10 ms·

The Evolution of Trust

440 points by awartani 9y ago

mLuby 9y ago
Very cool simulation. Would love to see it with inter-agent communication between rounds, where those you cooperate with tell you who cheated them.
sfsylvester 9y ago
This is by far one of the coolest things I've seen on this site. Informative, engaging and educational. Would be very keen to learn more subjects through this method.
- conradev 9y ago
  Nicky Case has a lot more where that came from :D http://ncase.me http://ncase.me
  - CupOfJava 9y ago
    Wow. I played "we become what we behold" just last week. I had no idea it was the same author. I'm gonna check out the rest now too!
- weinzierl 9y ago
  What makes it even cooler is that code and assets are on GitHub and released to the public domain. https://github.com/ncase/trust/#play-it-here-httpncasemetrust https://github.com/ncase/trust/#play-it-here-httpncasemetrus...
deleted 9y ago
[deleted]
arca_vorago 9y ago
This caught my attention: "So, it seems the math of game theory is telling us something: that Copycat's philosophy, "Do unto others as you would have them do unto you", may be not just a moral truth, but also a mathematical truth." Simpleton and copykitten for the win!
- brudgers 9y ago
  More notable to me is the premise of the simulation that it is ok to kill off the poor to make room for the rich. Because using the simulation to justify moral/ethical/rational acceptability of cheating sometimes means accepting that premise.
  - larsiusprime 9y ago
    This isn't the premise of the simulation at all. It explicitly says that the agent replacement phase is an abstraction and could just as easily be interpreted as agents changing their strategies. "Note: you don't have to wait for people to literally die & reproduce for culture to evolve -- all that's needed is that "unsuccessful" behaviors go away, and "successful" behaviors are imitated."
    - brudgers 9y ago
      The premise of the replacement is that poorest adopt the strategy of the richest and is premised on this being the right thing to do even if the change is from always cooperating to always cheating. In some ways the description of replacement rather death is a more explicit example of the premise underlying the simulation that cheating is morally/ethically/rationally justifiable. The underlying moral/ethical theory behind the simulation is not even Utilitarian (never mind Deontological) it is purely Randian where the justification of behavior is only what is in it for me. In that sense it completely misses the point of the Christmas Peace which from a deontological perspective reflected moral/ethical principles such as the golden rule and peace on earth and goodwill toward men. Even from a utilitarian perspective there was the idea that the greatest happiness for the greatest number included the enemy in that number. The individual benefits were a side effect that was only possible because of the higher level principle. And the individual benefits were always going to trend toward a short life. The shell with someone's name on it was still going to be lobbed on 26/12/14.
      - carapace 9y ago
        The "reward" is an unspecified scalar value. You are casting the terms of the model into "poor" and "rich". It's a mathematical model, not an ethical one.
j2kun 9y ago
Of course, this all breaks down when you have a cartel :) I recall in one of the major prisoners dilemma tournaments, the winning entry was actually a coalition of users who would use the first few moves to establish a code for membership in the cartel, and then one entry was the master while the others were slaves. The slaves always cooperated and the master always defected, to their victory.
- alliao 9y ago
  The eye!
- dodorex 9y ago
  Interesting, do you have a link?
- s_kilk 9y ago
  Indeed, the major weakness of the linked piece is that it doesn't account for any kind of social structure or any class behaviour. Which, in my book, makes it fairly worthless as an analysis of actual social behaviour.
  - 09094920394314 9y ago
    Not worthless. This has some clear assumptions on what holds. He looks at individuals playing a certain game, with no outside information. What the parent describes is two games: 1. Prisoners dilemma between each "slave" and the "master" 2. The actual tournament
deleted 9y ago
[deleted]
cryptica 9y ago
Wow that is extremely insightful. Now I understand why globalisation is dangerous; if people start to favor short term relationships (both personal and business) with many different partners (smaller number of rounds <interactions> per match <lifetime>), then society will evolve to become full of cheaters.
- sgk284 9y ago
  Interestingly enough, seemingly to compensate for this phenomenon, almost every new platform that requires people to interact with each other has a built in trust and reward system with ratings (e.g. Uber). And for physical businesses, we have things like Yelp. We are effectively trying to anticipate our opponents behavior through a trusted intermediary. There was a Black Mirror episode on giving every person on the globe their own rating. It seems that may be the actual destination that we're headed for.
  - nothrabannosir 9y ago
