, then he/she will do so on the condition that the beneficiary of the wager splits the winnings with the leader. Should be a no brainer since the trailing contestant would have another go at it the next day and a chance to win then. Also shouldn’t matter much to the leader who they face, unless they think their competition might be weaker the next day … no way to really know that.

  14. #14 |  Bob | 

    Any strategy where you “give” the other contestant half the cash is doomed simply because of the tax considerations.

    Just like the Prisoner’s dilemma… optimal choice is to always steal.

  15. #15 |  Mark Z. | 

    Any strategy where you “give” the other contestant half the cash is doomed simply because of the tax considerations.

    Declare it as a business expense.

  16. #16 |  Other Sean | 

    Alex, to answer your question from #9:

    First of all you missed the intent of the post. There’s a million clips of people burning their opponents in game shows like this. Buried amidst all that noise, Radley found one interesting variation. Your response was to immediately complain that this clip didn’t turn out like all the others. The things you didn’t like about the outcome here, were the only things that made it worthy of note.

    But the real folly is that you now insist moral considerations should be excluded from the discussion. Why? Nick the non-bald player, evidently wanted to test a moral hypothesis, by discovering whether it was possible to compel someone into a cooperative solution. He did that, but because you didn’t like him doing it, you simply announce that morality should be irrelevant to the question of strategy.

    But Alex, my droog, morality was the object of this stratagem. How can you possibly judge it apart from that?

  17. #17 |  CyniCAl | 

    There is a word in the English language for “non-bald.”

    That word is “hirsute.”

    That is all.

  18. #18 |  Tim | 

    ^^ “follicle-aly(?) challenged” comes to mind

  19. #19 |  Gilliss | 

    Hirsute means excessively hairy, not just “non-bald”.

  20. #20 |  Alex | 

    I’m certainly not complaining about the video! It’s a great video.

    There are literally 0 videos like this of the show. The reason this is an interesting video is because of its unique strategy. The uniqueness does not depend in any way on the non-bald guy ending up choosing to split; it has to do with the non-bald guy committing to stealing in order to affect the behavior of his opponent.

    Morality is relevant as far as the contestants value it. If non-bald values the other guy getting some money more than he values the money himself, then he acted correctly. But this is a game show–the entire point is to compete with other contestants and be smarter than them in order to win money for yourself rather than allow them to win money. If non-bald were literally stealing money, in my personal opinion morality would be more important. But in this case, where it can hardly be argued that it is “bad” to “steal,” I don’t think non-bald guy should have valued morality as he did. But of course, that is his decision to make.

  21. #21 |  ACGypsy | 

    While I wholeheartedly agree with Other Sean’s comments @16, I do have a non-moral counterpoint to Alex as well.

    First, you have to not the short time frame the guy has in which to read his opponent and act. Even if he’s pretty certain that he’s bullied the guy into choosing SPLIT, he can’t be 100% sure, and there is ample evidence to suggest that he’s pissed the guy off. The guy might be willing to STEAL out of spite just to punish the immorality that he sees in the guys actions. In fact, I have a hard time thinking of any other reason the bald guy would choose STEAL given the convincing disposition of the first.

    Now, you might suggest that this outcome is a loss for the hirsute gentleman, but I would submit that it still is better than a STEAL-STEAL outcome. Given that the only reason the bald guy should STEAL is if out of moral opposition to the guys expressed tactics, the result is then a windfall in the eyes of the winner who would likely be receptive to sharing at least a portion of the proceeds with the guy who ultimately made what the bald guy clearly has expressed he views as the moral choice.

    As for your valuation of choosing to SPLIT, I haven’t seen the entire episode, but I imagine both of these guys are identified by name, hometown and occupation at some point, if not repeatedly throughout. Depending on the rarity of the name, size of the hometown, and reputation of the occupation, the cost of being a complete bully on national television shouldn’t be discounted.

  22. #22 |  Frank Stein | 

    Thus we have determined that non-bald guy is a better human being than Alex. No offense to Alex.

  23. #23 |  MikeZ | 

    Well I wouldn’t go that far. This was a game show that seems from the clip to be exclusively aimed at lying to and manipulating your opponent. In that context there really is no way to say that any game decision in this case show a lack of moral character.

    Moderately-Hairy Player’s strategy was certainly interesting and entertaining and in choosing split you could certainly argue he was making a moral decision to share. However stealing and just taking the money wouldn’t have been immoral in this context at all.

  24. #24 |  AL | 

    Any strategy where you “give” the other contestant half the cash is doomed simply because of the tax considerations.

    Why is it doomed? Sure you have to pay taxes, but you still get something. Getting something and paying taxes on it still beats getting nothing which is what would’ve happened if the bald guy chose to steal (and the whole point of this strategy was to deter the bald guy from stealing).

    Just like the Prisoner’s dilemma… optimal choice is to always steal.

    Actually, in game theory terms, the decision to always steal leads to the Nash equilibrium, but that is not the same as the Pareto optimum. The Pareto optimum in this game is to both split.

  25. #25 |  yonemoto | 

    What if instead of offering to split 50-50, he offered to split 60-40?

  26. #26 |  CyniCAl | 

    #19 | Gilliss — “Hirsute means excessively hairy, not just “non-bald”.”

    Yeah, but you had to look it up to figure that out, douchebag.

  27. #27 |  Sean L. | 

    Alex: “it has to do with the non-bald guy committing to stealing in order to affect the behavior of his opponent.”

    You’re missing it… He didn’t commit to stealing. He just convinced the OTHER guy he was committed to stealing, knowing he was going to split all along.

    He set up a situation where either A) both would get something if the bald guy just acted rationally (if you KNOW the other guy’s taking steal, you might as well chance he’s an honest guy and give you something later) or B) make the bald guy feel so bad about wiping BOTH of their chances by taking steal, that he would give back half the money anyway!

    Radley’s right. This was masterful.

  28. #28 |  Sean L. | 

    And no, the correct name in America would be “Brass Balls.”

  29. #29 |  Bernard | 

    It’s worth noting that the tax consideration doesn’t apply in the UK because winnings aren’t taxable.

    It’s obviously still an issue for anyone plotting the usefulness of this strategy elsewhere, but it wouldn’t have been a factor for these two.

  30. #30 |  Colin Hall | 

    I always thought that if I was confronted with the Prisoner’s dilemma, after being arrested for some crime or other, I would plead that I am innocent and not connected to the other party at all. I would then argue in court that the offer that had been given to both myself and my co-accused was so weighted towards both parties confessing that my co-accused had simply taken the obvious path (guilty or not) to avoid a long sentence.

    I would hope that our legal system would want to avoid sending an innocent man to prison at all costs and release me, free of all charges.

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