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'Tit for Tat' Defeated In Prisoner's Dilemma Challenge
colonist writes "Tit for Tat, the reigning champion of the Iterated Prisoner's Dilemma Competition, has been defeated by a group of cooperating programs from the University of Southampton. The Prisoner's Dilemma is a game with two players and two possible moves: cooperate or defect. If the two players cooperate, they both have small wins. If one player cooperates and the other defects, the cooperator has a big loss and the defector has a big win. If both players defect, they both have small losses. Tit for Tat cooperates in the first round and imitates its opponent's previous move for the rest of the game. Tit for Tat is similar to the Mutual Assured Destruction strategy used by the two nuclear superpowers during the Cold War. Southampton's programs executed a known series of 5 to 10 moves which allowed them to recognize each other. After recognition, the two Southampton programs became 'master and slave': one program would keep defecting and the other would keep cooperating. If a Southampton program determined that another program was non-Southampton, it would defect."
Update: 10/14 15:08 GMT by J : If anyone wants to try writing their own PD strategy and see how it fares in a Darwinian contest, I'll host a tournament of Slashdot readers. Here are the docs, sample code, notes on previous runs, and my email address.
- If you confess and your partner denies taking part in the crime, you go free and your partner goes to prison for five years.
- If your partner confesses and you deny participating in the crime, you go to prison for five years and yor [sic] partner goes free.
- If you both confess you will serve four years each.
- If you both deny taking part in the crime, you both go to prison for two years.
This sounds pretty much like the RIAA might be involved. I would deny everything if I were you!The dangers of knowledge trigger emotional distress in human beings.
In other words, an in-group can work vs. tit for tat if it outnumbers it. I'd like to see a trial with a slow trickle of immigration of tit for tats into a large population of S/M programs. That might be illuminating. I suspect the outcome would be that tit for tat still does well.
What we call folk wisdom is often no more than a kind of expedient stupidity.-Edward Abbey
...fraternities and secret societies work so well!
I'm off to join the Freemasons. Be back in a few.
I claim first use of "Error No. 0B" - or "No. 0B error." It'll be the new ID 10T!
I generally hope that knowledge of the prisoner's dilemma will never become a practical factor in my life.
What we call folk wisdom is often no more than a kind of expedient stupidity.-Edward Abbey
Lameness filter encountered. Post aborted!
Reason: Don't use so many caps. It's like YELLING. It's not at all like a TALKING COMPUTER. You are a bad man. Go away.
I mean, the whole point of the Prisoner's Dilemma is that you don't have all the information. You don't know what your partner/opponent is going to do and you have decide based entirely on what little information you have based on your history with your partner/opponent. What these people are doing is creating a pattern to be recognized by another player, and then working as a team. And, it's not like they're people where one person might change their mind and decide to defect unilaterally... they're programs. Once they've locked onto each other as the same program, that's it. They'll play to their advantage until the end.
The real trick is to find a program that can beat other DIFFERENT programs, not beat itself. This seems really stupid, or am I missing something?
--
RumorsDaily
This seems to me to be an unfair way to "win." The point of the PD simulation is to talk about whether, in the absence of any social consequences, it is better to screw someone over for money or to work cooperatively with them. It's not a perfect model for that question, but that is still the question that makes us care about the PD in the first place.
All this has done is make a meta-PD game in which the two programs create a meta-game in which they agree to cooperate. That is to say, this is a solution to the PD problem that relies on the cooperation of a cohort (Someone to keep choosing loyalty while you defect and get all the money). Which is exactly not the point of PD.
So the real headline, I think, is "Trivial flaw found in definition of Prisoner's Dillema problem. University of Southhampton wastes money demonstrating flaw instead of writing a goddamn paper like a normal person would."
Philip Sandifer's academic website
Yeah, that's not the Prisoner's Dilemma. Or even the Iterated PD. This whole "signaligng Morse code" on the prison walls is nonsense, because it was not part of the original plan. Just because it's not in the rules doesn't mean you can do it. In Chess there's no rule specifically against me bringing a SuperGrape(TM) onto the board. The SuperGrape(TM) immediately destroys all pawns on a color of my choosing.
No, it doesn't work that way.
While this is an interesting experiment, it's not a true victory.
Small potatoes make the steak look bigger.
Just curious, thats all. Anyone have any experience in the field?
Physics is nothing like religion. If it was, we'd have an easier time trying to raise money!