    > There was a Black Mirror episode on giving every person on the globe their own rating. It seems that may be the actual destination that we're headed for. "Nosedive". One of the scariest things I've ever seen on screen. I joke about how realistic black mirror is but that episode was too much. Beyond uncanny. It was incredibly hard to watch and I hated every second of it. Awful. Cannot recommend it enough.
  - cJ0th 9y ago
    Trust, however, is not a miracle drug. For one thing, people can build trust with the intend to abuse it after a longer period of time. An abuser, for example, could plan to offer 20 "good rides" on Uber until s/he strikes. For another thing, many people have learnt to skillfully simulate trust which may pose a problem for you. For instance, you may believe to be in a loving relationship but all of a sudden you find out that the other person isn't interested in you at all and just didn't want to be alone etc.
    - rossdavidh 9y ago
tpeo 9y ago
The little animated chums strike me be as a bit too cute. One has to take care to not anthropomorphize models. Even models ostensibly created to model aspects of human behavior, such game theoretic models. Anthropomorphism might induce people either to think there's more under the hood than there actually is, and thus lead them to a hold a wrong mental representation of the model, or to naively assume that it's conclusions are robust to specification changes by making the conclusions a bit too familiar, even though even somewhat simple model extensions might significantly change their behavior (e.g. going from single to repeated games, which makes cooperatives strategies viable). Comparing tit-for-tat strategies with the Golden rule, while mixing in references toe the Christmas truce somehow seems to go in the opposite direction of being cautious regarding model interpretation.
- larsiusprime 9y ago
  > even though even somewhat simple model extensions might significantly change their behavior (e.g. going from single to repeated games, which makes cooperatives strategies viable). He explicitly examines this in the application, did you not run through it? He actively encourages you to modify the rules and see how it changes the results.
  - tpeo 9y ago
    I ran through it. I didn't suggest he didn't cover it. I just used it as a trivial example, because other readers supposedly also ran through it. Some other commenter suggested communication between agents as an extension, I could've used that if I knew what results from it.
ybaumes 9y ago
I've read it multiple times, I still do not understand the simpleton strategy...
- Rudism 9y ago
  Essentially, the simpleton is treating your previous move as either a reward or punishment. If you cooperated, then the simpleton thinks the thing it did last time must have been good and does it again. If you cheated, the simpleton thinks the thing it did last time must have been bad and does the opposite. It follows these rules based on its last move even if that last move was flipped from what it should have been due to the chance of mistake.
- JoshTriplett 9y ago
  "If I 'won', do the same thing again. If I 'lost', do the other thing." Also called win-stay-lose-switch or similar.
deleted 9y ago
[deleted]
Rjevski 9y ago
> Despite strict orders not to chillax with the enemy, British and German soldiers left their trenches, crossed No Man's Land, and gathered to bury their dead, exchange gifts, and play games. Is this actually true? I'd love to read more about it.
- clock_tower 9y ago
  Absolutely true: https://en.wikipedia.org/wiki/Christmas_truce https://en.wikipedia.org/wiki/Christmas_truce
  - Rjevski 9y ago
    Thanks - that was a heart-warming read.
deleted 9y ago
[deleted]
deleted 9y ago
[deleted]
deleted 9y ago
[deleted]
DanAndersen 9y ago
One extension I'd like to see to this simulation is the exploration of group/tribe dynamics, as a way of exploring questions regarding in-group loyalty (anthropomorphized in as "ethnocentrism" or something analogous) vs egalitarianism. It seems like much of the success of these agents can depend on whether Agent A can determine what sort of actor Agent B is -- communication that can be conveyed beyond just the framework of actual transactions between A and B. Are there any existing generic frameworks out there for testing out a wider range of agent/group-based game theory scenarios?
- dwaltrip 9y ago
  Another important missing factor here is the modeling of empathy and altruism. It can often simply feel good to help someone else, even if you get nothing tangible in return. This is a biological fact, as far as I'm aware. Incredibly crude approximation: some situations that appear as [empathetic helper +0, receiver +3] on the surface, might in reality be [empathetic helper +1, receiver +3]. There is a ton of complexity in how this works in the real world. The magnitude or presence of the non-tangible reward may depend heavily on a certain aspects of one's value system. It may be heavily contextual -- only certain situations foster the non-tangible reward. Sometimes there is a potential tangible reward that may come much later, after some weeks, months, or years. And so on... I think this is barely scratching the surface. Lastly, none of the people or dynamics in the system are static. The linked interactive tool was very cool. However, I'm increasingly skeptical of these types of analyses as they generally are forced to ignore most of the complexity of the real world. EDIT: I completely forgot about technology... things like the internet which completely change the nature of an interaction between people, or apps that mediate or flavor in-person interactions in ways that society has never seen before.
