Game theory allows for individuals to have benevolent preferences. However, they are incorporated directly into the utilities. You can't "double count" once you have already assigned payoffs. Note that the lecture explicitly stated that we are assuming that the individuals only want to minimize jail time. If we didn't, then the game would look more like a stag hunt, which is covered two lectures later.
I never really put forethought into it. I used to label them "cooperate" and "defect" (standard for the literature on the prisoner's dilemma), but then too many people complained that those were confusing.
Fantastically explained. I never really understood it until now. Also, this is why escrow is so great, he bids "keep quiet only if she also keeps quiet" and either everyone is better off, or she does not agree and escrow returns everyones position back to them to try again :-P
I always find the example disquieting, but for slightly different reasons. I consider the modified scenario (indistinguishable to the police) where there was no robbery or plan of same. Game theory predicts (of course) that both parties will (falsely) confess because they are worse off if they tell the truth. The example should not be allowed in real life.
I don't understand your calculations. Let p be the probability the other guy keeps quiet. (In your example, p = .5) Then my expected time in jail for not confessing is (p)(1) + (1-p)(12) = 12-11p. My expected time in jail for confessing is (p)(0) + (1-p)(8) = 8-8p. Note that 12-11p > 8-8p simplifies to 4 > 3p. This has to be true, since p at most can equal 1. Therefore, regardless of the other player's strategy, not confessing yields you more jail time. So you should confess. Clear?
The reason is simple, its a win-win situation for both players. It's a matter of trust and betrayal. To further explain, its more stable than the "both quiet" because if one betrays, the one goes free while the other takes the 12 months. And if you pick "Confess" it depends whether the other player takes the 12 months and you're free or split 50-50 of jail-time. how do you say this... "its foolproof and can't be betrayed"
Yes, it’s considered stable because there’s no incentive to defect from it while there is incentive to defect from the better outcome. But psychologically you can also think about it like “Nobody gets to benefit from screwing me if we equally screw each other, and if he doesn’t screw me but I screw him, even better”
@Andreas0424 You right that can get cooperation if you play this game repeatedly (and indefinitely), but there is no precedent to set in the one-shot version of the game (like the one in the video).
In reality the cost of confessing is much higher. A lot of people do not like a snitch. And although in this game when played once the rational decision is to confess, it'll make no sense when this game is repeated over and over again. Once they know you are a snitch, you will always spend 8 months in jail: so in essence the players lose and the game wins.
Confess = 8months 50% chance to not confess or 50% chance to confess No confess = Option (a) 1 month or Option (b) 12 months Option a: No confess - Confess = 1-8 = less 7 months in jail, Option 2: No confess - Confess = 12-8 = extra 4 months in jail Thus, the benefit on not confessing is 7months less jail time as apposed to an extra 4 months jail time for confessing. 3 months better off to not confess at 50% chance.Best option based on chance and risk is not to confess.
so this means that when they both keep quiet they have much profit .. however there is Nash equilibrium when they both confess but that does not do any good to them .. so it would be better if they both keep quiet
@A Ki You can quatify it because there are two variables in the boundaries of the equation. Furthermore you don't even need the % to make a decision. The comment I made earlier justifies not to confess if the purpose of game theory is to do what's best for yourself and the other parties involved. You must not stray away from the main purpose. But if you do, then I agree that the best thing to do for yourself is not to confess with the likelyhood of getting away free. But this goes against GT.
@Andreas0424 Kant called this precedent the categorical imperative. Plato refers to it in his defense of Justice. It is the ruling principle of Rule Utilitarianism. Our fear of living in a world without trust, and our awareness that our own abusing of trust brings that world closer, moves us to a sort of "selfish cooperation." Wasn't this Nash's crowning achievement? Isn't the solution (from the prisoners' perspective) then for neither to confess?
Game theory is a normative theory. To avoid disaster with any or all normative theories due to muladjustment, mul administration, mul application etc! It simply means you start by identifying the specific situations where it applies and where it has produced desirable results before trying to try it on something else.
