'Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation (2007)
phys.org
phys.org
- Unless provoked, the agent will always cooperate.
- If provoked, the agent will retaliate.
- The agent is quick to forgive.
- The agent must have a good chance of competing against the opponent more than once.
The fact that this strategy was a consistent winner in his competitions has led Dawkins to argue that "nice guys finish first" and could be a partial explanation for certain forms of so-called "altruistic" animal behavior -- behavior that seemingly gives no benefit to the altruist, except for the fact that too may benefit when it is their turn to be helped. See also:
(Dawkins was a prominent advocate of Axelrod's work, though. And "The Selfish Gene" is definitely a great read in its own right.)
I was actually thinking about this the other day. I was wondering how much the population size and matching algorithm in the iterated Prisoner's Dilemma matter to the strategy outcome. I suspect it's quite a lot, given that if you never play the same opponent again, strategies that defect often should come out quite well, but if you always play the same opponent, strategies that cooperate should do well. If grouping is bought into the system, such that there are multiple levels of subgroups with the smaller the group both are members in having higher chances of replaying in the same round, you might see interesting emergent behavior.
I also wonder if that might allow for special elements (the "sociopath") to have interesting divergent strategies that work well as long as they don't achieve more than a small fraction of the total population and keep a relatively large amount of interactions to strangers.
And this is interesting because it gives us a toy model of moralistic "Do unto others" (as opposed to rational exchange).
The reason cooperative strategies can work is that actions depend on previous actions. If you are not meeting the same partner, then your partner's actions will not depend on your previous actions, and you will always do better by defecting.
In this case you can afford to be nice in the first round, and then cut your losses. But even that strategy is only optimal if most of the rest of the community is nice in the first round too. If it is full of defectors, then you should defect in the first round too.
The problem with all economic simulations is that they assume extreme individualisation. Because that is what they want the world to be like.
In reality the world is a network. Reputation matters.
> The agent is quick to forgive.
Reminds me a bit of Marcus Aurelius:
"From Rusticus... I learned... with respect to those who have offended me by words, or done me wrong, to be easily disposed to be pacified and reconciled, as soon as they have shown a readiness to be reconciled."
Humanity is weird.
e: Never mind, I misread the original post.
https://www.sciencedaily.com/releases/2016/09/160915085719.h...
Two people can hunt deer together, but if they are alone, they can only hunt rabbits. The person belonging to the Envious group will choose to hunt rabbits because he or she will be at least equal to the other hunter, or maybe even better; the Optimist will choose to hunt deer because that is the best option for both hunters; the Pessimist will go for rabbits because that way he or she is sure to catch something; and the hunter who belongs to the Trusting group will cooperate and choose to hunt deer, without a second thought.
The largest group, accounting for 30%, being the Envious -- those who don't actually mind what they achieve, as long as they're better than everyone else;
Next are the Optimists -- who believe that they and their partner will make the best choice for both of them -- on 20%.
Also on 20% are the Pessimists -- who select the option which they see as the lesser of two evils -- and the Trusting group -- who are born collaborators and who will always cooperate and who don't really mind if they win or lose.
There is a fifth, undefined group, representing 10%,
https://en.wikipedia.org/wiki/Snowdrift_game (redirects to chicken game)
https://en.wikipedia.org/wiki/Superrationality
(Of course, the assumption "my opponent is exactly as rational as I am" never holds in real life.)
This runs into problems of computability though: if we run the opponent's code to see what it does, and it turns out that their program runs our code to see what we do, we can get stuck in an infinite loop.
Like most incomputable problems, we can take a conservative approach: try to prove that it cooperates, using some incomplete computable algorithm; defect if we can't prove it. One simple algorithm is to check if the source code is the same as ours; more sophisticated algorithms would perform static analysis of the code.
By design, the Snowdrift game rewards cooperation more than Prisoner's Dilemma, so it's no surprise that people cooperate more in Snowdrift. The real question is which game better models reality.