  - barrkel 9y ago
    Have you thought that perhaps things like emotions, both empathy and revenge have evolved to emulate Copycat / Copykitten play styles? That is, I don't think they're missing from the simulation. Rather, the simulation shows why those things exist.
bmc7505 9y ago
The creator of this project has a really amazing talk about his work, including interactive explainers, narrative games and chaos theory. Really interesting: https://www.youtube.com/watch?v=Zl9m0AQInBk https://www.youtube.com/watch?v=Zl9m0AQInBk
RonanTheGrey 9y ago
We like to think we are complex, free-will wielding creatures capable of doing complex and unpredictable things. It's striking to see how simple we really are and honestly - how easy it is to explain how we behave. I get it - this is a simulation and it leaves out alot of colors to human behavior. But it is the essence of our value-oriented decision making and really quite sad that a better world is actually? quite easy to make. I think software has the potential to create that world. I propose the creation of a formal group dedicated to exactly such a purpose.
trhway 9y ago
From Netflix's "Sense8" : What is the advantage of the Homo Sapiens over the Homo Sensorium (the telepathic humans)? Homo Sapiens is capable of lying.
egonschiele 9y ago
This is super impressive. I have been asking myself these questions for years, it is awesome to see such a nice visualization of the answers. The "30 minutes to play" almost made me click away but you got me hooked at the next screen.
minademian 9y ago
this is incredibly fascinating and insightful. side question: who composed the music? the guitar track is excellent. :)
- dentarg 9y ago
  there's a list of music/sound credits on the github page: https://github.com/ncase/trust/#play-it-here-httpncasemetrust https://github.com/ncase/trust/#play-it-here-httpncasemetrus...
freeflight 9y ago
This is great and really fun. 10 rounds with changed payoffs has some really interesting results. Punishing cheating from both sides, regardless of how high, still leads to the cheaters taking over. But if you increase the payoffs for both sides cooperating, even if it's just by +1, you already eliminate all the cheaters very quickly and even the copycats are gone pretty quick, leaving a population of only cooperate. Sure that's for the 10 round game without any of the other players, it's still very interesting how even in that setting it seems more beneficial to reward good behavior vs punishing bad behavior.
crawfordcomeaux 9y ago
"Nonviolent Communication" by Marshall Rosenberg teaches a structured framework enshrining the takeaways from this lovely bit of art.
hellbanner 9y ago
27 points, how'd you do HN?
roflc0ptic 9y ago
More reading on this: There is a paper by David Axelrod and W.D. Hamilton called "The Evolution of Cooperation". There is also a book by Axelrod of the same name. https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation
hftf 9y ago
The execution of this visualization was rather disappointing. I didn’t like the overly cute text (the description of the Simpleton algorithm was almost incomprehensible), the low-contrast captions and colorblind-unfriendly color scheme, and the limited navigation (there was no way to go to the previous slide within a chapter, for example). But more importantly: If you are going to design an entire interactive exercise like this, graphs are a much better way to explore the effects of varying different parameters. Trying to experiment (as instructed) with different parameters by watching animations in the various chapters and the "sandbox mode" included in this simulation was not only tedious, but prevented effective comparisons. If you just run each iterated tournament (from chapter 4 and onwards) by pressing the "Start" button, there is too much going on simultaneously at a high speed to follow along – I would recommend a sorted table or bar chart rather than many multi-digit numbers arranged in a circle – while stepping through is too slow to keep everything in your head. I noticed that some of the other "explorable explanations" by the same creator include graphs; I think omitting them from this visualization was a mistake. http://explorableexplanations.com/ http://explorableexplanations.com/
cryptonector 9y ago
This blew up on reddit: https://www.reddit.com/r/philosophy/comments/6q1i1e/game_theory_and_the_golden_rule/ https://www.reddit.com/r/philosophy/comments/6q1i1e/game_the...
udkl 9y ago
As a co-incidence, I just read this relevant article today - http://www.economist.com/news/economics-brief/21705308-fifth-our-series-seminal-economic-ideas-looks-nash-equilibrium-prison http://www.economist.com/news/economics-brief/21705308-fifth... Edit : to say - This site was a beautiful insightful experience.

