14 ms·

Outwitting the Prisoner's Dilemma

80 points by Natsu 15y ago

chris_wot 15y ago
That was awesome. But did you see Nick's face at the end at what Ibrahim said? Lol!
- Natsu 15y ago
  A little bit of game theory goes a long way. But something like that wouldn't work for very long before someone came along who was only faking it. There are a bunch of related videos of this show as well. It can be interesting to try to predict the outcomes to see just how good your internal lie detector really is. EDIT: Also, don't miss one of the comments. BCR came up with the clever solution of passing one of their balls to the other player. That's quite the game breaker, though, so it probably wouldn't be allowed. I guess I should also mention that this is technically a variant of the PD, and that I change the title because almost nobody would know what the story was about otherwise.
synctext 15y ago
This blog post+Youtube video+Amazon preview made me order the book. Good stuff. For many years I've been working as a scientist to break the Prisoner's Dilemma problem. Case study is swarming-based downloading, where cooperation is needed for speed and anonymity. However, for over a decade scientists/developers seems have largely failed to do better then tit-for-tat (with unbounded scalability in number of users). Book preview contains interesting text on paying taxes, parasite behavior and broad view of trust.
zorbo 15y ago
Schneier comments: > The game is turned on its head Is that really true? What has changed? Player B still can't trust that player A will give him 50% of the money outside of the game. Player could turn the tables by claiming he too will steal. Wouldn't that put them back to the original situation?
- dsr_ 15y ago
  You are assuming that social pressure either doesn't exist or is in favor of dishonesty. The first is not true, and the second is only true for limited peer groups. Consider how your family would treat you if you reneged on a verbal commitment you made on TV. For the vast majority of people, this is a major negative factor. Now add in your coworkers, employers, friends... Most people are honest most of the time, and especially so when there is a high likelihood of being caught cheating.
  - Natsu 15y ago
    That exact line of reasoning is brought up during the discussion in this video of the end of another game: https://www.youtube.com/watch?v=y6GhbT-zEfc&feature=relmfu https://www.youtube.com/watch?v=y6GhbT-zEfc&feature=relm... That said, you're right about the fact that reputations matter. They just don't matter to everyone.
  - ecmendenhall 15y ago
    Exactly. This is an example of a commitment strategy (http://plato.stanford.edu/entries/game-theory/#Com http://plato.stanford.edu/entries/game-theory/#Com), and it was only credible because others were watching. Reputation is a very common way we make credible commitments when we deal with one another, but the results might have been different without an audience. It's funny that the one-shot prisoner's dilemma is used so often as an example of rational self-interest leading to suboptimal outcomes or formal modeling failing to capture real behavior. This is true only for the most stylized models and simplest games. Really rational players will choose to restructure the rules and play a better game! Since prisoner's dilemmas were bad games, we figured out how to make credible commitments and overcome them. Since talk is cheap, we developed things like punishment and social norms to enforce commitments. Adding things like iteration, reputation, and punishment to simple games leads to complex cooperative outcomes that reflect real behavior—and we can model them by adding a few simple rules. I think it's a fascinating and optimistic view of human history: modern market-exchange societies are the outcome of a long process of figuring out how to turn bad-outcome games that encourage defection into positive-sum cooperative ones that benefit everyone. Yet we are still biased to ignore all the cooperation around us and see selfishness (here's one of my favorite papers on this subject: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=929048 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=929048). I've also found it a very valuable personal insight. When you find yourself playing a bad game, don't settle for choosing the least harmful payoff. Figure out how to change the rules.
philh 15y ago
Given the selection mechanism, I'd be tempted to try a blind strategy. "I'm not going to look at my ball before I pick it, but if you split and I steal, I'll give you half the money." It wouldn't be good against a pure money-maximiser, because his expected $value is higher for steal (1/2 versus (1+P(I'm honest))/4), but if he's risk-averse and trusting it might work out.
- thenonsequitur 15y ago
  It's not clear that this strategy is possible within the the framework of the game show though. The host instructs both players to look at the concealed choices before they're allowed to talk to each other. To employ the blind strategy you'd have to explicitly not look at them (and probably say something at that point to make it clear you don't plan on looking at them). This would be directly contradicting the host's instructions. While the host might allow it, I think it's more likely they'll say "sorry, but you have to look at them".
davidjohnstone 15y ago
That strategy only works in that particular version of the game where it is possible to split the reward. You can't split jail terms 50-50. That said, that was a great bit of TV. And Nick's double-take when Ibrahim said what he'd do with the money was gold. (In case you missed it, he said he'd respray his yacht.)
- ghshephard 15y ago
  re: "You can't split jail terms 50-50." - sure you can. You can both be sent to prison for 1/2 the expected time if you both keep mum. But, if one of you squeals, then that person gets rewarded with no time, and the person who keeps mum goes to jail for the full sentence. But, if you are both stupid enough to squeal, you both go to jail for the full sentence.
  - jimworm 15y ago
    I believe what was meant is that you can't split jail terms post-sentencing, and let someone else serve half your term.
    - davidjohnstone 15y ago
      Indeed. I considered editing my original post just after I wrote it to clear up that ambiguity, but I figured people would understand what I meant...
    - ghshephard 15y ago
      Thanks to my in-depth research of criminology (I watched two seasons of Boardwalk Empire, and several seasons of The Wire) - I can relate that criminals will sometimes agree to have one person do the time, while the other pays a bonus to them/makes it up somehow.
