Question

Prisoner's Dilemma

Asked by: DanRollins

I have recently come across several references to this (Prisoner's Dilemma) and I'm finding it fascinating.   Even my daughter mentioned it (by a differnet name) in regards to a college Sociology class -- she won a $10 prize by "doing the obvious" and defecting -- she couldn't understand why the other members of the class didn't come to the same conclusion!

If you don't know what I'm talking about,  please see
   Prisoner's dilemma (Wikipedia)
   http://en.wikipedia.org/wiki/Prisoner%27s_Dilemma

The "iterated prisoner's dilemma" is the interesting variation.  
It is discussed extensively in "The Selfish Gene" by Richard Dawkins.  It shows how an equilibrium can be (often must be) reached -- "unselfish" cooperation ends up being the stable thing to do, even when every participant is only out for his own greed.  

The "PD" also came up in an SF series I read by Kim Stanley Robinson ("Forty Signs of Rain," et. al).  It applies PD to social contexts and uses the term "to defect" -- meaning to not cooperate -- in a way that is being seen more and more often in common vernacular.

It was also mentioned in an episode o the TV show "Numb3rs."

I thought it might be interesting to discuss this, partly because of the novely to being able to cross post in these three areas...

   Philosophy and Religion -- cooperation is a key philosophical concept; evolution
   Puzzle and Riddles        -- PD is game theory
   Math & Science              -- Related scientific concepts such as "Nash Equilibrium" cellular automata, etc.

Some discussion points:
* Have you ever run across the idea of the PD in common media -- your
   reading, TV shows, whatever?
* The idea's been around for a while:  Did you study it in college?
* Name some practical uses for the "esoteric" game-theory concept

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Asked On
2008-07-02 at 22:01:35ID23535860
Topics

Math & Science

,

Philosophy & Religion

,

Puzzles & Riddles

Participating Experts
6
Points
500
Comments
33

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    Answers

     

    by: RobinDPosted on 2008-07-03 at 00:37:41ID: 21923425

    There's some ghastly tv show in the uk at the moment that uses that, just that, and nothing more to make it interesting that I have seen. Two contestants (that don't know each other) have a prize pot of money that they can make a secret bid to choose to share or steal.
    On the reveal, if they both chose to share they take half each, one shares other steals the stealer gets all the cash, both steal then neither of them get it.
    Its nearly the most annoying 'reality tv' thing around, they even let the contestants talk to each other and lie or try to convince the other. Naturally they are all daft and most choose to steal and so morally it is kind of ok.
     

     

    by: mrider01Posted on 2008-07-03 at 06:49:24ID: 21925370

    A Beautiful Mind
    (A blonde walks into a bar with her friends, and while the guys all talk about going for the blonde, Nash is thinking theory.)
    If we all go for the blonde and block each other, not a single one of us is going to get her. So then we go for her friends, but they will all give us the cold shoulder because no on likes to be second choice. But what if none of us goes for the blonde? We won't get in each other's way and we won't insult the other girls. It's the only way to win. It's the only way we all get laid.

     

    by: DanRollinsPosted on 2008-07-03 at 13:33:04ID: 21928790

    Excellent example, mrider01!
    And each guy is also thinking... If I can convince the other guys to go for the other girls, then I can take a shot at the blond!

    But apply the "iterated PD" to the situation:  If the technique of ignoring the blond worked once or several times in the past, then each participant would be more inclined to cooperate.  Occasionally, someone would "defect" (go for the blond) and thus harm the group.  That guy would not be invited to the next outing.  

    And more subtle...
    If this became a standard at all bars, then an equilibrium might be reached, where the blond got so few dates that she became "just one of the pack" (would be selected randomly rather than first) and she'd end up with her "fair share" of dates.

    And even more subtle...
    Somebody would realize that the best-looking girl was only being selected randomly rather than first, and would see a defection-for-profit opportunity...

     

    by: DanRollinsPosted on 2008-07-03 at 15:24:11ID: 21929851

    ... He might *pretend* to select randomly (i.e., let others select first) then jump in on the Blond.  He'd need to be careful to avoid detection.