440 points by awartani 9y ago

Very cool simulation. Would love to see it with inter-agent communication between rounds, where those you cooperate with tell you who cheated them.

sfsylvester 9y ago

This is by far one of the coolest things I've seen on this site. Informative, engaging and educational. Would be very keen to learn more subjects through this method.

conradev 9y ago
Nicky Case has a lot more where that came from :D http://ncase.me http://ncase.me
- CupOfJava 9y ago
  Wow. I played "we become what we behold" just last week. I had no idea it was the same author. I'm gonna check out the rest now too!
weinzierl 9y ago
What makes it even cooler is that code and assets are on GitHub and released to the public domain. https://github.com/ncase/trust/#play-it-here-httpncasemetrust https://github.com/ncase/trust/#play-it-here-httpncasemetrus...

deleted 9y ago

[deleted]

arca_vorago 9y ago

This caught my attention: "So, it seems the math of game theory is telling us something: that Copycat's philosophy, "Do unto others as you would have them do unto you", may be not just a moral truth, but also a mathematical truth." Simpleton and copykitten for the win!

brudgers 9y ago
More notable to me is the premise of the simulation that it is ok to kill off the poor to make room for the rich. Because using the simulation to justify moral/ethical/rational acceptability of cheating sometimes means accepting that premise.
- larsiusprime 9y ago
  This isn't the premise of the simulation at all. It explicitly says that the agent replacement phase is an abstraction and could just as easily be interpreted as agents changing their strategies. "Note: you don't have to wait for people to literally die & reproduce for culture to evolve -- all that's needed is that "unsuccessful" behaviors go away, and "successful" behaviors are imitated."
  - brudgers 9y ago
    The premise of the replacement is that poorest adopt the strategy of the richest and is premised on this being the right thing to do even if the change is from always cooperating to always cheating. In some ways the description of replacement rather death is a more explicit example of the premise underlying the simulation that cheating is morally/ethically/rationally justifiable. The underlying moral/ethical theory behind the simulation is not even Utilitarian (never mind Deontological) it is purely Randian where the justification of behavior is only what is in it for me. In that sense it completely misses the point of the Christmas Peace which from a deontological perspective reflected moral/ethical principles such as the golden rule and peace on earth and goodwill toward men. Even from a utilitarian perspective there was the idea that the greatest happiness for the greatest number included the enemy in that number. The individual benefits were a side effect that was only possible because of the higher level principle. And the individual benefits were always going to trend toward a short life. The shell with someone's name on it was still going to be lobbed on 26/12/14.
    - carapace 9y ago
      The "reward" is an unspecified scalar value. You are casting the terms of the model into "poor" and "rich". It's a mathematical model, not an ethical one.

j2kun 9y ago

Of course, this all breaks down when you have a cartel :) I recall in one of the major prisoners dilemma tournaments, the winning entry was actually a coalition of users who would use the first few moves to establish a code for membership in the cartel, and then one entry was the master while the others were slaves. The slaves always cooperated and the master always defected, to their victory.

alliao 9y ago
The eye!
dodorex 9y ago
Interesting, do you have a link?
s_kilk 9y ago
Indeed, the major weakness of the linked piece is that it doesn't account for any kind of social structure or any class behaviour. Which, in my book, makes it fairly worthless as an analysis of actual social behaviour.
- 09094920394314 9y ago
  Not worthless. This has some clear assumptions on what holds. He looks at individuals playing a certain game, with no outside information. What the parent describes is two games: 1. Prisoners dilemma between each "slave" and the "master" 2. The actual tournament

deleted 9y ago

[deleted]

cryptica 9y ago

Wow that is extremely insightful. Now I understand why globalisation is dangerous; if people start to favor short term relationships (both personal and business) with many different partners (smaller number of rounds <interactions> per match <lifetime>), then society will evolve to become full of cheaters.

sgk284 9y ago
Interestingly enough, seemingly to compensate for this phenomenon, almost every new platform that requires people to interact with each other has a built in trust and reward system with ratings (e.g. Uber). And for physical businesses, we have things like Yelp. We are effectively trying to anticipate our opponents behavior through a trusted intermediary. There was a Black Mirror episode on giving every person on the globe their own rating. It seems that may be the actual destination that we're headed for.
- nothrabannosir 9y ago
  > There was a Black Mirror episode on giving every person on the globe their own rating. It seems that may be the actual destination that we're headed for. "Nosedive". One of the scariest things I've ever seen on screen. I joke about how realistic black mirror is but that episode was too much. Beyond uncanny. It was incredibly hard to watch and I hated every second of it. Awful. Cannot recommend it enough.
- cJ0th 9y ago
  Trust, however, is not a miracle drug. For one thing, people can build trust with the intend to abuse it after a longer period of time. An abuser, for example, could plan to offer 20 "good rides" on Uber until s/he strikes. For another thing, many people have learnt to skillfully simulate trust which may pose a problem for you. For instance, you may believe to be in a loving relationship but all of a sudden you find out that the other person isn't interested in you at all and just didn't want to be alone etc.
  - rossdavidh 9y ago

tpeo 9y ago

The little animated chums strike me be as a bit too cute. One has to take care to not anthropomorphize models. Even models ostensibly created to model aspects of human behavior, such game theoretic models. Anthropomorphism might induce people either to think there's more under the hood than there actually is, and thus lead them to a hold a wrong mental representation of the model, or to naively assume that it's conclusions are robust to specification changes by making the conclusions a bit too familiar, even though even somewhat simple model extensions might significantly change their behavior (e.g. going from single to repeated games, which makes cooperatives strategies viable). Comparing tit-for-tat strategies with the Golden rule, while mixing in references toe the Christmas truce somehow seems to go in the opposite direction of being cautious regarding model interpretation.