judofyr 15y ago
He's only outwitting the Prisoner's Dilemma in the sense that he's shifted his main goal to get some money (instead of everything). There are more certain strategies if that's your goal though: You can get the other part to join a mutual agreement: if one of you steals (while the other splits) you agree to share the money. If the other part doesn't agree, you say you'll steal and take all the money (if he splits). The other part can only get money if he agrees with you, and every choice except for (steal, steal) is going to split the money between you two. Split is the only choice that makes sense. It would be much more interesting if they changes the stakes a bit: Stealing money gives you more than the sum of splitting.
stevenkovar 15y ago
What's interesting about this show is the pair forced into a Prisoner's Dilemma are given the chance to discuss the matter with each other, adding another layer to its complexity. In most examples I've seen personally, the two subjects are given their options in private and told to make a decision without having contact.
- sopooneo 15y ago
  If you assume the players in the classical prisoner's dilemma have common knowledge of the rules and that neither of their choices are revealed until both have made their choice, I don't think their being allowed to talk makes much difference at all to the underlying dynamics.
Anderkent 15y ago
Of course that's not a real prisoners dilemma, because the payouts are wrong. In the real prisoners dilemma Defect-Defect gives you a better payout than Cooperate-Defect. So when your opponent pre-commits to defect, you must defect.
- yonran 15y ago
  I believe you meant Defect-Cooperate gives the defector a better payout than Cooperate-Cooperate. At any rate, I’m not sure that it makes a difference in this video.
  - jgeralnik 15y ago
    No, he means Defect-Cooperate should give the person who lost less than he would have gotten from Defect-Defect. For example, in the Prisoner's Dilemma you might get 0 years of jail time if only you defect, 1 year if you both cooperate, 3 years if you both defect, and 10 years if only the other person defects. Then, knowing that the other person will defect it is still in your best interest to defect as well. In this challenge, if you know that the other person will defect you automatically get $0, whether you defect or not. In that case there is no particular reason for you to defect (except out of spite) and you are better off with the hopes that your opponent will keep his promise than with nothing.
- robertskmiles 15y ago
  The biggest reason it's not a real prisoner's dilemma is because the prisoners can communicate. Key to the standard prisoner's dilemma is that there is no way for the prisoners to talk to one another. Like the post says, it's a variant.
  - dbecker 15y ago
    Inability to communicate is not required in the classical prisoners dilemma. It's inability to credibly commit. The distinction is illustrated with the common application of the prisoner's dilemma to cartels. Cartel members can tell each other they will restrict production, but they do not observe each other's factories. So even if they agree ahead of time to reduce production, that is cheap talk... and they can produce whatever they want. It's quite similar to this game show, though as a previous commenter pointed out, the relative payoffs are different.
skore 15y ago
This is great. The Show offers each player with three possible outcomes, which makes negotiation hard because the highest incentive is on getting all the money (choosing Steal while tricking the opponent into choosing Split), while the lowest incentive is on nobody getting anything. What Nick does by saying that he will definitely Steal is reducing the choices for Abraham to two: Split or Loose. Actually just one: Loose, albeit with a promise to also split. The cunning bit about the plan, of course, is that Nick never intends to choose Steal. Choosing Steal is foolish to begin with: There is a 50% chance that nobody will get anything if you choose steal, so by default, players should stay away from it. "Count your blessings", so to speak. What is clever about this is that Nick has replaced the technical bet with a social one: He has done something that appeals to his opponent, by challenging his intellect, turning the game on its head. For Nick, the chances are now that either he gets half or nothing. He, internally, accepts a lower possible payout to himself to maximize the probability that the "group" will cash out. In any outcome, this would mean that it's no longer "He tried to get the money", but "He tried to make sure we get the money". I would say there is a pretty good chance that Abraham would have decided to give him half, even had he decided to Steal, basically matching Nicks generosity. This is supported by the fact that Nick really did end up displaying the Split - Had Abraham revealed a Steal at that point, he surely would have felt like quite bad about this ("He did it to help us both, after all!"). Nick has simply maximized the chances of a Split on all available vectors.
- sopooneo 15y ago
  Morality aside, choosing steal is foolish unless it works, then it seams pretty sensible.
  - skore 15y ago
    Superficially, choosing either Steal or Split gives you two sets of equal, 50% chances: Steal: 50% Everybody looses, 50% I get everything Split: 50% Everybody wins, 50% Opponent gets everything In very basic, almost evolutionary terms, the dumbest thing to do is both choosing Steal, because that would mean that there are two losers. Only choosing split yourself makes sure that there is a winner. Steal only seems sensible if you care about winning yourself.
AznHisoka 15y ago
I would think threatening the other person to split would be a dominant strategy. I wouldn't wanna steal if I knew the other person was gonna harass me the rest of my life.
codehotter 15y ago
If you don't think you can trust the other participant, you could do the following: Point at one of the other's balls. Say "I will choose steal unless you pick that one. If you do pick that one, you may choose the ball I'll pick." Unfortunately, your expected value is only 37.5% with this strategy, not 50%. You can still do better if you trust each other.
thejteam 15y ago
When the person comes to collect your answer, make them believe you left through the window and then hide and run out the door while they are investigating. And lock it. At least it worked in "The Mysterious Benedict Society and the Prisoner's Dilemma".
deleted 15y ago
[deleted]

