Game theory.....is it useful?

[gnome]

If you have to choose between certain doom and nearly-certain doom, nearly-certain is the best choice. It's not a good choice, but it's the best.

Them's the breaks.

If you know the other guy thinks like you, however, you're better off with whatever choice will do best for you if it's duplicated in your counterpart. Chance doesn't really come into it much, it's not like the other guy is throwing a coin.

 

[Chaos]

"Cam"?

That has nothing to do with language... that was a good, old-fashioned typo.

You asked for it, mate...."How good is your Romanian?"

(Interesting stuff, though....good summary, and well written, too!)

Glad you liked it. BTW, I have an interesting article about typos lying around somewhere... I´m afraid it´s in German, though.

As for my Romanian, it is about as good as my Mongolian - that is, I know the language exists, and I may have heard a word or two of it at some time, but that´s it. But then, nobody´s perfect.

 

[CFLarsen]

That has nothing to do with language... that was a good, old-fashioned typo.

If you say so. If you say so.

Glad you liked it. BTW, I have an interesting article about typos lying around somewhere... I´m afraid it´s in German, though.

It would be in German, wouldn't it?

As for my Romanian, it is about as good as my Mongolian - that is, I know the language exists, and I may have heard a word or two of it at some time, but that´s it. But then, nobody´s perfect.

I thought you were a nobody?

 

[Chaos]

If you say so. If you say so.

Tsk, tsk, tsk... how unskeptical of you. I am shocked.

It would be in German, wouldn't it?

Since I already said so, this is not exactly a feat of genius to figure out...

But, although I cannot recall why, I noticed that I do have an English version of that article. It´s funny as hell (naturally, since I wrote it), and if you are very, very nice to me, I might let you read it.

I thought you were a nobody?

I think I have created enough of an electronic "paper trail" on the internet (*cough* http://www.skepticreport.com/general/amazingmeeting3b.htm*cough*)to confirm that I am indeed a somebody.

 

[bpesta22]

The best paying management profs are strategy people. A lot of them use game theory to try to explain things like competitive advantage and how/why some businesses succeed and others fail.

 

[69dodge]

The dilemma, of course, is that if both parties make the "correct" choice they get screwed.

Each gets screwed because of the other's choice, not because of his own. So it's not such a dilemma.

 

[AmateurScientist]

Each gets screwed because of the other's choice, not because of his own. So it's not such a dilemma.

No, gnome is correct. It is a dilemma; that's why game theorists call it the Prisoner's Dilemma. The whole point of it is to illustrate the mini-max principle. Each prisoner must decide to confess or to remain silent and not cooperate with police. His expectation of gain or loss is dependent not only on which decision he makes, but also on the decision his co-conspirator fellow prisoner makes. The greatest gain for each prisoner is for each to remain silent; by doing so the state cannot prove its case against them and they go free. The worst possible outcome for each is to remain silent, but have the other prisoner admit his crime to the police and agree to testify against the other. In this instance, the non-cooperating prisoner receives a long sentence, say 25 years. By confessing, however, the prisoner is promised and will receive a lesser sentence, say 5 years.

Thus, there are three possible outcomes each prisoner may receive. 1) He may go free because both prisoners independently decide to remain silent; 2) he may get confess, be convicted, and receive a 5-year sentence; or 3) he may remain silent, be convicted because the other prisoner cooperated, and receive a 25-year sentence.

This is where the dilemma comes in. The police interrogate the prisoners separately. The police tell each of the prisoners that the other has already confessed, and that they will receive leniency by confessing to the crime too. What to do? Remain silent, and risk the possibility that the partner in crime has turned against him and confessed, so that the prisoner remaining silent will not receive leniency upon conviction, or confess and receive a guarantee of a conviction, but also receive leniency? In other words, the prisoner can guarantee only one outcome -- that he gets 5 years -- by confessing. Remaining silent could result in the biggest gain, going free, or it could result in the biggest loss, going to prison for 25 years. Remaining silent is the wildcard. It turns out that a rational actor will decline to seek the maximum benefit and will seek to minimize his loss by confessing. That's the mini-max principle in action, and that's what the Prisoner's Dilemma is all about.