Doesn't that contradict Nash's existence theorem? I believe Snowdrift has 2 (pure) Nash equilibria, namely CD and DC.
[0]https://en.wikipedia.org/wiki/Chicken_(game)#Best_response_m...
Re some of the other comments about Robert Axelrod's tournament and evolution:
- As part of the project, the Axelrod library developers have written Python wrappers for the original Fortran code (https://github.com/Axelrod-Python/axelrod-fortran)
- Have used reinforcement learning to train strategies based on machine learning paradigms (https://arxiv.org/abs/1707.06307). EDIT: here are a couple of blog posts about recent research work http://vknight.org/unpeudemath/math/2017/07/28/sophisticated... and http://marcharper.codes/2017-07-31/axelrod.html
Disclaimer: I'm one of the maintainers of the project.
https://wiki.snowdrift.coop/about/snowdrift-dilemma has more specifically and https://wiki.snowdrift.coop/about covers the concepts for the whole project.
You live in a townhouse next to another family that shares a driveway which turns onto a medium traffic density one-way street (there are traffic lights a few hundred feet away which control flow). Gaps in traffic tend to exist around when the lights change.
The frequency of snowstorms this year is higher than normal, and the overworked snowplows have made a snow bank too tall and wide to see around in your car. The only way onto the street is to turn blindly and hope that either no one is coming, or that they see you in time to stop.
Your salary is $x/hour, and it would take two hours to manually trim the snowbank to the point where you can see above it. Thus, it would cost $2x to remove the snowbank (assuming you could work overtime and earn the money).
Each party makes a choice if they would shovel the bank alone, with help, or not at all. If they both do it, they both lose $1x in OT wages. If one does it alone, $2x. But if neither do it, the hazard remains and each party rolls a 6-sided die. Anybody rolling a 1 loses $kx (where k is larger than x), and no longer have a car to participate with.
That covers one day. It will take 7 days for the city to remove the snow bank if no one else does. Any parties with a car will repeat this 6 additional times until the snow bank is removed.
Then rank the dollars lost and award real world prizes for the top positions. If there are 10 people and the top 5 get the exact same prize, shoveling might become attractive (through co-operation, as it is extremely likely at least one of the two parties per trial will be eliminated).
https://www.reflectionproducts.com/images/View-car-200-feet-...
Second, there isn't always a great option for that, no.
If you really want to cooperate, buy two, and sell one to your neighbor at cost.
I really hate, hate, hate shoveling snow.
If you had installed it in prior years, it'd probably be buried (the real life snow bank this is based on was approximately 6-7 feet tall).
It explores IPD with a few different strategies, and I found it quite interesting. I'd be curious to see how the various mechanics of it would work with ISD.
I mention this because it's clear that we're changing the way we trust and interact with each other online. Whether it's virtue signaling or trolling, we're adopting new strategies for "winning"... whatever that prize may be.
Of course the PD only models certain kinds of human/animal interactions. Knowing that a particular person is a cheater or is vindictive or whatever is obviously important for evolutionary strategy as a whole. But the question is more about heterogenous populations. Is there an optimal strategy that wins more than any other across a wide range of opposing strategies, including if everyone else is actually using the same strategy?
The iterated game proves the participants are randomly selecting an option, because they know it's a game.
Otherwise we need to create a model that explains why participants aren't consistent.
Define righteous? Define immoral?
Capitalism rewards providing actual value to people. It doesn't reward shallow niceties and self-righteousness, those are common.
If you think that everyone who gets rewarded in a capitalist society do so because they provide value then you have to ask: What value do scam artists provide?
I don't know any rich scam artists. I do know hundreds of wealthy technology professionals, however.
The net worth of one's parents makes quite a difference in practice.
That includes things like being born with a right of residence in a developed, stable country vs. in a refugee camp in a war-torn part of the world.
