

Outwitting the Prisoner's Dilemma - Natsu
https://www.schneier.com/blog/archives/2012/04/amazing_round_o.html

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synctext
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.

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davidjohnstone
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.)

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ghshephard
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
I believe what was meant is that you can't split jail terms post-sentencing,
and let someone else serve half your term.

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ghshephard
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.

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Anderkent
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.

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robertskmiles
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.

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dbecker
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.

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robertskmiles
I suppose this will have been discussed in other comments, but it seems to me
the ability to credibly commit here isn't bad. I'm not sure if verbal
contracts are legally binding in the UK, but they certainly have a lot of
witnesses, and the social consequences for breaking a very public verbal
contract can be substantial.

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zorbo
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?

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dsr_
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.

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ecmendenhall
Exactly. This is an example of a commitment strategy
(<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>).

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.

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drostie
I like to add to any discussion of Prisoner's Dilemma a similar note,
something like:

This is why contracts matter. It's clear that both parties would love to sign
a contract saying "I'll scratch your back and you scratch my back," if the
consequences of not obeying that contract were sufficiently severe, because
they see that they can get a mutually better reward. The reason why criminals
do better than game theory professors on the prisoner's dilemma game is not
necessarily because they act irrationally, but because they're part of a
social order which creates and enforces those sorts of cooperative systems,
and which doesn't do business with folks who break them.

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skore
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.

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sopooneo
Morality aside, choosing steal is foolish unless it works, then it seams
pretty sensible.

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skore
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_.

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sopooneo
I think you are making a big assumption with your number of "50%". It's true
that there are two _possible outcomes_ for either choice I could make. But
what makes you say they are equally likely? To my mind, the estimating of that
probability is actually the crux of the game.

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skore
Yes, that was what I was talking about - If you make a choice and then depend
on another person making a choice, your chances are _precisely_ 50/50. That's
the prerequisite of the game.

Of course, it gets a lot more complicated after that, particularly because you
can talk to your partner. (That's kind of why I wrote "superficially", but it
seems that word has triggered the downvote police.) Not sure whether it
changes much of the math, though - after all, anything that you weigh in favor
of something could always be a lie.

I was pointing out that of the basic choices that are offered to you, one is
_very_ disadvantageous, so it should be an advantage to prevent it from even
possibly happening by choosing Split. You can literally prevent 1 in 4
outcomes with your decision. This realization, paired with some very social
engineering in the example is what made this so impressive to me.

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philh
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.

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thenonsequitur
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".

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judofyr
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.

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codehotter
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.

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stevenkovar
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.

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sopooneo
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.

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thejteam
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".

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AznHisoka
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.

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

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Natsu
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.