It's not clear to me how the entries determined who would be the 'master' and who would be the 'slave'. It seems that if you had lots of 'colluders' around who could be induced to 'suicide' for another's benefit, you'd very quickly get cheaters who worked to be the 'master' in all situations.
This strikes me as a lot more reminiscient of the Hawk/Dove situation.
PHEM - party like it's 1997-2003!
Why should Tat get all the fun?
But the proper test is really whether the master half of these programs can do better than tit for tat on a large scale basis. I suspect that the S/M program will still do less simply because it plays a pattern during the interaction phase which is likely to result in tit for tat still coming out ahead- if there is one tit for tat, it won't do so well since the costs of being tit for tat are relevant if you don't know the master sign and most of those you interact with are expecting to hear it. But that's already well known. If tit for tat's numbers start growing, it does better. You see, tit for tat has an identification mechanism too, which is simply that it always starts out nice and immediately gets nasty if it gets fucked. If the number of tit for tats increases to a reasonable critical mass, they can have enough positive reactions to do very well. In fact, they'd become a secret society within the S/Ms!
In short, if tit for tat is isolated, it won't do so well since everyone is fucking with it. If there are just a few tit for tats out there, their power increases significantly with each one added.
What we call folk wisdom is often no more than a kind of expedient stupidity.-Edward Abbey
Not precisely cheating, as the rules are set up to play this way...but this certainly violates the spirit of the original Prisoner's Dilemma. Why?
Real prisoners only get to choose ONCE.
By taking advantage of the multiple-iteration aspect of the simulation with this sort of 'portknocking' strategy, the winning programs kind of take a cheap shot at the original PD.
Of course, it's all hypothetical anyway, and come to think of it Tit For Tat technically takes advantage of the multiple-iteration aspect as well by doing whatever the opponent did the last time...
Ah well, at least the Wikipedia entry makes a distinction between regular "Prisoner's Dilemma" and "Iterated Prisoner's Dilemma".
"The result is that Southampton had the top three performers -- but also a load of utter failures at the bottom of the table who sacrificed themselves for the good of the team."
J.
You're only jealous cos the little penguins are talking to me.
Repeated games have radically different outcomes than one-time games. It's long been known that where cooperation is possible, cooperation can beat solitary strategies in repeated games. I really don't think there's anything surprising here.
See what I've been reading.
ok, here's a weird thought. In many Asian countries, the mentality is to work as a group, rather than individually, with the individual sacrificing themselves for the group if necessary. In the USA and most of the "western" world, we tend to act more as individuals. We tend to think think our system is better, but what if we're wrong? Perhaps, as this experiment shows, the Asian mentality may actually be the superior strategy?
China has been most consistently the biggest superpower over mankinds history, and it looks like it's going to be that way again in a couple of decades. Perhaps these things are related...
It is easy to score better than Tit-for-Tat in Axelrod's (original) tournament. He included a program that played random moves. It is not difficult to recognise this program after, say, ten moves have been played. You can always defect against random, because its moves are unrelated to its history. So, a program that plays Tit-for-Tat by default, but always defects against Random, scores better than Tit-for-Tat.
Does this dillute Tit-for-Tat's accomplishment? Of course not. Tit-for-Tat still plays well. And it is such a simple strategy that it can be programmed in two lines ("C on move 1, then copy opponent's previous move"), which none of the other programs achieve. Tit-for-Tat is simple, elegant, and strong. It's beautiful.
Southamptom entries, on the other hand, are complex, sneaky, and cheating against (perhaps unwritten, but nonetheless agreed-upon) rules. They're ugly. They only prove that backstabbing cheating bastards may defeat just-and-fair if the referee is looking the other way for a moment.
Communication between secret partners has been one of the most undefeatable stratgies in cards for a long time. Didn't take a computer to figure that out. Someone just figured out how to do in the rules given for this competition.
I used to wonder what was so holy about a silent night, now I have a child.
What is tat?
Where do I get it?
And how do I exchange it for the other thing?
--Dennis Miller (IIRC)
A mathematical treatment of population genetics in groups was given by W. D. Hamilton in "Innate Social Aptitudes of Man". In the last sentence of that paper, Hamilton, the originator of modern kin selection theory, states:
What Hamilton is referring to is the fact that in any structure of components vs composite, there is the opportunity to defect. An individual gene can defect against the organism within which it resides via, say, meiotic drive. An individual may defect against his tribe made up of his close relatives. A tribe may defect against the others making up a nation. A nation may defect against others making up a geographic race. A geographic race may defect against others making up humanity as a whole.It is indeed a dilemma but it isn't without a rigorous treatement within genetic theory.
