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'Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation (2007)

163 points by MichaelAO 9y ago

jstanley 9y ago
Incredible that only 48% of people got out of their car to shovel the snow... how can you feel good about yourself, sitting in your car, watching somebody else clear a path for you, and not helping?
- TheSpiceIsLife 9y ago
  48% of people over 12 iterations of a game. "... 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.
  - pavel_lishin 9y ago
    Exactly. In the real world, this is likely iterated dozens of times every winter, against neighbors you'll see repeatedly. 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.
    - logfromblammo 9y ago
      Also, the real world is rarely so symmetric. Most of the time, one party has diminished ability to retaliate, and so gets defected against much more often.
Danihan 9y ago
The benefits of cooperation can't be modeled so simplistically, since the concepts of both long-term reputation and long-term retribution need to be taken into account.
- svachalek 9y ago
  The iterated game (which they studied here) accounts for retribution, but not reputation.
  - TheSpiceIsLife 9y ago
    The iterated game... 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.
    - slg 9y ago
      You don't need any model to explain inconsistency. People are not consistent because they are learning the rules and results of the game as they play. The players' first move might be somewhat random, but every subsequent move is based upon their previous experiences with the game. That is why you do these things iteratively.
- AznHisoka 9y ago
  Sometimes I wish life was just like that Black Mirror episode with reputation scores for everybody. Nobody wants to cooperate because there is hardly any long term reputation to worry about when interacting with most people (ie cutting off that car in the highway, being rude to that stranger next to you)
  - Danihan 9y ago
    There are reputation scores for everyone: net worth and credit score. ;p
TheSpiceIsLife 9y ago
These experiments are nonsense. 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.
- rizzom5000 9y ago
  >> “In principle, natural selection predicts individuals to behave selfishly” is a faulty premise. 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).
  - baddox 9y ago
    > I'm fairly certain that cooperating to raise your own offspring is still considered selfish behavior. Why? Because it leads to more descendants? In that case, the premise is a tautology.
    - nostrademons 9y ago
      The "individual" in evolutionary game theory is generally considered the gene, not the human. A lot of facts of life - like raising offspring at all, or death - make zero sense if you consider the actor to be a person, but make a lot of sense if you consider the actor to be a gene.
glenstein 9y ago
I don't want to be gratuitously negative here. So let's start with the fact that it's great to have a model of cooperation as something out there to be improved upon, or refuted, or defaulted to in the absence of obviously better models. 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.
- TheSpiceIsLife 9y ago
  I despise these contrived experiments and think they should be ridiculed. 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.
  - svachalek 9y ago
    More descendants, too. :-)
    - dane-pgp 9y ago
      More dependants, too. :-)
  - burkaman 9y ago
    These experiments are about trying to explain what you mean by "cooperate". Your points feel right, but even if they're true they aren't very helpful in actually explaining behavior. For example, your explanation seems to directly apply to adoption, but most people don't choose to adopt despite the enormous number of orphans in the world. Why not?
scj 9y ago
I just invented a different snowdrift game, modeled on something that happened to me a couple of years ago. 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).
- rhizome 9y ago
  Is there an option to install a fisheye mirror so people in the driveway can see perpendicularly down the street? https://www.reflectionproducts.com/images/View-car-200-feet-half.jpg https://www.reflectionproducts.com/images/View-car-200-feet-...
  - jerf 9y ago
    First, the point of these discussions is explicitly to stay within the lines. We all know there's a billion elaborations that you could make, but those are different problems. Worthy and interesting problems, even, but different problems. Second, there isn't always a great option for that, no.
lisper 9y ago
Note that the SD is not actually a dilemma. The PD is a dilemma because you ALWAYS do better for yourself in any given iteration by defecting no matter what your opponent does. In the SD, if your opponent defects, you still do better for yourself by cooperating. So of course people will cooperate more under those circumstances. The only thing left to argue about is what the payoff matrix for real-world situations looks like.
- quadrangle 9y ago
  You're correct in most of your description, but it's STILL a dilemma. It's a game of chicken. The dilemma is wanting to wait to see what the other player decides, so the dilemma is everyone refusing to decide. https://en.wikipedia.org/wiki/Snowdrift_game https://en.wikipedia.org/wiki/Snowdrift_game (redirects to chicken game)
  - lisper 9y ago