The point here was that credit scores do not only rate your own behavior, but also those of people around you. If your neighborhood is bad, your credit score might reflect that instead of your own performance as a debtor. And if your neighborhood becomes hip and gains a better reputation, your credit score might improve even though you're still the same person.
On the other end of the scale, criminal law punishes you for large transgressions, and sometimes prizes reward you for good deeds (although the latter is mostly achieved via market mechanisms).
Both criminal law and awards also work via reputation, by publicising your actions to a wide audience.
It's also interesting to contrast the discussion in this threat to any number of HN threats on freedom of speech in the last weeks. There, the idea that someone's reputation could be tarnished by their participation in a neo-nazi torch parade was generally considered to be the end of freedom.
However, if the idea is that a model is good at "explaining" cooperation by setting up a hypothetical where people choose it a lot, then I guess the "best" model would make people choose cooperate all the time.
So you can set up the points for cooperation to be infinity and the points for all non-cooperation to negative infinity. And you can wrap it all up in a hypothetical story about what the choices mean. Now you have a perfect model where people choose cooperate 100% of the time. But I don't feel like I'm any closer to understanding how cooperation evolved in humans.
Cooperation evolved in humans because:
a. Our young are helpless, and take over a decade to reach sexual maturity. Those who cooperate to raise the young have more descendants.
b. Cooperation is a sexual fitness signal because of point a
The end.
Edit: fix a word, thanks.
It's not clear to me what you mean by this.
In the example of the experiment in the example cooperate means the snow is cleared faster.
In my example cooperate means raise the young together.
> but most people don't choose to adopt
Because our biology drives us to want to have our own offspring. It seems obvious that if our biology drove us to want to raise other people's offspring we wouldn't be having this conversation. Although this has been an extraordinarily successful strategy for dogs and cats.
But just a few minutes ago you said our biology drives us to "cooperate to raise the young." Do you see how this topic might deserve some more study? Basically, my only issue with your comment is "The end."
I don't think that's the point. I think the point is that SD is closer to the average case for cooperation than the PD, so it might be a better tool, in general, for talking about and reasoning about cooperation. (Both PD and SD have the nice property that they are simple and straightforward, and both have the problem that they are only approximations.)
But even that's a tough sell for me, since the ideas you suggest as substitutes for the term "explain" are things I would put under the umbrella of what is meant by explaining.
Btw, if you are into data viz or simply enjoy Bret Victor-inspired interactive programming, Nicky has tons of similar experiments worth checking out [2].
[2] http://ncase.me/
Or maybe another way of putting it is that clearly rational and human behavior varies with the payoff structure, so it would make sense to include that as another variable.
"... which involved 96 participants ... Each pair repeated (“iterated”) both games 12 times, though were initially told the number of repetitions was randomly determined. The researchers created global competition by revealing that the players with the four highest pay-offs would receive monetary awards."
What people say they would do in a simulation might be different to what they would. Maybe they didn't bring a shovel. Maybe there's already 96 people at the snow face and you'd only be getting in the way.
In a college classroom, where someone tells you you'll get fifty bucks if you score high on a game? If they tell me I get bonus points for stealing their shovel, why wouldn't I choose that option? Nothing is at stake.
But sticking to just the rules, rather than the results. Is is the snowdrift game just a payoff score tweak? Or is there some structural difference that I missed?
In PD, if you don't cooperate, I'm better off not cooperating
In SD, if you don't cooperate, I'm better off still cooperating
This means that don't cooperate / don't cooperate is not the nash equilibrium in SD like it is in PD.
In SD the nash equilibriums are one person shoveling.
That appears to be an error in the article. If your opponent is shoveling, then you shoveling hurts you (300 drops to 200).
One could back out their car and pretend to have dug out the whole thing :)
Firstly, from the article: “In principle, natural selection predicts individuals to behave selfishly” is a faulty premise. Obviously humans who cooperate to raise children to sexual maturity will have more descendants.
Secondly, in these simulated games it seems likely to me the participants would be, at least to some extent, randomly selecting cooperate / defect because a potential monetary reward for participation isn't the same as "cooperate or everyone freezes to death in their car tonight", or whatever real-world consequences might apply where you don't get "12 iterations".
The way I see is: while our worldview is "everything is a competition" that is how we will interpret what we see. Evolution and economics being the most strident examples. Anything that doesn't automatically fit the worldview needs explaining by science, which is code for "publish or perish". If we had a different worldview I'm sure we would shoehorn everything to fit.
I'm fairly certain that cooperating to raise your own offspring is still considered selfish behavior. Something like taking resources from your offspring to give to someone else would be more in line with the definition of selfless (e.g. taking food from your own malnourished child to give to another child).
Why? Because it leads to more descendants? In that case, the premise is a tautology.
> “In principle, natural selection predicts individuals to behave selfishly,” Rolf Kümmerli, co-author of the study, told PhysOrg.com. “However, we observe cooperation in humans and other organisms, where cooperation is costly for the actor but benefits another individual.
That is clearly referring to the human, no?
Care to elaborate?
Similarly, death is obviously bad for an individual - it's the termination of your existence. However, it frees up resources for new individuals who may be better adapted to conditions of the time. Species where individuals rarely die may see the whole species die off at once as they get outcompeted by other species whose individuals are better adapted to the environment.
(There's a societal analogue as well here: historically, societies that hold tight to tradition and preserve the internal firms & institutions within them end up being conquered, en masse, by more competitive societies where the individual firms within them either adapt or die.)
Spending time and energy raising one's children isn't selfish of the parent as an individual. But it's selfish from the view of their genes.
Cooperation is selfish.
I think this strengthens my point about how the dominant worldview colours our thoughts.
It could be argued that even a sports game, the epitome of competition, requires magnitudes of order more cooperation in order for it come about that the game can be played.
But then it could be argued that it is the selfish desire of the individual to want to play that drives the cooperation to compete.
This reminds me how all(?) Wikipedia articles can lead to philosophy.
If you think that the idea that competition is rife is merely a product of our world view, stop competing for a while and see what happens. You may have to think carefully about what all constitutes "competition"; you come from a very long line of survivors and there's a lot of competitive behaviors that come naturally to you. Squeezing them all out may take some work.
Competition is a second-order effect; the primary cause is the limited nature of desirable resources, and the ability of resources consumers to step up their rate of consumption exponentially in the face of an increase of resources. Unless you can prove that resources are not limited here and now, you're going to get competition.
Competition isn't always the best way to cope with limited resources.
Competition between different groups within which there is cooperation, that's another option, of course.
I think there's an enormous gulf between the way logic-dorks think people behave, and how people actually behave.
All this game theory stuff needs to go in the trash, frankly.
What explains human behaviour is that with every action we program ourselves to follow certain strategies and rules and that others can judge to some extent which strategies we programmed ourselves to follow. Thus we have an incentive to follow strategies that lead others to trust us, so that we'll have more opportunities for cooperation in the future.
Always start by cooperating and then do the same as the other party : cooperate if he does, retaliate if he doesn't. It is the most effective strategy in both games.
Most importantly, this scenario involves only a binary decision. In reality, there are no binary decisions. Every single possible decision involved countless contingencies to consider which are limited only by the awareness and imagination of the person making the decision. Trying to apply this false paradigm to reality is nonsense. You might as well try to discern real-world data about the number of angels that people believe will fit on the end of a pin.
>Compare this with the Prisoner’s Dilemma. For a quick synopsis, two prisoners being questioned each have the choice to either defend the other’s innocence or betray the other’s guilt.
The underlying assumption is that innocence and guilt are the only factors driving the prisoners decision. What if the prisoner's primary motivation is the rejection of coercion by his captors? Making assumptions about motivation completely nullifies any potentially valuable insights about human behavior.