AS

 

[CFLarsen]

Tsk, tsk, tsk... how unskeptical of you. I am shocked.

I am swayed by your evidence, that's all.

Since I already said so, this is not exactly a feat of genius to figure out...

Ah, irony. Wasted on Germans.

But, although I cannot recall why, I noticed that I do have an English version of that article. It´s funny as hell (naturally, since I wrote it), and if you are very, very nice to me, I might let you read it.

Depends on what you consider "nice".

I think I have created enough of an electronic "paper trail" on the internet (*cough* http://www.skepticreport.com/general/amazingmeeting3b.htm*cough*)to confirm that I am indeed a somebody.

But it isn't peer-reviewed in a respectable scientific journal, is it?

 

[AmateurScientist]

Hi, my name is Irina Cristescu and i am a student in the 4th year of study at the Faculty of Psychology. This year i must elaborate a final diploma paper, and i have decided to study Game Theory in Psychology, especially in the domain of Organizational Psychology. In my country this domain is not yet developped, so I have found little if not no books at all in the library of my faculties (i also study sociology). So, not having acces to books, i tried the ressources on the internet, and i have found that a new theory has been developed in Game Theory: Psychological or Behavioral Game Theory. The ortodox Game Theory sustains that the decident is rational, and he takes the decisions on the basis of rational calculus. But here comes psychology and says that decidents are not emotional geniuses, and that they are not always rational, because of the interference of psychological variables.
This is the lead i tend to follow.
But I havn't studied Game Theory at school, and the internet ressources are very vague and not very helpful if i don't have a few directions to follow. I really need a psychological approach. I know that two nobel prizes have been won on the psychological approach in Game Theory, in 2002 and in 2005, but i couldn't find any detailed informations about the work of Schelling, Aumann, Kahneman, Smith, the winners of the prizes.
I would be very grateful if somebody could recommend me a few directions, suggestions about a psychological/organizational approach on game theory. I feel alone in a country where nobody I asked knows anything consistent about game theory, nobody can give me directions or reccommend me materials to read.
I would be very greatfull if you could help me, i really need help.
Thank you very much,
With respect
Irina
ps: sorry for the grammar errors, my english is not exactely accurate

Hi Irina. I think your proposed topic is great. I studied mathematics and politics at university, and I stumbled upon game theory in both of them. It has always fascinated me, and I think game theory can be applied to virtually any domain in which there are limited resources, possible gains and losses, and two or more actors.

I also agree with you that too often traditional game theorists, and economists in particular, assume that all actors in their scenarios are perfectly rational. To some extent, I understand that such an assumption may be necessary in order to grasp the basics of game theory, but in reality, as you note, actors are rarely perfectly rational, as emotional and psychological factors often overwhelm rationality.

Although most of my study of game theory was in my political studies, it was poker that motivated formal study of the subject. As noted above in this thread, modern game theory is recognized as having been founded by a mathematician and an economist who wrote a scholarly paper together. They were John von Neumann and Oskar Morgenstern, respectively, and their first work was Theory of Games and Economic Behavior, first published in 1944 by Princeton University Press. Von Neumann was a recreational poker player who began pondering strategies and how to quantify them more than twenty years earlier.

There is a short, non-scholarly book available on amazon.com that can serve as an interesting introduction to game theory. It is Strategy in Poker, Business & War by John McDonald, W.W. Norton & Co., 1950. It was updated in 1996, but I have only the original version, so I cannot address the newer version. McDonald discusses game theory in practical and theoretical terms, and draws upon basic psychology and economics. He cites such varied sources as Anatole France, Daniel Bernoulli, Plato, Fyodor Dostoyevsky, John Maynard Keynes, and of course von Neumann and Morgenstern. It's easy to read, but gives some important insight, particularly about the importance of having better information about the circumstances of the "game" (or battle, or political situation, or economic market) than one's opponent(s). Good strategy depends upon good information.

Anyway, you can read reviews about the book and order it here. http://www.amazon.com/gp/product/039331457X/104-2148114-3107919?v=glance&n=283155&s=books&v=glance

Good luck with your paper. Feel free to report what you find here if you like.

AS

 

[Chaos]

*snip*
Ah, irony. Wasted on Germans.

Ah, irony. Wasted on Danes...