I hear what you're saying about stability, but I'm not satisfied. Of course the fundamental issue is trust: even if both players understand the trap and agree beforehand not to fall into it, neither can be absolutely sure that the other player won't try to exploit that trust and confess. The problem is that this dilemma exists in isolation, whereas in reality they do not. We're not only trusting in the agreement, we're trusting in their understanding that they are setting a precedent.
Hey William! I really enjoy your videos. Game theory is an awesome form of mathematics! I have a game, or an economic concept, I am not sure, but it involves the economics of medicine. In my economics class we had covered the equilibrium price and other concepts. For a paper, not for class, but for my own intellectual exercise, I would like to find the equilibrium between cured patients vs non-cured patients: for example Number of people with cancer cured and not cured. Using only math and...
Remarkable work! I stumbled upon a piece with a similar message, and it was nothing short of incredible. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell
and not being bias, I would like to prove its not economically wise for any drug company to cure a particular ailment. From the info gathered I would like to find the equilibrium cured vs non cured and see if my calculations are accurate to the actual statistics.
What if the woman has a higher chance of keeping quiet? You don't take into account the probability of that outcome vs her confessing? Or is it just too random to try to predict a human? Or is this just a simplified example?
This is a simple game that is understandably basic. There are other versions of the prisoner’s dilemma that bring into account probabilities of “player types”, these are called Bayesian games
correct me if I'm wrong, but is confessing the better option because the possiblilty of -8 and 0 average -4 and keeping quiet (-1 and -12) average -6.5?
keep quiet for both players all the times have more advantages for both player but i dont get why they choose confess .just to play the game safe all da times
What if they knocked at his door at 12:00:59 pm? Since it is only one second left, the prisoner (overconfident on his theory) would be relaxed that he will be killed on Thursday, but when they knock the door, the prisoner will be surprised.
I always hated this dilemma because it is very poorly designed scenario that comes off as misleading, and thus illogical, of game theory. The criminal statistics of such scenarios where people incriminate fellow criminals are something like >30% murder/ attempted rate, not counting other criminal law punishments. Should add confess + 30% chance of death of you or loved ones to "confess" boxes. Now which is the better move? Need a better game, because using such an example is too illogical to respect game theory for beginners.
You assumption is wrong. You cannot quantify the likelihood of a confession and where you got the 50 percent figure is a mystery to me. This isn't a coin flip.
Please do not apply this video to game shows that use the prisoner's dilemma. The optimal strategy in that case is to tell your opponent you're going to pick steal but will split the prizes with them making them feel like they have no choice but to split and then you can pick split too.
Genuinely curious if he and she are still commonplace for Player 1 and Player 2 in today’s academic climate lol. Anyone know if this is still the norm?
Game theory allows for individuals to have benevolent preferences. However, they are incorporated directly into the utilities. You can't "double count" once you have already assigned payoffs.
Note that the lecture explicitly stated that we are assuming that the individuals only want to minimize jail time. If we didn't, then the game would look more like a stag hunt, which is covered two lectures later.
I never really put forethought into it. I used to label them "cooperate" and "defect" (standard for the literature on the prisoner's dilemma), but then too many people complained that those were confusing.
Fantastically explained. I never really understood it until now.
Also, this is why escrow is so great, he bids "keep quiet only if she also keeps quiet" and either everyone is better off, or she does not agree and escrow returns everyones position back to them to try again :-P
I always find the example disquieting, but for slightly different reasons. I consider the modified scenario (indistinguishable to the police) where there was no robbery or plan of same. Game theory predicts (of course) that both parties will (falsely) confess because they are worse off if they tell the truth. The example should not be allowed in real life.
Yup, that's definitely a problem if the police create this type of incentive structure.
A really good in depth explanation to a very difficult topic, going to take some time for me to wrap my mind around it though!
I don't understand your calculations. Let p be the probability the other guy keeps quiet. (In your example, p = .5) Then my expected time in jail for not confessing is (p)(1) + (1-p)(12) = 12-11p. My expected time in jail for confessing is (p)(0) + (1-p)(8) = 8-8p. Note that 12-11p > 8-8p simplifies to 4 > 3p. This has to be true, since p at most can equal 1. Therefore, regardless of the other player's strategy, not confessing yields you more jail time. So you should confess.