80 points by Natsu 15y ago

chris_wot 15y ago

That was awesome. But did you see Nick's face at the end at what Ibrahim said? Lol!

Natsu 15y ago
A little bit of game theory goes a long way. But something like that wouldn't work for very long before someone came along who was only faking it. There are a bunch of related videos of this show as well. It can be interesting to try to predict the outcomes to see just how good your internal lie detector really is. EDIT: Also, don't miss one of the comments. BCR came up with the clever solution of passing one of their balls to the other player. That's quite the game breaker, though, so it probably wouldn't be allowed. I guess I should also mention that this is technically a variant of the PD, and that I change the title because almost nobody would know what the story was about otherwise.

synctext 15y ago

This blog post+Youtube video+Amazon preview made me order the book. Good stuff. For many years I've been working as a scientist to break the Prisoner's Dilemma problem. Case study is swarming-based downloading, where cooperation is needed for speed and anonymity. However, for over a decade scientists/developers seems have largely failed to do better then tit-for-tat (with unbounded scalability in number of users). Book preview contains interesting text on paying taxes, parasite behavior and broad view of trust.

zorbo 15y ago

Schneier comments: > The game is turned on its head Is that really true? What has changed? Player B still can't trust that player A will give him 50% of the money outside of the game. Player could turn the tables by claiming he too will steal. Wouldn't that put them back to the original situation?