    Dawkins' book describes a number of scenarios where the balance would (or did) shift back-and-forth.  And a predictable result is an increase in the ability to be deceptive.

    In another excellent book
        "The Red Queen: Sex and the Evolution of Human Nature" by Matt Ridley
    I thought the most interesting musings (always de-emphasized for lack of proof) were around the idea that the ungainly and evolutionarily-risky size of the human brain is due in part (or even *mainly*) to the extreme advantage of being able to deceive one's mate into helping you care for your offspring while you simultaneously mate with others who are likely to produce more (or better) offspring.  

    And what follows is the (perhaps more important) ability to *detect* such deception.   When there is an "arms race" like that, evolutionary selection pressure can happen relatively quickly.

     

    by: mrider01Posted on 2008-07-03 at 19:44:26ID: 21930735

    Well, it seems that now we're going to start redefining the 'game' or 'strategy'.  If all the guys are discussing their strategy, and they all agree to go for the girlfriends (which is what I think we ultimately are talking about) then I think a better way to do things would be to cycle through who gets the blonde, when we start dealing with Iterated PD.  Or does a 'strategy' by definition not change?  Could the everyone in the group each have the strategy of "Every fifth group of girls that enters will have the blonde that I can hit on," given that there are five guys.  But in the end, everything comes down to the rule of PD, being that everyone follows their strategy and does not stray away from it.

    Then, if people stop following the agreed 'strategy,' is when you enter the 'arms race' scenario, which is truely a lose-lose situation.  So you have to take a look at which you value more: having yourself succeed, or having others lose...  which then rolls back to the 'selfish gene'...

     

    by: DanRollinsPosted on 2008-07-03 at 20:03:03ID: 21930783

    A successful variation of the "Tit-for-Tat" strategy is one that randomly (but rarely) defects when the opponent cooperates and randomly (but rarely) cooperates in response to a defection.

    The idea is to break up a lose/lose chain against an opponent who uses a similar basic strategy.

    BTW, the other reason I asked this question is because I so rarely get to type "Tit" in these discussions :-)

     

    by: SunBowPosted on 2008-07-04 at 02:03:09ID: 21931830

    Ditto RobinD. It does not work in practice. Games are never really balanced fairly anyway.

     

    by: SunBowPosted on 2008-07-04 at 02:03:33ID: 21931835

                                                                   - bye -

     

    by: divdovePosted on 2008-07-05 at 19:26:14ID: 21939103

    Forget Prisoners for there time, let them do there time then think about them.

     

    by: mrider01Posted on 2008-07-07 at 08:17:10ID: 21945786

    So I'm getting some points for being the only person to add anything meaningful to this post? ;-)

     

    by: DanRollinsPosted on 2008-07-07 at 12:04:55ID: 21947672

    Sure!  Everyone who contributes in an interesting way to discussions I've started will get a share of the points.  Now if only I could think of a way to use EE Points as the reward in a PD-based game... :-)

     

    by: gilbarPosted on 2008-07-07 at 12:39:52ID: 21947976

    Dan,
    If Everyone contributes a valuable something, then they equaly divide the points.
    If ONE person disses all the other somethings, then that person receives ALL the points.
    If Everyone disses each other, then Dan deletes and refunds points to himself.

     

    by: mrider01Posted on 2008-07-07 at 12:44:43ID: 21948014

    In that case, I am dissing all the other somethings.

    And call for the game to be over immediately.

    :-P

     

    by: RobinDPosted on 2008-07-07 at 15:08:58ID: 21949081

    >Now if only I could think of a way to use EE Points as the reward in a PD-based game

    I thought of one but you may lose a few friends if you experiment on them.

    Post a question with the rules that you only share the points amongst the even numbered posts. 1st post gets none, 2nd a share, 3rd none etc. You'd have to allow multiple posts per person as a minimum or there wouldn't be the opportunity to test the collaboration. It would be interesting to see it develop.