Steve Sailer has written an an excellent review of the politically touchy issue of ethnic nepotism given from Hamilton's group selective perspective.
Seastead this.
This story illustrates the power of groups and societies to coordinate to the detriment of individuals and outsiders. The Southampton team used a "secret handshake" to recognize members of the society and discriminate against outsiders. It is a natural explanation for people's fear of closed/secret societies -- people fear the group's ability to break the rules of individualistic "fair play."
If the agents in the game were capable of higher order reasoning and could see these coordinated actions between members, then they would become paranoid -- all the Southampton team members were "out to get them."
Two wrongs don't make a right, but three lefts do.
Tit for tat has a secret handshake too, but it's a code of ethics. It is robust in any iterated situation. That's what makes it neat.
What we call folk wisdom is often no more than a kind of expedient stupidity.-Edward Abbey
Except Tit for Tat is more robust than other plans, deals well with a wide variety of opponents, and is easy for opponents to "figure out" and is "forgiving" so it does not get caught in endless loops of mutual punishment easily.
Being that, beating Tit for Tat isn't that big of a deal. Doing BETTER than Tit for Tat consistently _IS_ a big deal.
The game is a positive sum game, so it pays off to end up in a cooperative (or semi-cooperative) sequence over repeated "defections".
For some good reading on the Prisoner's Dilemma Game and how it fits in some biological systems read;
"The Evolution of Cooperation" by Robert Axelrod (and newer books)
"The Selfish-Gene" by Richard Dawkins
There may be more recent books too, it's been while since I studied the subject.
Having one plan that can beat Tit for Tat
1st iteration - Traitor defects, TfT cooperates, TfT loses and Traitor wins.
Nth iteration - both defect, minor losses for both
Thus Traitor beats TfT... What am I missing?
The length of the code is one of the largest problems to overcome. Performing any signal other than all-cooperate produces a net loss of 1 or 4 points per round for your team in traditional (0,1,3,5) IPD. Simple signalling, ie 4th round defect was very effective. While the master/slave aspect was amazingly effective in my research, the "spoiler" was not. A small population of master/slaves could invade an arbitrariliy large block of TitForTat if evolution was by duplicating winner and removing loser after n iterations. The population of "spoilers" stagnates very quickly in a large TFT population. TFT should be considered a friend, not an enemy because they are a positive growth environment. Going "spoiler" on any non-TFT/ally was quite effective as any bot not prone to cooperate posed the only real risk of "master" losing.
Once I experimented with letting the agents recognize which "species" they were in and which "species" their opponent was. The runaway winner, of course, was the one which always cooperated with itself, and was less nice to every other species. (In my version, "less nice" meant playing Tit-For-Tat, but the idea's the same.)
Being able to do this is like having the teacher's edition. If recognizing which species other agents belong to is allowed, that's a pretty trivial strategy. It's not called cooperation. It's called xenophobia, or to put it into the most familiar anthropomorphization, racism.
(The life lesson, if I may go out on a limb, is that in an environment where some recognize a quality called "race" and discriminate based on it, being unable to see that quality is a liability. Being truly color-blind means you are unable to recognize not only race but racism, which means you will be taken advantage of.)
When I ran my first tournament and got some interesting results based on this, I realized that knowledge of what "species" an agent belongs to is too powerful, it throws a monkey wrench into the works. So I scrapped it and moved on to stuff I found more interesting.
But the winner of this PD tournament was even craftier; he submitted a ton of entries, all of which were xenophobic in this way, except that they all recognized one "species" as the top dog. The other "species" essentially committed suicide to give the highest score to the top dog. That wouldn't have worked in my tournament, since they literally would have committed suicide (my agents starve to death if they don't score high enough) and that would have shaped the resulting environment. Every tournament is artificial in some way, and the human submitting entries to this one was clever enough to take advantage of these particular artificialities.
Since it's now been shown that inter-agent communication is possible, that's going to be fair game for every tournament from now on. The next step is going to be designing tournaments to work with this trick, not against it. As I wrote to this tournament's organizers:
That's right, traitor (hawk) beats TfT in any given trial.
BUT, in an environment made up of a few players playing each strategy, then you have the following matchups:
Hawk vs Hawk. Horrible horrible loss for both of them.
TfT vs Hawk. Hawk wins, but only by a single round.