dsr_ 15y ago
You are assuming that social pressure either doesn't exist or is in favor of dishonesty. The first is not true, and the second is only true for limited peer groups. Consider how your family would treat you if you reneged on a verbal commitment you made on TV. For the vast majority of people, this is a major negative factor. Now add in your coworkers, employers, friends... Most people are honest most of the time, and especially so when there is a high likelihood of being caught cheating.
- Natsu 15y ago
  That exact line of reasoning is brought up during the discussion in this video of the end of another game: https://www.youtube.com/watch?v=y6GhbT-zEfc&feature=relmfu https://www.youtube.com/watch?v=y6GhbT-zEfc&feature=relm... That said, you're right about the fact that reputations matter. They just don't matter to everyone.
- ecmendenhall 15y ago
  Exactly. This is an example of a commitment strategy (http://plato.stanford.edu/entries/game-theory/#Com http://plato.stanford.edu/entries/game-theory/#Com), and it was only credible because others were watching. Reputation is a very common way we make credible commitments when we deal with one another, but the results might have been different without an audience. It's funny that the one-shot prisoner's dilemma is used so often as an example of rational self-interest leading to suboptimal outcomes or formal modeling failing to capture real behavior. This is true only for the most stylized models and simplest games. Really rational players will choose to restructure the rules and play a better game! Since prisoner's dilemmas were bad games, we figured out how to make credible commitments and overcome them. Since talk is cheap, we developed things like punishment and social norms to enforce commitments. Adding things like iteration, reputation, and punishment to simple games leads to complex cooperative outcomes that reflect real behavior—and we can model them by adding a few simple rules. I think it's a fascinating and optimistic view of human history: modern market-exchange societies are the outcome of a long process of figuring out how to turn bad-outcome games that encourage defection into positive-sum cooperative ones that benefit everyone. Yet we are still biased to ignore all the cooperation around us and see selfishness (here's one of my favorite papers on this subject: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=929048 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=929048). I've also found it a very valuable personal insight. When you find yourself playing a bad game, don't settle for choosing the least harmful payoff. Figure out how to change the rules.

philh 15y ago

Given the selection mechanism, I'd be tempted to try a blind strategy. "I'm not going to look at my ball before I pick it, but if you split and I steal, I'll give you half the money." It wouldn't be good against a pure money-maximiser, because his expected $value is higher for steal (1/2 versus (1+P(I'm honest))/4), but if he's risk-averse and trusting it might work out.

thenonsequitur 15y ago
It's not clear that this strategy is possible within the the framework of the game show though. The host instructs both players to look at the concealed choices before they're allowed to talk to each other. To employ the blind strategy you'd have to explicitly not look at them (and probably say something at that point to make it clear you don't plan on looking at them). This would be directly contradicting the host's instructions. While the host might allow it, I think it's more likely they'll say "sorry, but you have to look at them".

davidjohnstone 15y ago

That strategy only works in that particular version of the game where it is possible to split the reward. You can't split jail terms 50-50. That said, that was a great bit of TV. And Nick's double-take when Ibrahim said what he'd do with the money was gold. (In case you missed it, he said he'd respray his yacht.)

ghshephard 15y ago
re: "You can't split jail terms 50-50." - sure you can. You can both be sent to prison for 1/2 the expected time if you both keep mum. But, if one of you squeals, then that person gets rewarded with no time, and the person who keeps mum goes to jail for the full sentence. But, if you are both stupid enough to squeal, you both go to jail for the full sentence.
- jimworm 15y ago
  I believe what was meant is that you can't split jail terms post-sentencing, and let someone else serve half your term.
  - davidjohnstone 15y ago
    Indeed. I considered editing my original post just after I wrote it to clear up that ambiguity, but I figured people would understand what I meant...
  - ghshephard 15y ago
    Thanks to my in-depth research of criminology (I watched two seasons of Boardwalk Empire, and several seasons of The Wire) - I can relate that criminals will sometimes agree to have one person do the time, while the other pays a bonus to them/makes it up somehow.

judofyr 15y ago

He's only outwitting the Prisoner's Dilemma in the sense that he's shifted his main goal to get some money (instead of everything). There are more certain strategies if that's your goal though: You can get the other part to join a mutual agreement: if one of you steals (while the other splits) you agree to share the money. If the other part doesn't agree, you say you'll steal and take all the money (if he splits). The other part can only get money if he agrees with you, and every choice except for (steal, steal) is going to split the money between you two. Split is the only choice that makes sense. It would be much more interesting if they changes the stakes a bit: Stealing money gives you more than the sum of splitting.

stevenkovar 15y ago

What's interesting about this show is the pair forced into a Prisoner's Dilemma are given the chance to discuss the matter with each other, adding another layer to its complexity. In most examples I've seen personally, the two subjects are given their options in private and told to make a decision without having contact.

sopooneo 15y ago
If you assume the players in the classical prisoner's dilemma have common knowledge of the rules and that neither of their choices are revealed until both have made their choice, I don't think their being allowed to talk makes much difference at all to the underlying dynamics.