    You're right. In fact, upon reflection, it is the PD which is not really a dilemma but rather a paradox. The logically correct move in PD (assuming a purely utilitarian quality metric) is always clear: if the game is non-iterated (or iterated with a known horizon) then defect. Otherwise play tit-for-tat. This is true no matter what your opponent does. In the SD the logically correct move depends on your prior on what your opponent is likely to do.
    - kobeya 9y ago
      That resolution only holds if you assume the other player to be equally rational in the PD.
      - Smaug123 9y ago
        In fact the strategy is simpler if the other player is exactly as rational as you: simply cooperate. The other player, being exactly as rational as you, will follow the same reasoning as you do to come to the same conclusion, and will do exactly the same thing as you. I would always cooperate with a copy of myself, for instance. https://en.wikipedia.org/wiki/Superrationality https://en.wikipedia.org/wiki/Superrationality (Of course, the assumption "my opponent is exactly as rational as I am" never holds in real life.)
mslate 9y ago
Snowdrift is just a variation of the Prisoner's Dilemma with a specific constraint on payoffs. This is not novel research
- quadrangle 9y ago
  The article is from 2007, but the research provides real value even if the fundamental concept isn't novel. It says that besides the hypothesis that this adjustment has a particular impact, here's data from real research testing that hypothesis.
PeachPlum 9y ago
See also https://www.sciencedaily.com/releases/2016/09/160915085719.htm 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%,
- arthurcolle 9y ago
  I'm at the edge of my seat!
  - damnfine 9y ago
    There are two types of people; those that can extrapolate for incomplete data.
- avenius 9y ago
  The fifth group must be the nihilists ;)
jdonaldson 9y ago
As mentioned elsewhere in this thread, the payoff for these games never takes into consideration reputation effects. That is, what's the result of other participants observing your actions? Are they more likely to trust you or not trust you when you interact? 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.
- morogop 9y ago
  All actual study of these games involves both one-time and repeated versions of the games, which changes those dynamics. Reputational effects are interesting. If you wanted a reputation as an intelligent person, you'd learn something before you post. But you realized that HN rewards snarkiness and superiority, not actual intelligence, so you're posting ignorantly, and pretending you're making some wise point. Your post will get upvoted because of your decision to embrace ignorant arrogance. Mine, on the other hand, will be downvoted, because I was very slightly mean to you, and HN doesn't tolerate rudeness toward white men who think they're smarter than they are. After all, that's HN's core demographic.
- jzl 9y ago
  See my other comment. In the competitions discussed in The Selfish Gene, PD strategies are allowed to have memory and the simulation is run thousands of times per round. However it is pretty consistently the case that long-term memory is not an outright win for either the competitor or the opponent, compared to the simple "tit-for-tat" strategy which only remembers the previous iteration. 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?
StanislavPetrov 9y ago
In my opinion the PD has always been worthless because it is based on a series of false paradigms. 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.
quadrangle 9y ago
https://snowdrift.coop https://snowdrift.coop is an in-progress fundraising platform for public goods (particularly free/libre/open software and cultural works) based specifically on addressing the cooperation needed to solve the snowdrift dilemma… https://wiki.snowdrift.coop/about/snowdrift-dilemma https://wiki.snowdrift.coop/about/snowdrift-dilemma has more specifically and https://wiki.snowdrift.coop/about https://wiki.snowdrift.coop/about covers the concepts for the whole project.
whack 9y ago
TLDR: In Prisoner's Dilemma, defecting is a dominant strategy, and both players defecting is the only Nash equilibrium. In Snowdrift, there is no single dominant strategy, and no Nash Equilibrium exists at all. 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. http://www.gametheory.net/dictionary/DominantStrategy.html http://www.gametheory.net/dictionary/DominantStrategy.html https://en.wikipedia.org/wiki/Nash_equilibrium https://en.wikipedia.org/wiki/Nash_equilibrium
- cgmg 9y ago
  "In Snowdrift... no Nash Equilibrium exists at all." Doesn't that contradict Nash's existence theorem? I believe Snowdrift has 2 (pure) Nash equilibria, namely CD and DC.
- throwa_way_ 9y ago
  You are wrong. There do exist Nash equilibria in the game [0]. [0]https://en.wikipedia.org/wiki/Chicken_(game)#Best_response_mapping_and_Nash_equilibria https://en.wikipedia.org/wiki/Chicken_(game)#Best_response_m...
  - whack 9y ago
    You're right, my bad.
jzl 9y ago