     

    by: DanRollinsPosted on 2008-07-07 at 16:02:18ID: 21949350

    Odd/even probably can't work unless we could prevent people from posting several times in a row.
    Perhaps this:

    Cooperate= "Say something nice about the previous poster"
    Defect=        "Say something rude about the previous poster"

    In a way, we see a standard escalation whenever we see a forum flamewar.   Everything is on-topic and on-track, when somebody takes offense... And now you've suddenly got two posters shouting obscenities at one another... (tat!  Tat!  TAT!  TAT!  TAT!!!)

     

    by: RobinDPosted on 2008-07-07 at 17:06:53ID: 21949705

    I was imagining a near equilibrium where rather than try and hog all the positions, all would slow down to let the prize be shared more equally. It would only take two people posting hard and furiously to put each other off.  

     

    by: mrider01Posted on 2008-07-08 at 16:51:22ID: 21959417

    Robin,
    Consider this to be me putting you off.  Or as Dan noted it, something "rude".

    Unfortunately, I'm not sure how much we'll be able to disagree on the rules of a relatively standard game.  Other than joking about the stupidity of other people's rules, I don't think there will be anything but pseudo-heated debate.  But I'll do whatever I need to do to get points.  Tell me how to defect, then sit back and watch.

     

    by: RobinDPosted on 2008-07-08 at 17:05:11ID: 21959475

    'course the other problem is that unlike a tv game where the money goes up the further they get, in here the points get spread thinner and thinner until there isn't so much of an incentive to try to win them.

    >something "rude". - I'm ignoring your comment will that do?

     

    by: mrider01Posted on 2008-07-09 at 05:58:52ID: 21963032

    I'm not sure how "PD" this is, you'll have to let me know, but how about if all the points go to the fourth person to post after this message.  If less than four people post, then the points get split among the three or less.

     

    by: mrider01Posted on 2008-07-09 at 06:00:58ID: 21963058

    But acually, it would be ridiculus for three people to split it, because then a fourth person would steal the points.  So in reality, the only split should be a two-way.

     

    by: gilbarPosted on 2008-07-09 at 06:11:55ID: 21963166

    Clearly, the points should go to the first person who came up with a way to use PD to distribute points.

     

    by: mrider01Posted on 2008-07-09 at 09:49:14ID: 21965739

    Nah, I think Ozo should get them.  I mean, come on, he posted some links.  Nothing says "I really care!" like posting a wikipedia article.  And I see you have your game on, gilbar by saying defecting and saying something rude about other posts.

     

    by: gilbarPosted on 2008-07-10 at 07:38:19ID: 21973825

    Oh Oh! Now y'all got me actually thinking about the PD.
    I've decided that the 'real' PD (not the iterated one) isn't a dilemma at all.
    The possible outcomes (best case/worst case) are the same for each choice of the dilemma. Either you walk, or you don't. Since the worst case outcome for you isn't any worse if you defect, and the best case isn't any better if you ally, you'd be stupid not to defect, since that way you're in control of your destiny.
    If defecting meant a possible reduced sentence (but still a sentence), and alliance meant a possible total freedom; then you'd have to do more thinking about whether to keep your mouth shut.\
    Or, if a successful defection meant that you'd get out of jail; but that you'd need witness relocation, you'd have to do more thinking about whether to squeal.
    As it is, the prisoners 'dilemma' isn't much of a dilemma.
    Oh I have it!

    The Prisionera's dilemma
    Do you tell your daughter (that thinks she's your sister's daughter) that you (who see thinks is her mother's maid) are ACTUALLY her mother who has escaped from a mexican jail, knowing that this knowledge will tear her world apart; or do you just keep working for your mean sister? When you find out that your dream man Daniel is ACTUALLY the brother of the man you killed after he raped you, do you continue the relationship? And what about Lulu? Will her master, SATAN(!) enable her to destroy your chances of happiness?
    Gosh I miss TeleMundo   :(

     

    by: DanRollinsPosted on 2008-07-10 at 12:02:11ID: 21976419

    In most PD variations, cooperating (keeping silent) gets a walk for both you and your partner-in-crime.  The whole point is that there is a true dilemma:

    Cooperate:  If everybody else does, then everybody wins
           Defect:  Regardless of what anyone else does, you lose, but to a lesser degree.

    A dilemma comes when there are two options, usually where both of them have drawbacks.  In this case, the drawbacks are different -- hard to weigh against one another -- because there is no way to know what the other guy will do.  

    If you could be certain that he'd cooperate, then it's a no-brainer:  You should cooperate.  
    But how sure are you?  
    For instance, if you are 90% certain, then the extra reward needs to cover that 10% risk.  

    When money is used as the incentive, then the calculations are easier than when a jail term is involved.  Even then, you might be weighing apples against oranges -- a $1000 reward is not the same to Bill Gates as to some homeless junky in need of a fix.

     

    by: gilbarPosted on 2008-07-10 at 12:07:33ID: 21976457

    I'd thought that if you defected and he didn't then you'd walk, and if you both defected you'd get the same punishment. I guess I'm wrong.

    But lets get to the important issue of hijacking this thread and making it be about mexican soap operas

     

    by: DanRollinsPosted on 2008-07-10 at 12:19:58ID: 21976557

    In many games of chance, the players must do constant risk/benefit calculations.  For instance, in backgammon, you might move a checker to a place where it is in danger of being sent back to the start...  That's a costly risk, so you weigh how likely it is to get "hit"  against the benefits of having that checker at that location.  The board is constantly changing; early in the game, being hit may not be much of a loss.  Later, for instance, if most of the inner board is blocked, the risk is much more substantial.

    Sometimes, you can do a very simple calculation; for instance:  Three rolls (of 36) hit the checker -- call it a 12% chance of being hit.  If hit, you lose, if missed, you win.  When playing for $100, then that move "costs" you $12 but gains you $100.   Some other move might cost you $50, so you select the one that is less costly.  Or, some other move might "cost" only $3, but leaves you with a specific chance of leaving a much riskier situation later.

    In the PD, you can also "do the math" but there is a huge unknown variable -- what will the other guy do?  The beauty of the iterated PD is that it provides a means to adjust your calculations based on a history of previous encounters.

     

    by: mrider01Posted on 2008-07-10 at 12:45:03ID: 21976731

    Actually the way the Wikipedia article noted in the initial post describes the PD is similar to the one you are describing.  It's a little more detailed than either walking or not walking.  It is stated that if both people defect, then they each serve 5 years.  If one person defects, they go free while the other gets 10 years.  If they both cooperate, then they both serve 6 months.  But you are still right when you say that regardless of what the other person chooses, you will be better off if you defect.  If you were friends with the other prisoner, that would be a dilemma because you wouldn't want to put your pal away.  But if you were both strangers, then I'd agree and say it's no dilemma at all.  However, your TeleMundo situation is more of a damned-if-you-do/damned-if-you-don't.

     

    by: DanRollinsPosted on 2008-07-28 at 00:05:25ID: 22101133

    Just when I thought this thread was over... I saw the movie

    The Dark Knight (http://www.imdb.com/title/tt0468569/)

    ..in which an awsome variant of Prisoner's Dilemma was portrayed.  Without giving away a major spoiler, I can say that it had something even I had not thought of:  Each minute that the clock ticks is, in a way, a separate game of an itterative PD.

    My daughter is home from college and when we discussed the movie, she reminded me about the PD experiment that I mentioned at the top.  She actually won $100 (not $10)  so it was a serious challenge with a significant payoff.

     

    by: DanRollinsPosted on 2008-08-28 at 14:34:41ID: 22340149

    Although we did get some good discussion here, I'll admit that I'm a bit disappointed in the lack of response to this question. To me, it's a fascinating topic, but I guess it's less so to other EE Members.

    Anyway, thanks to all who participated.

     

    by: RobinDPosted on 2008-08-28 at 14:46:40ID: 22340230

    Thanks Dan

    20120131-EE-VQP-002

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