The Iterated Prisoner's Dilemma and The Evolution of Cooperation
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Published 2016-07-02
THE PRISONER'S DILEMMA • The Prisoner's Dilemma
FOOT NOTES
Additional requirements for an iterated prisoner’s dilemma game
For a one off prisoner’s dilemma, they payoffs can just be like 5 greater than 3 greater than 1 greater than 0 (like in the video). But for an iterated prisoner’s dilemma game to be an iterated prisoner’s dilemma game, the total payout for both cooperating has to be bigger than the total payout for one person cooperating and one person defecting. Basically 2x3 greater than 5+0.
If it was like 8 points for defecting while the other cooperates, it would still follow the on off prisoners dilemma format, 8 greater than 3 greater than 1 greater than 0. But with an iterated prisoner’s dilemma game the best strategy would be to go back and forth between cooperating and defecting (giving them on average 4 each, rather than 3 for both cooperating). Which can happen for sure, but it’s a different sort of game.
With a one-off prisoner’s dilemma this doesn’t matter so much. Trade might change the relationship, but it should still appear as a prisoner’s dilemma. The incentives that make it the prisoner’s dilemma would be the same. Their best strategies would still be to always defect.
Tournament 1 vs tournament 2 (A set number of rounds vs not knowing when it ends)
There is a bit of a logical quirk when the players know how many rounds there are. A big part of game theory is getting into your opponents head, predicting what they will do. Also thinking about the whole game and reasoning backwards.
So when they know how many rounds there are, the last round against any given opponent, has no consequences. If you defect in the first round the opponent can reciprocate and you probably won’t be better off or it. But an opponent can’t reciprocate against any defecting in that last round. And since no matter what the other person is going to do, defecting gives a better payout. A player should defect in the last round... so should everyone really. They will only get more for doing that. We should expect them to do it.
But then if everyone is defecting in the last round, not in response to anything that happened before, then really the second to last round also has no consequences. Nobody is going to defect because you defected in the second to last round. What they’re doing in that next round is already set, if we defect in the second to last round we’re not giving up future gains we could have gotten while cooperating. So everyone should defect in the second to last round because there are no consequences and the payoff is higher. But then if everyone is defecting in these rounds, then the third to last round also has no consequences…. Blah blah, defect the whole time. With this reasoning the correct strategy is to always defect.
But we already know that ALWAYS DEFECT isn’t a great strategy here. Because defecting has consequences.
But reasoning backwards, in this context, only works if everyone is doing it. If everyone has thought that way. If everyone reasoned this way, then everyone is always defecting. Then always defecting is the best strategy against that.
But the people who submitted for this tournament clearly didn’t reason this way.
Maybe because most of the time in the real world, we don’t know how many rounds there are, so we always think our actions will have consequences. Also we rarely interact with one person in isolation. We can build a reputation for being un-cooperative. If we are dicks to people who we are about to never see again those who will may not want to cooperate with us as much. So those who submitted thought like this.
Maybe because they didn’t know about the idea.
But even still, in the context of that tournament it would still better to defect in the last round. I suspect TIT FOR TAT or FORGIVING TIT FOR TAT modified to defect in the last round would have won... in the tournaments at least. If you're done with a relationship and you kill them and take your stuff, the people watching you won'y want to cooperate with you.
For that tournament they actually changed the definition of what a “nice” strategy was to allow defecting in those last few rounds against an opponent. The weird space where the two ideas meet.
Cooperating with whom?
Cooperation and defection refer to between the two players. Not necessarily with outside forces like with the police.
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All Comments (21)
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Well done! Repeated games are one of the more difficult topics to explain, and this presentation should help many more people understand tit-for-tat and cooperation in the repeated prisoner's dilemma.
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Whenever anyone says "nice guys finish last", I just refer them to this dilemma.
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silent for half a year and then you reward us with 2 videos in a month? This is madness... THIS IS ... This place. <3 <3
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You know that they're not milking the video for revenue when the run time is 9:58
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him: everyone likes points me:wait... golf.
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I had a contest like this in my computer science class. Each strategy played each other one 200 times. My program started by cooperating, then acted like tit-for-tat unless one of two things was true: either the opponent had defected more often than cooperated or the opponent had defected 5 or more times. I also submitted an alternate program that was the same, except it always defected on the last round.
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You know, it's always nice to have your worldview -- that cooperation is better than competition -- validated statistically.
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waiting for the day that people discover this channel and it blows up ill be watching like a proud father
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"Video's over now." Three videos in and I already love you. That was excellent.
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What a great video! Most people don't realize it, but game theory is build in to our very genes, and indeed the genes of every living organism. You really illustrate this point in an easy to understand way. I remember reading about these tournaments in The Selfish Gene, a book that quite literally changed my view of what life is in a radical way.
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Why good beats evil in the end, proven with math
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Where can I get the letter G? There is no link in the discription
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You are, by far, one of the best channel I know on YouTube. I'd put You on the same level as Vsauce or Kurzegesagt, if not even higher.
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I love how the Prisoner's Dilemma has so many applications to the real world. Evolution, company rivalry, and even how people interact with each other.
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I have watched 3 to 4 video about Prisoner's Dilemma but this is the first one with such in depth look into the strategies, really liked it. Thanks making this!
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I love this video so much! I see life as an (endless) iterated prisoner's dilemma, I was just never able to put it in words why I think we are all better off cooperating (with an occasional punishment). Thank you for making this! :)
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I remember hearing of this, in a "Social Darwinism" context. People always asume that the most complex one are the best adapted. But this is an actuall test where one of the least complex tactics (just copy the other sides last move) won. It was way less complex then any other strategy entered (except maybe "always play nice") but still won out.
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I really wasn't expecting such a complete video on this subject
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This is by far my favourite video on youtube right now. actually - aside from music or other amusement related videos i would say it is the most easy to follow and interesting videos ive seen sofar. i really am happy to find this masterpiece
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This channel beats almost every other channel I'm subscribed to. The visuals and the small touches are priceless.