TfT vs TfT. Both TfT 'win' - neither betray the other.
So, overall, TfT does better than hawk.
The interesting part isn't beating TfT (which, as you point out, isn't THAT hard to do) but in doing consistently better than it against a wide variety of programs. Which is what TfT has long been the baseline for.
Curse these researchers, now black hats will be using this technique to let exploit code escape from chroot prisons!
Tit for Tat is outperformed by "Tit for Two Tats", because it is better at avoiding long runs of damaging mutual recrimination. That was 5 years ago. The performance of any of these strategies is only determined by the opponent strategies that they face, which is arbitrary. It is therefore meaningless to talk of one strategy being 'better' than another - most advanced strategies can beat Tit for Tat given the right opponents.
foo mane padme hum
By using this "recognition system", the program is capable of "knowing" in a deterministic fashion what some of the other programs will do in advance.
In other words, at the very least, a cheat.
They "cheated", and the other guy didn't, so they won big! Wasn't that the whole premise?
-Serpent
Isn't this the way the terrorist organisation works? The actual attackers totally lose (they lose even their life), and their masters profit from it. The experiment shows that tit for tat isn't a good strategy against this.
The Tao of math: The numbers you can count are not the real numbers.
I've been giving talks on the Prisoner's Dilemma for a few years. (No original research, just following the thing and explaining the game to the Youth)
It is kind of an orthodoxy in the literature: Tit for Tat always ties or loses by a little bit, but in tournaments, it is the best strategy.
Well - it ain't. Someone found a way around it. Instead of urging rule-changes to prevent this new challenger, we should all be happy and excited that PD tournaments have just got MORE INTERESTING.
I can't wait to see what happens next - what new programs will emerge to have the advantages of Tit for Tat but also the ability to defend against Master-Slave programs that communicate with each other.
The game has changed - now let's leave it alone and watch.
God is real unless declared integer
The omerta, or code of silence, is the ideal that the mob works toward when caught. If you get caught, you simply clam up and take whatever's thrown at you as a point of honor. It is instructive, however, that this of course does not apply universally (everyone knows that the mob is rife with snitches.)
What we call folk wisdom is often no more than a kind of expedient stupidity.-Edward Abbey
Everyone is posting about how this is bogus because it's really not the same game as PD.
But even if you don't agree with that view, another important question is:
in what meaningful sense is this new strategy a "victory"?
After all, it achieves "victory" for half of the cooperators, at the cost of sacrificing the other half.
To use one nuclear-war analogy, it's a choice between strategy "A",
where you acquiesce to the death of half of your populace, with the reward that the remaining populace is completely unaffected --
and strategy "B", with the guaranteed result that no one dies but everyone is injured.
Which populace would *you* choose to join on the eve of war?
And GPL is more or less 'Tit for Tat' in which it will only cooperate with those also cooperating.
I think what will become more interesting is that, now that we know the best lone player (tit for tat) can be defeated by players playing together, can we write our players to look for a player trying to communicate to another player so as to take advantage of it. Can my player play tit for tat against normal players, but, when it sees a S/M player, convince the S/M player to play slave for my gain?
I do security
For all of those saying, "Isn't this just cheating?" I say this:
Creativity is "just cheating." Creativity is breaking the rules in a novel way that sheds new light on reality. And isn't that the holy grail of AI?
So, was this just cheating? Hell yes. And it's fantastic.
I agree that this defnition of the "Prisoner's Dilemma" is no more than a "meta-game," and not really a problem of philosophical ethics (though it may appear to be to some people.)
;-) ). I'd say that just because someone committed a crime does not mean they necessarily want to continue committing crimes...
What I find disturbing this is the way that the problem is framed presupposes no underlying system of ethics. To wit....
* If you confess and your partner denies taking part in the crime, you go free and your partner goes to prison for five years. * If your partner confesses and you deny participating in the crime, you go to prison for five years and yor partner goes free. * If you both confess you will serve four years each. * If you both deny taking part in the crime, you both go to prison for two years. What do you do?
How about: Tell the truth? Regardless of what your partner does, tell the truth. I find it disturbing that the problem is framed in a way that the actual truth of the matter is irrelevant. (i.e. the problem would be unchanged if I replaced "You and your partner have committed a crime and are caught" with "You and a friend have been accused of a crime which you may or may not have committed.")