*snip*
But it isn't peer-reviewed in a respectable scientific journal, is it?

Indeed. Nobody could call that SkepticReport rag a "respectable journal".


AmateurScientist
Good summary of the Prisoner´s Dilemma. I bow to your superior expertise.

 

[69dodge]

AS, I was thinking of a different setup.

In your version, why wouldn't both prisoners remain silent? That would result in the best possible outcome for each, and they both know it. So why should either suspect that the other will confess, and therefore be tempted to confess himself?

In the version I was thinking of, if both remain silent, they both get a fairly light sentence, say 5 years. If both confess, they both get a somewhat stiffer sentence, say 10 years. But if one confesses and one remains silent, the confessor gets off very easy, say 1 year, and the silent one gets the book thrown at him, say 20 years.

Now, each prisoner reasons as follows: if the other guy remains silent, it's better for me to confess (1 year vs. 5 years). If the other guy confesses, it's still better for me to confess (10 years vs. 20 years). So, I'll confess.

So they both confess, and they each get 10 years.

The dilemma is that, had they both remained silent, they both would have been better off, getting only 5 years each.

Does my original comment make more sense now?

 

[Kevin_Lowe]

AS, I was thinking of a different setup.

In your version, why wouldn't both prisoners remain silent? That would result in the best possible outcome for each, and they both know it. So why should either suspect that the other will confess, and therefore be tempted to confess himself?

AS goofed. Your version is correct. What AS described is a different game, sometimes called an "assurance game", and also sometimes referred to by other names.

In AS' game, the best move depends on what the other person does. If they cooperate you should cooperate, if they defect you should defect.

The whole point of the prisoners dilemma is that regardless of what the other person does, you are always better off defecting.

 

[gnome]

AS, I was thinking of a different setup.

In your version, why wouldn't both prisoners remain silent? That would result in the best possible outcome for each, and they both know it. So why should either suspect that the other will confess, and therefore be tempted to confess himself?

In the version I was thinking of, if both remain silent, they both get a fairly light sentence, say 5 years. If both confess, they both get a somewhat stiffer sentence, say 10 years. But if one confesses and one remains silent, the confessor gets off very easy, say 1 year, and the silent one gets the book thrown at him, say 20 years.

Now, each prisoner reasons as follows: if the other guy remains silent, it's better for me to confess (1 year vs. 5 years). If the other guy confesses, it's still better for me to confess (10 years vs. 20 years). So, I'll confess.

So they both confess, and they each get 10 years.

The dilemma is that, had they both remained silent, they both would have been better off, getting only 5 years each.

Does my original comment make more sense now?

Yes, I am going with 69dodge's version... and yet I maintain that if you believe your partner is as rational a thinker as you, you're better off picking something that is the best choice if BOTH of you pick the same thing. Of course, if you're the brains of the outfit, your partner is not likely to go through as sophisticated a decision making process, so I would probably confess defensively.

 

[Roboramma]

Of course, if you're the brains of the outfit, your partner is not likely to go through as sophisticated a decision making process, so I would probably confess defensively.

And on the other hand, knowing that no matter what you decide, it won't change your partner's decision, even if you do know that he's following the logic that he should cooperate with you for a lighter sentence, you should still confess.
After all, what you're saying seems to be that if you can reason that your partner won't confess, neither should you. But if doesn't confess, it's still best to confess!

Basically, since your current actions can't change those of your partner (what he does is independant of what you do), there's no reason not to confess.
There is no outcome of that particular game in which you would have been better off not confessing than confessing.

If, however, there were some way that your actions could influence those of your partner, that might change things. And that's why multiple games makes other strategies than "always confess" work. Because now he has to think not only about the best strategy for this game, but for the sum of all games.

 

[AmateurScientist]

AS goofed. Your version is correct. What AS described is a different game, sometimes called an "assurance game", and also sometimes referred to by other names.

In AS' game, the best move depends on what the other person does. If they cooperate you should cooperate, if they defect you should defect.

The whole point of the prisoners dilemma is that regardless of what the other person does, you are always better off defecting.

You're right. I did goof, and the point of the dilemma as commonly presented is as you describe it.