Anderkent 15y ago

Of course that's not a real prisoners dilemma, because the payouts are wrong. In the real prisoners dilemma Defect-Defect gives you a better payout than Cooperate-Defect. So when your opponent pre-commits to defect, you must defect.

yonran 15y ago
I believe you meant Defect-Cooperate gives the defector a better payout than Cooperate-Cooperate. At any rate, I’m not sure that it makes a difference in this video.
- jgeralnik 15y ago
  No, he means Defect-Cooperate should give the person who lost less than he would have gotten from Defect-Defect. For example, in the Prisoner's Dilemma you might get 0 years of jail time if only you defect, 1 year if you both cooperate, 3 years if you both defect, and 10 years if only the other person defects. Then, knowing that the other person will defect it is still in your best interest to defect as well. In this challenge, if you know that the other person will defect you automatically get $0, whether you defect or not. In that case there is no particular reason for you to defect (except out of spite) and you are better off with the hopes that your opponent will keep his promise than with nothing.
robertskmiles 15y ago
The biggest reason it's not a real prisoner's dilemma is because the prisoners can communicate. Key to the standard prisoner's dilemma is that there is no way for the prisoners to talk to one another. Like the post says, it's a variant.
- dbecker 15y ago
  Inability to communicate is not required in the classical prisoners dilemma. It's inability to credibly commit. The distinction is illustrated with the common application of the prisoner's dilemma to cartels. Cartel members can tell each other they will restrict production, but they do not observe each other's factories. So even if they agree ahead of time to reduce production, that is cheap talk... and they can produce whatever they want. It's quite similar to this game show, though as a previous commenter pointed out, the relative payoffs are different.

skore 15y ago

This is great. The Show offers each player with three possible outcomes, which makes negotiation hard because the highest incentive is on getting all the money (choosing Steal while tricking the opponent into choosing Split), while the lowest incentive is on nobody getting anything. What Nick does by saying that he will definitely Steal is reducing the choices for Abraham to two: Split or Loose. Actually just one: Loose, albeit with a promise to also split. The cunning bit about the plan, of course, is that Nick never intends to choose Steal. Choosing Steal is foolish to begin with: There is a 50% chance that nobody will get anything if you choose steal, so by default, players should stay away from it. "Count your blessings", so to speak. What is clever about this is that Nick has replaced the technical bet with a social one: He has done something that appeals to his opponent, by challenging his intellect, turning the game on its head. For Nick, the chances are now that either he gets half or nothing. He, internally, accepts a lower possible payout to himself to maximize the probability that the "group" will cash out. In any outcome, this would mean that it's no longer "He tried to get the money", but "He tried to make sure we get the money". I would say there is a pretty good chance that Abraham would have decided to give him half, even had he decided to Steal, basically matching Nicks generosity. This is supported by the fact that Nick really did end up displaying the Split - Had Abraham revealed a Steal at that point, he surely would have felt like quite bad about this ("He did it to help us both, after all!"). Nick has simply maximized the chances of a Split on all available vectors.

sopooneo 15y ago
Morality aside, choosing steal is foolish unless it works, then it seams pretty sensible.
- skore 15y ago
  Superficially, choosing either Steal or Split gives you two sets of equal, 50% chances: Steal: 50% Everybody looses, 50% I get everything Split: 50% Everybody wins, 50% Opponent gets everything In very basic, almost evolutionary terms, the dumbest thing to do is both choosing Steal, because that would mean that there are two losers. Only choosing split yourself makes sure that there is a winner. Steal only seems sensible if you care about winning yourself.

AznHisoka 15y ago

I would think threatening the other person to split would be a dominant strategy. I wouldn't wanna steal if I knew the other person was gonna harass me the rest of my life.

codehotter 15y ago

If you don't think you can trust the other participant, you could do the following: Point at one of the other's balls. Say "I will choose steal unless you pick that one. If you do pick that one, you may choose the ball I'll pick." Unfortunately, your expected value is only 37.5% with this strategy, not 50%. You can still do better if you trust each other.

thejteam 15y ago

When the person comes to collect your answer, make them believe you left through the window and then hide and run out the door while they are investigating. And lock it. At least it worked in "The Mysterious Benedict Society and the Prisoner's Dilemma".

deleted 15y ago

[deleted]