I'm not trolling or off-topic here. I'm dead serious. This formulation of the PD is ethically doomed from the get-go, and thus the results of the experiment may be of interest to mathematical game theorists of this particular game, but I find it unwise to think the results make any significant implications about ethics (or anything else for that matter).
Someone will counter that since this is a "Prisoner's" dilemma the person involved must be a criminal with no "ethical" principles other than an interest in self-preservation (i.e. the person is already debased as can contribute nothing meaningful on the subject of ethics!
As a microbiologist with interest in evolution, I have followed this field from afar for years. Looking over the results, I was surprised at how relatively poorly "Pavlov" (win-stay lose-shift) did, since it performs so strongly in noisy, evolutionany, versions of the game. [see:c gi?hold ing=npg&cmd=Retrieve&db=PubMed&list_uids=8316296&d opt=Abstract
http://www.ncbi.nlm.nih.gov/entrez/query.f
It was also a bit dismaying to see how well "Grim" (hold a grudge forever) did in both games. In evolutionary versions of the game, Pavlov helps keep down the population of "suckers" (thereby decreasing the food supply for more predatory and parasitic strategies) while still rewarding "provokable" cooperators (thereby increasing the total aggregate "reward" of the ecosystem.
Also, one essential part of the payoff structure that deserves emphasis is that the payoff for cooperating has to be more than half the average of the winner and loser's payoff for defection, else one benefits by simply alternating each turn. This is a little bit like the winners did here, where they got the top spots at the cost of a lower total take for their "team". One real world example of slashdot interest where this might make sense is if you take these losses in order to eliminate your rivals from the game and then reap monopoly benefits once you control the game (not to mention any names...).
Maybe someone who has analyzed the results in more detail could comment on how the various well known strategies fared and why.
While entering a team into a tournament scored for individuals and then sacrificing the whole team for one player is by no means a new idea, what makes it so remarkably successfull here is the existance of a "guaranteed draw" strategy (in this case, always defect). The best individual response to "always defect" is to defect yourself, anything else is a suicide, so if you always defect you can force a draw. Then all your team loses to one team member, and he is the winner.
:) But now we can gauge any strategy: enter one player or a team, recognize your own team members or not, transfer money between team members as you wish, but can you make money, overall, from this tournament?
Compare this with, for example, a chess tournament. You could secretly enter a team and have them all lose to you. While this will keep you from ending last, it won't assure victory, unless all players are roughly equal. If there is a very strong player, he'll win against all your team, yourself included. So you can cheat by redistributing players of comparable strenghts, but at least you can't rob a clear champion of his deserved victory.
This is not the case in the PD tournament. But let's redefine the problem slightly: say, if both sides cooperate, each gets a dollar. If then defect, each pays a dollar. Sucker's reward is paying 10 dollars. Now the Southampton team's strategy boils down to using the tournament to give all their money to one player, while paying a hefty tax in the process. There is a cheaper way to do this, just give all money to one guy outside the tournament
Optimistic Tit-for-Tat models human behaviour well in a social setting--we give others the benefit of the doubt, and continue to cooperate when others do. When someone violates our trust, we stop trusting them and punish them, but if they act beneficially towards us again, we might be willing to forgive. Most notable, OTFT produces the best overall score, which in competition between social groups is the deciding factor.
The Southampton strategy is dependent upon large numbers of people who will sacrifice all for the good of the other, and not for the good of their community (the collective performance is worse than OTFT.) I can see sacrifice for the greater good, but this is sacrifice to another person without hope of recompensation or an increase in general wellbeing. This does happen in human societies (I think it's happening now in some political systems), but only when the winner has managed to convince the losers that its all in everyone's best interest. What Southampton has added to this mix is a capacity for extreme self-delusion that directly contravenes the economic assumption of informed choice and self-interest. For purposes of economic modelling, Southampton should probably be disqualified, or these assumptions dropped. But this should also tell you something about what could happen to those nice economic models when they hit the messy world of human beings, who for the most part aren't very informed and often work against their own best interests as a result.
The consequence for a societal group running Southhampton against an OTFT group would be the defeat of the Southhampton group every time. Selection works at individual AND group levels. So the challenge should probably be two-tier: run the programs individually against each other, and run them as tribes against each other.
So, essentially, the winning program(s) hacked (or exploited, if you prefer) the game in order to win ? That's pretty clever, but does this count as a true victory ? It's sort of like what Captain Kirk did to rig his Kobiyashi Maru scenario. Sure, he won on a technicality, but in doing so he missed the whole point of the challenge.
>|<*:=
Easy: