What if you modify the game a bit...?

Give players the ability to remember players they have engaged with and add a third option: 1. Cooperate 2. Defect 3. Wait (defer, don't engage, don't play). New players will seek out players and offer to engage with them. When you defect, your reputation history declines, and when you die, your reputation history resets to zero and you lose the option to defer.

HYPOTHESIS: Cooperators will wait/defer, Defectors will wait/defer, new players will choose to cooperate or defect, and since defecting against defer is an all-but-certain lose, new players will choose to cooperate hoping the other player will too. Cooperators will naturally organize into groups of cooperators and flourish. Players in cooperator groups will cooperate tit-for-tat with known cooperators and will wait/defer with known defectors or new/unknown players no one in the cooperator group has engaged with (call it the no-fools strategy). New players and players who have been struggling in the wilderness outside of cooperative groups will want to get into a cooperative group and so they will seek to engage with players using the tit-for-tat strategy until they find a cooperative group (call it the pay-it-forward strategy). Fools who don't learn will stumble around in the wilderness until they eventually die off.

Really cool suggestions - they actually encompass a couple of ideas that we've had.

First, we discovered in the experiment that PD actually has 3 actions. Cooperate, defect, and ... wait as long as possible to defect to punish your opponent who is not cooperating. This happened because participants are playing in a real-time web app, and they have some time to make a decision. Although there is a lot of literature on how costly punishment can be used to enforce cooperation, it was pretty amazing how it emerged organically in our study after a few days. Someone could certainly grab our dataset and get a free publication out of just that.

Also, given the month-long design of the study, we were thinking of something where players get to stay on or "die" based on their daily score, and therefore the population evolves based on who gets the highest payoffs. Evolutionary game theory has some ideas about this, but they are all theoretical or simulation, and not conducted with real people. I'm actually not sure if cooperation would be sustained or not in this design, but I agree that it would go a long way toward pinning down the origins of cooperation. I also agree with you that groups or network structure would affect the result a lot, allowing cooperative bands to flourish even when defectors are running around.

One way to set the stage for a "wait/defer" option would be to remove the limit of 10 rounds per game by using random time length games where players don't know how long the game will last or how many rounds it will be. Playing more successful rounds would mean more points so this should incentivize cooperators to cooperate fast without waiting/deferring if they have confidence in the other player, and it reduces the incentive to try and game the last rounds.

To add the option to "wait/defer", you could include informational incentives/variance where players gain the ability to increase their perspective and degrees of freedom by being privy to more information sooner. For example, once a player achieves some level of points/reputation, they gain the ability to see the other player's move before they move -- this would in effect be giving them the power to defer. The other player may or may not know the extent of the other player's abilities at that time -- one or both may have the ability to see (defer), and neither may know for sure. For example, rather than explicitly stating upfront to new players that through their play they can improve their ability to see, let players discover this once they cross a threshold. Further increased powers might include the ability to see into the other player's past games, see their group's dynamics or portions of the wider network, and communicate with other group members and/or the other player during games.

As stated by Axelrod in EoC, one feature of the tit-for-tat strategy is that it's easy enough that it can be understood by anyone, and it's simple enough that it can be communicated/signaled from one player to the other through their play. It would be interesting to see how learned players -- who have gained the ability to see -- use or abuse their elevated powers of sight, either by working to better signal/communicate their intent and teach the winning strategy to the less enlightened players or by choosing to try and exploit the naivety of the other player who may be relatively blind.

Are you familiar with Jonathan Haidt's work on the psychology of morality and the formation of superorganisms?

https://en.wikipedia.org/wiki/Jonathan_Haidt

NB: Also see this timely post on "information theory and the foundations of life" https://news.ycombinator.com/item?id=13496133

I've read some of Haidt's work but not that one in particular. Thanks for the pointer.

Here is one of Haidt's TED talks that touches on these ideas, cooperation, group selection, and the free-rider problem:

http://www.ted.com/talks/jonathan_haidt_humanity_s_stairway_...

Also this Edge article on "Contingent Superorganism" https://www.edge.org/response-detail/10386

"Forgive but never forget".

The 3rd option used most widely in business today. Defectors are "punished" by refusing to do business with them after a defection.

Thanks for taking time to answer questions! I have two short questions.

1. Are there any plans to make the dataset available?

2. I missed this, what incentive is there for players to "unravel", or move the first round of defection earlier? My naive thought is that turkers want to maximize monetary payoff by getting a high bonus (1 cent for each 2 points earned) and playing quickly (to free up time for other HITs). From your payoff matrix, both players cooperating all ten rounds in one game each get 50 points. A player could instead defect on round 10 to get 52 points. He could also defect on round 9 and expect mutual defection on round 10 to get 50 points. But if he defects even earlier on round 8 and expects mutual defection afterwards, he gets 48 points. In this experiment, earlier and earlier defections seem worse than cooperating on all rounds, even for the defector.

Data is already available at https://osf.io/64z8u/. Full qualitative survey data will be available soon; but for now take a look at the supplementary materials.

If your opponent is going to defect at some point anyway, then if you defect right before he does you will be better off (at least for that game). That's the pressure to unravel.

I wonder if a better one sentence conclusion might be something like "Predictably nice players consistently distribute their gains to the group". After all, the interesting variable here is repeatability; that is, as certain players learn which players are consistently "nice" through repeated trials, they get iteratively better at gaming them to forfeit their (potential) gains.

In other words, over time, the "compound interest" on the gains the nice individuals lose gets rewarded to the group. Any individual in the group who can game "niceness" benefits the group at the expense of the nice individual. "Good guys finish last," or something of that nature?

Stabilized long-running cooperation seems like a very bad desired(?) outcome, by the way; is that what you're saying is a good thing? Pareto improvements are usually realized / discovered / gained by individuals who eschew tradition and playing nice.

It is true in our experiment that there are players who are consistently nice, and they experience lower daily payoffs than the other players. So, in one sense, "good guys finish last".

However, it's not true if you look at it from a long-term perspective. If the nice players know that not being nice would cause everyone to converge to the highly inefficient Nash equilibrium, then they are actually better off by being nice (and promoting cooperation) than they would be in the latter case. So even though they're not doing as well as the "selfish" players, they're better off than they would be in the dystopian alternate reality. (Ahem, ahem.)

Hi, interesting findings!

You say as a summary :

> a minority of nice people can make everyone better off

Was it possible for you to identify the "nice people" group vs the other group?

If yes, overall which group was better off ?

Once the non nice people start cooperating, i guess you can't make the difference between a nice person and a non nice one

Yes, in our paper, we identified the "nice" group versus the other group. The nice group is significantly worse off, but (see https://news.ycombinator.com/item?id=13509853) still better off than they would be in the world if they weren't being nice.

We can tell the difference between the two types of people, because the nice people never defect first.

Finally, with regard to identifying these types in general, one could use the (very large) dataset from this experiment to train a simulated agent that plays against a human, and quickly determine which type they fall into.

Has anyone tried to test test how different kinds of prejudges affect these games?

I'm thinking about same game setting, except that players are asked to give their mugshot and real or fake mugshots of males, females, people different ethnicity, looks and ages are shown to them.

Priming effects definitely have a huge effect on initial PD play. In one experiment researchers phrased it as "the cooperation game" vs "the wall street game" and saw much lower cooperation.

In our case, however, we made the same people play for a month. I believe that learning effects strongly dominate priming over that time period.

Were conditional cooperators playing a tit-for-tat strategy or something different? I see you citing Axelrod and Rapoport but after reading through most of the supplementary material exit questions, I most often saw descriptions similar to “I chose to cooperate unless the other person chose the defect at which point I chose to defect too for the rest of the game.”

Also, how often is the number of rounds known in studies like this? From an algorithm perspective of maximization of points for computer agents, typically the number of rounds is random.

First, hat tip to you for getting to those questions. Usually no one looks at the supplementary material at all.

So the cooperators' strategy looks like tit-for-tat, but I don't think it really is because tit for tat means if someone started cooperating again after defecting, they would switch. We think it's actually a strategy where if you get defected on, you just stop cooperating altogether in the future (at least for this length of a game). However, because we never see people switch back to cooperating after defecting (after the first day where people are trying random things), we can't distinguish between these two strategies. But effectively it doesn't really matter.

A game with a finite number of rounds is a finitely repeated PD, for which the NE is to all defect. An undetermined number of rounds is ~= an infinitely repeated PD with a discount factor, for which there are many ways to sustain cooperation according to the theory.

The most hopeful thing I have seen all week. On a slightly whimsical note, are you familiar with the legend of Lamed Vavniks from the Talmud? From the wikipedia article: "It is said that at all times there are 36 special people in the world, and that were it not for them, all of them, if even one of them was missing, the world would come to an end." https://en.wikipedia.org/wiki/Tzadikim_Nistarim

Is this like saying something like "if enough people self-sacrifice by donating to support public goods, it can be stable enough and we all get public goods, even if others freeride"? In other words, a critical mass of cooperators can keep going and support one another even if they are suffering from the effect of defectors who all still have incentive to keep defecting. Right?

But what cost do they incur? Is it made up for in some way to them?

See my comment at https://news.ycombinator.com/item?id=13509853.