I've seen a couple of oblique references to this in other comments, but I'll go a little deeper: if you want to truly understand the prisoner's dilemma scenario and how it relates to human, or more generally, animal behavior, there is incredible coverage of the topic in Richard Dawkins' The Selfish Gene. He pioneered the idea of running PD "competitions" in an attempt to discover the best evolutionary strategy for PD, and how these strategies might predict large-scale behavior in animal populations. Each competitor (other scientists and researchers) submitted a strategy for handling the PD in the form of written code that could face off against other strategies. Each round of competition consisted of thousands of iterations of the game. Some strategies were simple and some were incredibly complex. Across two competitions, the second with 60 competing strategies, the simple and "non-cynical" strategy called tit-for-tat won handily. (Tit-for-tat is mentioned briefly in the original article without any explanation.) This is the strategy: - 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: https://en.wikipedia.org/wiki/Nice_Guys_Finish_First https://en.wikipedia.org/wiki/Nice_Guys_Finish_First
- pasiaj 9y ago
  I thought Tit-for-tat was the strategy that always repeated opponents last move. "Tit-for that with forgiveness" was the strategy that would occasionally cooperate even after an opponents defection.
  - jzl 9y ago
    I copied those bullet points from the wikipedia article but yeah the wording is a little inexact. I think "quick to forgive" just means "retaliation only has a memory of one move".
- iainmerrick 9y ago
dandare 9y ago
I always considered the pay-offs in PD to be variables with various positive or negative values. That would make SD is just a subset of PD with different pay-offs.
- shkkmo 9y ago
  There is a difference in the relations between the two payoff schemes. 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.
jamie_ca 9y ago
I came across an interactive applet last month (on Reddit maybe?) at http://ncase.me/trust/ http://ncase.me/trust/ 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.
bluetwo 9y ago
For me the point of Prisoner's Dilemma is that math alone can't give you the answer. The answer lies in your ability to trust the other side and to believe they will trust you.
Nomentatus 9y ago
Uhhh... what made PD important was that it was, precisely, the extreme of non-cooperation; a situation where cooperation was logically possible, but not rational. EVERY other game where cooperation is at least possible is better at promoting cooperation, not just one. If peeps have thought iterated PDs are the acme of cooperation, that's pretty crazy, too.
freech 9y ago
This does not at all explain human behaviour: Most people would not shovel all the snow themselves while their counterpart chills in their car. And many people cooperate in prisoner's dilemma situations. 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.
- GuB-42 9y ago
  This is tit-for-tat. 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.
  - freech 9y ago
    No it's not. What needs to be explained is why you cooperate if you know that you will never play with the same person again. And the answer is that by doing so you get in the habit of automatically cooperating in similar situations in the future and other people recognize this habit and trust you.
xaa 9y ago
I get why game theory is an attractive model to explain human behavior. But I always wonder why they invent the game, and try to explain behavior in terms of a particular model, rather than using real behavior to fit model parameters, so you could get (pseudo-) empirical numbers for "payoffs" etc. 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.
chrstphrhrt 9y ago
Building on this stuff is Scott Aaronson's "Eigenmorality": https://www.scottaaronson.com/blog/?p=1820 https://www.scottaaronson.com/blog/?p=1820
guiambros 9y ago
You can't talk about explaining Prisoner's Dilemma these days without mentioning Nicky Case's excellent "Evolution of Trust". My 5yo simply loves the game. 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]. [1] http://ncase.me/trust/ http://ncase.me/trust/ [2] http://ncase.me/ http://ncase.me/
adrianratnapala 9y ago
People have been doing Prisoner's Dilemma with different payoff amounts since the dawn of PD, and of course this can result in qualitatively different strategies. 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?
- ykler 9y ago
  In snowdrift, in the case where your opponent is uncooperative, it is better for you to be cooperative.
Buge 9y ago
>while shoveling snow always helps you out That appears to be an error in the article. If your opponent is shoveling, then you shoveling hurts you (300 drops to 200).
loa_in_ 9y ago
About the game: One could back out their car and pretend to have dug out the whole thing :)
drvinceknight 9y ago
The Axelrod library is a Python implementation of the Prisoner's dilemma (tournaments, evolutionary dynamics etc) with over 200 strategies. It can also be used to study other games (http://axelrod.readthedocs.io/en/stable/tutorials/advanced/games.html http://axelrod.readthedocs.io/en/stable/tutorials/advanced/g...) so it would be straightforward to study the snowdrift game using it :) 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 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 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-ipd-strategies-beat-simple-ones.html http://vknight.org/unpeudemath/math/2017/07/28/sophisticated... and http://marcharper.codes/2017-07-31/axelrod.html http://marcharper.codes/2017-07-31/axelrod.html Disclaimer: I'm one of the maintainers of the project.

163 points by MichaelAO 9y ago

Incredible that only 48% of people got out of their car to shovel the snow... how can you feel good about yourself, sitting in your car, watching somebody else clear a path for you, and not helping?

TheSpiceIsLife 9y ago
48% of people over 12 iterations of a game. "... 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.
- pavel_lishin 9y ago
  Exactly. In the real world, this is likely iterated dozens of times every winter, against neighbors you'll see repeatedly. 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.
  - logfromblammo 9y ago
    Also, the real world is rarely so symmetric. Most of the time, one party has diminished ability to retaliate, and so gets defected against much more often.

Danihan 9y ago

The benefits of cooperation can't be modeled so simplistically, since the concepts of both long-term reputation and long-term retribution need to be taken into account.

svachalek 9y ago
The iterated game (which they studied here) accounts for retribution, but not reputation.
- TheSpiceIsLife 9y ago
  The iterated game... 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.
  - slg 9y ago
    You don't need any model to explain inconsistency. People are not consistent because they are learning the rules and results of the game as they play. The players' first move might be somewhat random, but every subsequent move is based upon their previous experiences with the game. That is why you do these things iteratively.
AznHisoka 9y ago
Sometimes I wish life was just like that Black Mirror episode with reputation scores for everybody. Nobody wants to cooperate because there is hardly any long term reputation to worry about when interacting with most people (ie cutting off that car in the highway, being rude to that stranger next to you)
- Danihan 9y ago
  There are reputation scores for everyone: net worth and credit score. ;p

TheSpiceIsLife 9y ago

These experiments are nonsense. 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.

rizzom5000 9y ago
>> “In principle, natural selection predicts individuals to behave selfishly” is a faulty premise. 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).
- baddox 9y ago
  > I'm fairly certain that cooperating to raise your own offspring is still considered selfish behavior. Why? Because it leads to more descendants? In that case, the premise is a tautology.
  - nostrademons 9y ago
    The "individual" in evolutionary game theory is generally considered the gene, not the human. A lot of facts of life - like raising offspring at all, or death - make zero sense if you consider the actor to be a person, but make a lot of sense if you consider the actor to be a gene.

glenstein 9y ago

I don't want to be gratuitously negative here. So let's start with the fact that it's great to have a model of cooperation as something out there to be improved upon, or refuted, or defaulted to in the absence of obviously better models. 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.

TheSpiceIsLife 9y ago
I despise these contrived experiments and think they should be ridiculed. 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.
- svachalek 9y ago
  More descendants, too. :-)
  - dane-pgp 9y ago
    More dependants, too. :-)
- burkaman 9y ago
  These experiments are about trying to explain what you mean by "cooperate". Your points feel right, but even if they're true they aren't very helpful in actually explaining behavior. For example, your explanation seems to directly apply to adoption, but most people don't choose to adopt despite the enormous number of orphans in the world. Why not?

scj 9y ago

I just invented a different snowdrift game, modeled on something that happened to me a couple of years ago. 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).

rhizome 9y ago
Is there an option to install a fisheye mirror so people in the driveway can see perpendicularly down the street? https://www.reflectionproducts.com/images/View-car-200-feet-half.jpg https://www.reflectionproducts.com/images/View-car-200-feet-...
- jerf 9y ago
  First, the point of these discussions is explicitly to stay within the lines. We all know there's a billion elaborations that you could make, but those are different problems. Worthy and interesting problems, even, but different problems. Second, there isn't always a great option for that, no.

lisper 9y ago

Note that the SD is not actually a dilemma. The PD is a dilemma because you ALWAYS do better for yourself in any given iteration by defecting no matter what your opponent does. In the SD, if your opponent defects, you still do better for yourself by cooperating. So of course people will cooperate more under those circumstances. The only thing left to argue about is what the payoff matrix for real-world situations looks like.

quadrangle 9y ago
You're correct in most of your description, but it's STILL a dilemma. It's a game of chicken. The dilemma is wanting to wait to see what the other player decides, so the dilemma is everyone refusing to decide. https://en.wikipedia.org/wiki/Snowdrift_game https://en.wikipedia.org/wiki/Snowdrift_game (redirects to chicken game)
- lisper 9y ago
  You're right. In fact, upon reflection, it is the PD which is not really a dilemma but rather a paradox. The logically correct move in PD (assuming a purely utilitarian quality metric) is always clear: if the game is non-iterated (or iterated with a known horizon) then defect. Otherwise play tit-for-tat. This is true no matter what your opponent does. In the SD the logically correct move depends on your prior on what your opponent is likely to do.
  - kobeya 9y ago
    That resolution only holds if you assume the other player to be equally rational in the PD.
    - Smaug123 9y ago
      In fact the strategy is simpler if the other player is exactly as rational as you: simply cooperate. The other player, being exactly as rational as you, will follow the same reasoning as you do to come to the same conclusion, and will do exactly the same thing as you. I would always cooperate with a copy of myself, for instance. https://en.wikipedia.org/wiki/Superrationality https://en.wikipedia.org/wiki/Superrationality (Of course, the assumption "my opponent is exactly as rational as I am" never holds in real life.)

mslate 9y ago

Snowdrift is just a variation of the Prisoner's Dilemma with a specific constraint on payoffs. This is not novel research

quadrangle 9y ago
The article is from 2007, but the research provides real value even if the fundamental concept isn't novel. It says that besides the hypothesis that this adjustment has a particular impact, here's data from real research testing that hypothesis.

PeachPlum 9y ago

See also https://www.sciencedaily.com/releases/2016/09/160915085719.htm 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%,

arthurcolle 9y ago
I'm at the edge of my seat!
- damnfine 9y ago
  There are two types of people; those that can extrapolate for incomplete data.
avenius 9y ago
The fifth group must be the nihilists ;)

jdonaldson 9y ago

As mentioned elsewhere in this thread, the payoff for these games never takes into consideration reputation effects. That is, what's the result of other participants observing your actions? Are they more likely to trust you or not trust you when you interact? 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.

morogop 9y ago
All actual study of these games involves both one-time and repeated versions of the games, which changes those dynamics. Reputational effects are interesting. If you wanted a reputation as an intelligent person, you'd learn something before you post. But you realized that HN rewards snarkiness and superiority, not actual intelligence, so you're posting ignorantly, and pretending you're making some wise point. Your post will get upvoted because of your decision to embrace ignorant arrogance. Mine, on the other hand, will be downvoted, because I was very slightly mean to you, and HN doesn't tolerate rudeness toward white men who think they're smarter than they are. After all, that's HN's core demographic.
jzl 9y ago
See my other comment. In the competitions discussed in The Selfish Gene, PD strategies are allowed to have memory and the simulation is run thousands of times per round. However it is pretty consistently the case that long-term memory is not an outright win for either the competitor or the opponent, compared to the simple "tit-for-tat" strategy which only remembers the previous iteration. 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?

StanislavPetrov 9y ago

In my opinion the PD has always been worthless because it is based on a series of false paradigms. 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.

quadrangle 9y ago

https://snowdrift.coop https://snowdrift.coop is an in-progress fundraising platform for public goods (particularly free/libre/open software and cultural works) based specifically on addressing the cooperation needed to solve the snowdrift dilemma… https://wiki.snowdrift.coop/about/snowdrift-dilemma https://wiki.snowdrift.coop/about/snowdrift-dilemma has more specifically and https://wiki.snowdrift.coop/about https://wiki.snowdrift.coop/about covers the concepts for the whole project.

whack 9y ago

TLDR: In Prisoner's Dilemma, defecting is a dominant strategy, and both players defecting is the only Nash equilibrium. In Snowdrift, there is no single dominant strategy, and no Nash Equilibrium exists at all. 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. http://www.gametheory.net/dictionary/DominantStrategy.html http://www.gametheory.net/dictionary/DominantStrategy.html https://en.wikipedia.org/wiki/Nash_equilibrium https://en.wikipedia.org/wiki/Nash_equilibrium

cgmg 9y ago
"In Snowdrift... no Nash Equilibrium exists at all." Doesn't that contradict Nash's existence theorem? I believe Snowdrift has 2 (pure) Nash equilibria, namely CD and DC.
throwa_way_ 9y ago
You are wrong. There do exist Nash equilibria in the game [0]. [0]https://en.wikipedia.org/wiki/Chicken_(game)#Best_response_mapping_and_Nash_equilibria https://en.wikipedia.org/wiki/Chicken_(game)#Best_response_m...
- whack 9y ago
  You're right, my bad.

jzl 9y ago

I've seen a couple of oblique references to this in other comments, but I'll go a little deeper: if you want to truly understand the prisoner's dilemma scenario and how it relates to human, or more generally, animal behavior, there is incredible coverage of the topic in Richard Dawkins' The Selfish Gene. He pioneered the idea of running PD "competitions" in an attempt to discover the best evolutionary strategy for PD, and how these strategies might predict large-scale behavior in animal populations. Each competitor (other scientists and researchers) submitted a strategy for handling the PD in the form of written code that could face off against other strategies. Each round of competition consisted of thousands of iterations of the game. Some strategies were simple and some were incredibly complex. Across two competitions, the second with 60 competing strategies, the simple and "non-cynical" strategy called tit-for-tat won handily. (Tit-for-tat is mentioned briefly in the original article without any explanation.) This is the strategy: - 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: https://en.wikipedia.org/wiki/Nice_Guys_Finish_First https://en.wikipedia.org/wiki/Nice_Guys_Finish_First

pasiaj 9y ago
I thought Tit-for-tat was the strategy that always repeated opponents last move. "Tit-for that with forgiveness" was the strategy that would occasionally cooperate even after an opponents defection.
- jzl 9y ago
  I copied those bullet points from the wikipedia article but yeah the wording is a little inexact. I think "quick to forgive" just means "retaliation only has a memory of one move".
iainmerrick 9y ago

dandare 9y ago

I always considered the pay-offs in PD to be variables with various positive or negative values. That would make SD is just a subset of PD with different pay-offs.

shkkmo 9y ago
There is a difference in the relations between the two payoff schemes. 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.

jamie_ca 9y ago

I came across an interactive applet last month (on Reddit maybe?) at http://ncase.me/trust/ http://ncase.me/trust/ 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.

bluetwo 9y ago

For me the point of Prisoner's Dilemma is that math alone can't give you the answer. The answer lies in your ability to trust the other side and to believe they will trust you.

Nomentatus 9y ago

Uhhh... what made PD important was that it was, precisely, the extreme of non-cooperation; a situation where cooperation was logically possible, but not rational. EVERY other game where cooperation is at least possible is better at promoting cooperation, not just one. If peeps have thought iterated PDs are the acme of cooperation, that's pretty crazy, too.

freech 9y ago

This does not at all explain human behaviour: Most people would not shovel all the snow themselves while their counterpart chills in their car. And many people cooperate in prisoner's dilemma situations. 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.

GuB-42 9y ago
This is tit-for-tat. 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.
- freech 9y ago
  No it's not. What needs to be explained is why you cooperate if you know that you will never play with the same person again. And the answer is that by doing so you get in the habit of automatically cooperating in similar situations in the future and other people recognize this habit and trust you.

xaa 9y ago

I get why game theory is an attractive model to explain human behavior. But I always wonder why they invent the game, and try to explain behavior in terms of a particular model, rather than using real behavior to fit model parameters, so you could get (pseudo-) empirical numbers for "payoffs" etc. 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.

chrstphrhrt 9y ago

Building on this stuff is Scott Aaronson's "Eigenmorality": https://www.scottaaronson.com/blog/?p=1820 https://www.scottaaronson.com/blog/?p=1820

guiambros 9y ago

You can't talk about explaining Prisoner's Dilemma these days without mentioning Nicky Case's excellent "Evolution of Trust". My 5yo simply loves the game. 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]. [1] http://ncase.me/trust/ http://ncase.me/trust/ [2] http://ncase.me/ http://ncase.me/

adrianratnapala 9y ago

People have been doing Prisoner's Dilemma with different payoff amounts since the dawn of PD, and of course this can result in qualitatively different strategies. 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?

ykler 9y ago
In snowdrift, in the case where your opponent is uncooperative, it is better for you to be cooperative.

Buge 9y ago

>while shoveling snow always helps you out That appears to be an error in the article. If your opponent is shoveling, then you shoveling hurts you (300 drops to 200).

loa_in_ 9y ago

About the game: One could back out their car and pretend to have dug out the whole thing :)

drvinceknight 9y ago

The Axelrod library is a Python implementation of the Prisoner's dilemma (tournaments, evolutionary dynamics etc) with over 200 strategies. It can also be used to study other games (http://axelrod.readthedocs.io/en/stable/tutorials/advanced/games.html http://axelrod.readthedocs.io/en/stable/tutorials/advanced/g...) so it would be straightforward to study the snowdrift game using it :) 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 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 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-ipd-strategies-beat-simple-ones.html http://vknight.org/unpeudemath/math/2017/07/28/sophisticated... and http://marcharper.codes/2017-07-31/axelrod.html http://marcharper.codes/2017-07-31/axelrod.html Disclaimer: I'm one of the maintainers of the project.