69dodge, your version is the one commonly used, and mine is not, but it's not accurate to state that the other prisoner screwed the player. Kevin is right that the correct strategy is to defect against the other player, regardless of how the other player approaches the game. This does illustrate the mini-max principle, but it's also about the conflict between cooperation (with the other player in maintaining silence, not cooperation with the police) and defection.

Here are a couple of links describing why.

http://plato.stanford.edu/entries/prisoner-dilemma/

http://www.econlib.org/library/Enc/PrisonersDilemma.html

AS

 

[69dodge]

[...] but it's not accurate to state that the other prisoner screwed the player.

I'm not sure what you mean.

Here's what I meant.

Suppose we were the two prisoners, and we both confessed. Would you say, "Bummer, I wish I had remained silent"? Or would you say, "Bummer, I wish 69dodge had remained silent"?

Or conversely, suppose we both remained silent. Would you say, "Whew, I'm glad I remained silent"? Or would you say, "Whew, I'm glad 69dodge remained silent"?

If we both confess, each of us is worse off than if we both remain silent. But the reason I'm worse off is that you confessed, and the reason you're worse off is that I confessed.

It seems paradoxical to say that the rational choice for each prisoner is to confess, when the outcome of that choice is worse for each of them than another possible outcome (namely, the outcome where they both remain silent). But neither prisoner can choose from among all the possible outcomes. Each can decide only what he will do; he has no control over what the other prisoner will do. He can choose between the other guy confesses, I remain silent and the other guy confesses, I confess, and he can choose betwen the other guy remains silent, I remain silent and the other guy remains silent, I confess. But he can't choose between we both confess and we both remain silent, because those two possibilities differ not only in what he does but also in what the other guy does, and what the other guy does is not up to him---it's up to the other guy.

 

[gnome]

While I don't disagree with the explanation offered for why to confess... I maintain that if you know the other person thinks like you, you can take advantage of that to earn the lesser punishment of neither confessing.

It's all well and good to say, "I know how he thinks, he's going to try to go for a double-silence, so I'll screw him and confess." But--the other person thinks like you and will make the same decision.

Your decision doesn't change the other person's decision--BUT, the way you arrive at it is the same. It behooves you to come up with a strategy that would benefit both of you, unless you expect asymmetrical thinking.

 

[Roboramma]

Basically you're saying that if you know that somehow the other player will make the same decision as you, then you should remain silent.

But how do you ever know that?

 

[gnome]

Basically you're saying that if you know that somehow the other player will make the same decision as you, then you should remain silent.

But how do you ever know that?

I agree that it is far more likely that a stranger to me would not draw the same conclusion. In fact, i would never trust anyone that had not heard of the Prisoners' dilemma or what Douglas Hofstadter called "Super-rational thinking" to use that line of reasoning.

 

[69dodge]

I agree that it is far more likely that a stranger to me would not draw the same conclusion. In fact, i would never trust anyone that had not heard of the Prisoners' dilemma or what Douglas Hofstadter called "Super-rational thinking" to use that line of reasoning.

But suppose you knew that the other prisoner had read Hofstadter, was totally convinced by his reasoning, and was therefore sure to remain silent. Wouldn't it still be better for you to confess?

Of course, it would.

It seems to me that Hofstadter's reasoning is equivalent to the assumption that you can control the other person's choice, which everyone agrees you can't do.

I'm not sure exactly what "rational" means, as we're using it here. I think it would be interesting to try to formulate a careful definition. But, in the meantime, it seems clear to me that the assumption of rationality, together with the assumption that you can't control the other person's choice, implies that, when trying to decide what choice to make, you should compare outcomes that are identical except for your choice, because your choice is all that you control.

The two prisoners face the same situation, so it is certainly true that if they both follow the same reasoning process they will both make the same choice. In particular, if they are both rational (whatever that means), they will both make the same choice. However, that doesn't imply that, when you're trying to decide what choice to make, it is correct to say, "If I remain silent, so will the other prisoner." At that point in time, while you're still deciding, you don't yet know what the rational choice is---that's what you're trying to figure out. If the rational choice is to confess, which is still a possibility as far as you know, then by remaining silent you are not being rational, therefore the original assumption that both prisoners are rational no longer holds, and therefore there's no reason to suppose that they will both make the same choice.