Clear?
Excellent explanation
i like how you proceed to refer to them as p1 and p2 anyway lol
The reason is simple, its a win-win situation for both players.
It's a matter of trust and betrayal.
To further explain, its more stable than the "both quiet" because if one betrays, the one goes free while the other takes the 12 months.
And if you pick "Confess" it depends whether the other player takes the 12 months and you're free or split 50-50 of jail-time.
how do you say this... "its foolproof and can't be betrayed"
Yes, it’s considered stable because there’s no incentive to defect from it while there is incentive to defect from the better outcome. But psychologically you can also think about it like “Nobody gets to benefit from screwing me if we equally screw each other, and if he doesn’t screw me but I screw him, even better”
@Andreas0424 You right that can get cooperation if you play this game repeatedly (and indefinitely), but there is no precedent to set in the one-shot version of the game (like the one in the video).
Thanks for the videos! They are remarkably well done! I'm using them for a Sociology presentation on Game Theory.
In reality the cost of confessing is much higher. A lot of people do not like a snitch. And although in this game when played once the rational decision is to confess, it'll make no sense when this game is repeated over and over again. Once they know you are a snitch, you will always spend 8 months in jail: so in essence the players lose and the game wins.
Yeah, this is a limited game. Real world scenarios have additional variables (and less than rational actors)
Confess = 8months
50% chance to not confess or 50% chance to confess
No confess = Option (a) 1 month or Option (b) 12 months
Option a: No confess - Confess = 1-8 = less 7 months in jail, Option 2: No confess - Confess = 12-8 = extra 4 months in jail
Thus, the benefit on not confessing is 7months less jail time as apposed to an extra 4 months jail time for confessing. 3 months better off to not confess at 50% chance.Best option based on chance and risk is not to confess.
so this means that when they both keep quiet they have much profit .. however there is Nash equilibrium when they both confess but that does not do any good to them .. so it would be better if they both keep quiet
If you confess, you get eight months if the other guy confesses as well. You get no time in jail if he keeps quiet.
Finally. I understand the whole dilemma. great, thank you! :)
Good luck!
@athinggoinon Confess is a strictly dominANT strategy, not a strictly dominATED strategy.
@A Ki You can quatify it because there are two variables in the boundaries of the equation. Furthermore you don't even need the % to make a decision. The comment I made earlier justifies not to confess if the purpose of game theory is to do what's best for yourself and the other parties involved. You must not stray away from the main purpose. But if you do, then I agree that the best thing to do for yourself is not to confess with the likelyhood of getting away free. But this goes against GT.
@Andreas0424 Kant called this precedent the categorical imperative. Plato refers to it in his defense of Justice. It is the ruling principle of Rule Utilitarianism.
Our fear of living in a world without trust, and our awareness that our own abusing of trust brings that world closer, moves us to a sort of "selfish cooperation." Wasn't this Nash's crowning achievement? Isn't the solution (from the prisoners' perspective) then for neither to confess?
Game theory is a normative theory. To avoid disaster with any or all normative theories due to muladjustment, mul administration, mul application etc! It simply means you start by identifying the specific situations where it applies and where it has produced desirable results before trying to try it on something else.
@Andreas0424 @Andreas0424 Nash didn't really come up with any of these games. The "stag hunt" seems to be what you are looking for, though.
I hear what you're saying about stability, but I'm not satisfied. Of course the fundamental issue is trust: even if both players understand the trap and agree beforehand not to fall into it, neither can be absolutely sure that the other player won't try to exploit that trust and confess. The problem is that this dilemma exists in isolation, whereas in reality they do not. We're not only trusting in the agreement, we're trusting in their understanding that they are setting a precedent.
That does not take into account the relationship of the two persons, does it?
Hey William! I really enjoy your videos. Game theory is an awesome form of mathematics! I have a game, or an economic concept, I am not sure, but it involves the economics of medicine. In my economics class we had covered the equilibrium price and other concepts. For a paper, not for class, but for my own intellectual exercise, I would like to find the equilibrium between cured patients vs non-cured patients: for example Number of people with cancer cured and not cured. Using only math and...
