05 Dec 08
Originally posted by telerionIt's true that for a finite amount of iterations, the NE will also be that everyone always defects. However, there is a loophole that does allow the cooperate option to be at equilibrium, and that is if the amount of iterations is unknown beforehand. If you don't know that the last iteration is happening, you do not have to defect per se.
I don't work directly in game theory, and it's been a few years since I took the course for my grad studies; but isn't it the case that in order for "both cooperate" to occur along the equilibrium path in one of these simple PD's, the horizon must be infinite? The problem with finitely repeated games is that they unravel through backward iteration. Genera ...[text shortened]... hough. Again, if I've messed up something above, please jump in and correct me.
About your comment on belief: yes, this is an interesting variation and it leads to interesting situations. People tend to adapt their strategies in prisoner's dilemmas based on their previous experiences. For example, in countries with a lower perception of crime, people tend to trust random strangers more.
http://www.nationmaster.com/graph/lif_tru_peo-lifestyle-trust-people
05 Dec 08
1 edit
Originally posted by KazetNagorraGood point. I was thinking of just the standard PD when I made the statement about horizon length. There are likely a lot of different augmentations to the basic repeated problem that can return cooperation equilibria.
It's true that for a finite amount of iterations, the NE will also be that everyone always defects. However, there is a loophole that does allow the cooperate option to be at equilibrium, and that is if the amount of iterations is unknown beforehand. If you don't know that the last iteration is happening, you do not have to defect per se.
About your andom strangers more.
http://www.nationmaster.com/graph/lif_tru_peo-lifestyle-trust-people
That said, even if the number of iterations is unknown ex ante, one would still need some other conditions to be true, particularly the product of the discount rate and the continuation probability would have to be sufficiently large.
As a simple example, imagine that each (or any) player discounts the future at a rate of zero. Then the game, in all but words, returns to the one-shot case.
One doesn't need the product to actually be zero to destroy the cooperating equilibrium sequence. It just has to be small enough so that the expected continuation value is less than the gain from defecting in a given period.
05 Dec 08
Originally posted by telerionYes, there are a lot of subtleties. The most rational strategy in iterated prisoner's dilemmas is not easy to establish as it also depends on the strategies of the other actors within the system.
Good point. I was thinking of just the standard PD when I made the statement about horizon length. There are likely a lot of different augmentations to the basic repeated problem that can return cooperation equilibria.
That said, even if the number of iterations is unknown ex ante, one would still need some other conditions to be true, particularly the ...[text shortened]... so that the expected continuation value is less than the gain from defecting in a given period.
05 Dec 08
Originally posted by KazetNagorraAbsolutely. When looking for any sort of NE, we are by definition considering the strategies of all players.
Yes, there are a lot of subtleties. The most rational strategy in iterated prisoner's dilemmas is not easy to establish as it also depends on the strategies of the other actors within the system.
05 Dec 08
Originally posted by telerionYes, but it becomes extra difficult if you don't know the strategies of the other players; you then have to base your strategy on what you estimate the other players' strategy to be.
Absolutely. When looking for any sort of NE, we are by definition considering the strategies of all players.
05 Dec 08
No source, but I think there once was a sort of competition with different algorithms for an iterated prisoner's dilemma. If I'm not mistaken, the winner was an algorithm that always did the same as the other player in the previous period, with random cooperate thrown in. It obviously lost against always defect, but was quite successful when paired with most other algorithms.
05 Dec 08
Originally posted by BartsCorrect. Winning strategies are often similar to "Tit for Tat" (do the same as the previous player). However it still depends on the other strategies; when other players have a relatively high degree of cooperation, a more cooperative strategy will be better.
No source, but I think there once was a sort of competition with different algorithms for an iterated prisoner's dilemma. If I'm not mistaken, the winner was an algorithm that always did the same as the other player in the previous period, with random cooperate thrown in. It obviously lost against always defect, but was quite successful when paired with most other algorithms.
06 Dec 08
Originally posted by KazetNagorraWe should also point out that in these cases where one strategy wins (for instance in a computational run-off), the outcome is almost certainly never a Nash Equilibrium.
Correct. Winning strategies are often similar to "Tit for Tat" (do the same as the previous player). However it still depends on the other strategies; when other players have a relatively high degree of cooperation, a more cooperative strategy will be better.
06 Dec 08
Originally posted by KazetNagorraStill nothing on how this relates to, well, anything actually. Rational people make irrational decisions or, tweak a few dials on the game then rational people make rational decisions, if that is possible then if you tweak them the other way you can make irrational people make rational decisions.
Correct. Winning strategies are often similar to "Tit for Tat" (do the same as the previous player). However it still depends on the other strategies; when other players have a relatively high degree of cooperation, a more cooperative strategy will be better.
No wonder Nash went potty trying to reconcile his ideas.
06 Dec 08
Originally posted by WajomaUsually it's just that the model is not capturing some critical part of the actual process. The basic PD works well for police officers working to criminals against each other. They do it all the time and get convictions.
Still nothing on how this relates to, well, anything actually. Rational people make irrational decisions or, tweak a few dials on the game then rational people make rational decisions, if that is possible then if you tweak them the other way you can make irrational people make rational decisions.
No wonder Nash went potty trying to reconcile his ideas.
In other cases, the basic PD doesn't do well. That's why other elements like learning and reputation have been added and do a better job in some cases.
07 Dec 08
Originally posted by WajomaWhy are you so focused on irrationality when it has no place in the prisoner's dilemma?
Still nothing on how this relates to, well, anything actually. Rational people make irrational decisions or, tweak a few dials on the game then rational people make rational decisions, if that is possible then if you tweak them the other way you can make irrational people make rational decisions.
No wonder Nash went potty trying to reconcile his ideas.
07 Dec 08
Originally posted by KazetNagorraI want to know your reasons for bossing other people around or rather, engaging the services of guvamint thugs to do it for you, I want you to show the relevance of the PD to socialised health care.
Why are you so focused on irrationality when it has no place in the prisoner's dilemma?
Presumably if a person makes a bad choice for themselves that must be considered irrational.
07 Dec 08
Originally posted by WajomaWhat alternative to government do you suggest for avoiding the PD?
I want to know your reasons for bossing other people around or rather, engaging the services of guvamint thugs to do it for you, I want you to show the relevance of the PD to socialised health care.
Presumably if a person makes a bad choice for themselves that must be considered irrational.
07 Dec 08
1 edit
Originally posted by telerionDo all these models reject the notion of honor amongst thieves? Someone did mention that many people caught up in this dilemma are likely to have to continue living amongst the people they would have potentially "shopped". You would think the fear of reprisal would help people stay silent.
Usually it's just that the model is not capturing some critical part of the actual process. The basic PD works well for police officers working to criminals against each other. They do it all the time and get convictions.
In other cases, the basic PD doesn't do well. That's why other elements like learning and reputation have been added and do a better job in some cases.
The other thing must be that would be felons obviously don't watch cop shows. Anyone with even the most casual acquaintance with Police Drama 101 should know that you tell them nothing, and that the cops almost never have enough evidence to convict without a confession.