Remarkable work! I stumbled upon a piece with a similar message, and it was nothing short of incredible. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell
and not being bias, I would like to prove its not economically wise for any drug company to cure a particular ailment. From the info gathered I would like to find the equilibrium cured vs non cured and see if my calculations are accurate to the actual statistics.
game theory does not consider that I ain't no snitch
What if the woman has a higher chance of keeping quiet? You don't take into account the probability of that outcome vs her confessing? Or is it just too random to try to predict a human? Or is this just a simplified example?
This is a simple game that is understandably basic. There are other versions of the prisoner’s dilemma that bring into account probabilities of “player types”, these are called Bayesian games
Excellent video! Thank you 💜
Thank you for this series. It is very helpful.
correct me if I'm wrong, but is confessing the better option because the possiblilty of -8 and 0 average -4 and keeping quiet (-1 and -12) average -6.5?
You’d have to use Bayesians if you want to involve weighted probabilities based on “player types”
SFIA referred me here.
But hey its just a theory...a game theory! Thanks for watching
LOL
Subbed.
Heck, anyone can do a month. The real incentive to rat is fear that the other guy will (or has). Cops are expert at making prisoners believe that.
Very nice. Thank you!
You should say "plea bargain" or "rat out the the other" rather than "confess".
@JimBobJenkins Oh OK, thanks for clearing that up! Did Nash develop any one-play games where cooperation is immediately preferable?
Richard Dawkins : "The Shelfish Gene" (1976). my introduction to the prisoners dilemma.
Mmm clams and scallops.
I wonder how much is your book now?
The digital version is $5 and has been expanded since this video was published. It also now has a physical edition for $14.
Doesn't the whole "dilemma" stem from the fact that each suspect DOESN'T know what the other will do?
yes, because if they both keep quiet the outcome is better...however the risk of the other guy not following through makes this strategy dominated
Who is Dawkins? I don't understand. (Sounds British, though.)
keep quiet for both players all the times have more advantages for both player but i dont get why they choose confess .just to play the game safe all da times
What if they knocked at his door at 12:00:59 pm? Since it is only one second left, the prisoner (overconfident on his theory) would be relaxed that he will be killed on Thursday, but when they knock the door, the prisoner will be surprised.
Why does the video mention a distinction between man and woman?
I would like help on how to frame my work if you have any ideas
I always hated this dilemma because it is very poorly designed scenario that comes off as misleading, and thus illogical, of game theory.
The criminal statistics of such scenarios where people incriminate fellow criminals are something like >30% murder/ attempted rate, not counting other criminal law punishments.
Should add confess + 30% chance of death of you or loved ones to "confess" boxes. Now which is the better move?
Need a better game, because using such an example is too illogical to respect game theory for beginners.
Add matrix for snitches go in ditches.
the one thing you're assuming that they have something to confess to in the first place.
I feel like there is a reason it’s 10 years or 3 years and not 8 or 12 months. Different ball game
You assumption is wrong. You cannot quantify the likelihood of a confession and where you got the 50 percent figure is a mystery to me. This isn't a coin flip.
its interesting that truth has no place here.
I am going to hav a presentation of game of theory...so plz help me out wid more examples...i will appreciate that.....plz
Please do not apply this video to game shows that use the prisoner's dilemma. The optimal strategy in that case is to tell your opponent you're going to pick steal but will split the prizes with them making them feel like they have no choice but to split and then you can pick split too.
totalli undestand thanks :)
Being colorblind sucks...
Genuinely curious if he and she are still commonplace for Player 1 and Player 2 in today’s academic climate lol. Anyone know if this is still the norm?
If you use the word "CONFESS" the results are actually contradictory
wait player 2 a girl then luigi isn't a brother to mario instead a sister
Dawkins "brought" me here....and i fucking HATE whatever has got to do with maths.. :)
cool
How about ... Don't do the crime
Basically you have to think of this without caring at all about what happens to the other person. BE GREEDY
Calm down, Satan.
*Your*
This video brought to you by the united council of police officers.