larsiusprime 9y ago
> even though even somewhat simple model extensions might significantly change their behavior (e.g. going from single to repeated games, which makes cooperatives strategies viable). He explicitly examines this in the application, did you not run through it? He actively encourages you to modify the rules and see how it changes the results.
- tpeo 9y ago
  I ran through it. I didn't suggest he didn't cover it. I just used it as a trivial example, because other readers supposedly also ran through it. Some other commenter suggested communication between agents as an extension, I could've used that if I knew what results from it.

ybaumes 9y ago

I've read it multiple times, I still do not understand the simpleton strategy...

Rudism 9y ago
Essentially, the simpleton is treating your previous move as either a reward or punishment. If you cooperated, then the simpleton thinks the thing it did last time must have been good and does it again. If you cheated, the simpleton thinks the thing it did last time must have been bad and does the opposite. It follows these rules based on its last move even if that last move was flipped from what it should have been due to the chance of mistake.
JoshTriplett 9y ago
"If I 'won', do the same thing again. If I 'lost', do the other thing." Also called win-stay-lose-switch or similar.

deleted 9y ago

[deleted]

Rjevski 9y ago

> Despite strict orders not to chillax with the enemy, British and German soldiers left their trenches, crossed No Man's Land, and gathered to bury their dead, exchange gifts, and play games. Is this actually true? I'd love to read more about it.

clock_tower 9y ago
Absolutely true: https://en.wikipedia.org/wiki/Christmas_truce https://en.wikipedia.org/wiki/Christmas_truce
- Rjevski 9y ago
  Thanks - that was a heart-warming read.

deleted 9y ago

[deleted]

deleted 9y ago

[deleted]

deleted 9y ago

[deleted]

DanAndersen 9y ago

One extension I'd like to see to this simulation is the exploration of group/tribe dynamics, as a way of exploring questions regarding in-group loyalty (anthropomorphized in as "ethnocentrism" or something analogous) vs egalitarianism. It seems like much of the success of these agents can depend on whether Agent A can determine what sort of actor Agent B is -- communication that can be conveyed beyond just the framework of actual transactions between A and B. Are there any existing generic frameworks out there for testing out a wider range of agent/group-based game theory scenarios?

dwaltrip 9y ago
Another important missing factor here is the modeling of empathy and altruism. It can often simply feel good to help someone else, even if you get nothing tangible in return. This is a biological fact, as far as I'm aware. Incredibly crude approximation: some situations that appear as [empathetic helper +0, receiver +3] on the surface, might in reality be [empathetic helper +1, receiver +3]. There is a ton of complexity in how this works in the real world. The magnitude or presence of the non-tangible reward may depend heavily on a certain aspects of one's value system. It may be heavily contextual -- only certain situations foster the non-tangible reward. Sometimes there is a potential tangible reward that may come much later, after some weeks, months, or years. And so on... I think this is barely scratching the surface. Lastly, none of the people or dynamics in the system are static. The linked interactive tool was very cool. However, I'm increasingly skeptical of these types of analyses as they generally are forced to ignore most of the complexity of the real world. EDIT: I completely forgot about technology... things like the internet which completely change the nature of an interaction between people, or apps that mediate or flavor in-person interactions in ways that society has never seen before.
- barrkel 9y ago
  Have you thought that perhaps things like emotions, both empathy and revenge have evolved to emulate Copycat / Copykitten play styles? That is, I don't think they're missing from the simulation. Rather, the simulation shows why those things exist.

bmc7505 9y ago

The creator of this project has a really amazing talk about his work, including interactive explainers, narrative games and chaos theory. Really interesting: https://www.youtube.com/watch?v=Zl9m0AQInBk https://www.youtube.com/watch?v=Zl9m0AQInBk

RonanTheGrey 9y ago

We like to think we are complex, free-will wielding creatures capable of doing complex and unpredictable things. It's striking to see how simple we really are and honestly - how easy it is to explain how we behave. I get it - this is a simulation and it leaves out alot of colors to human behavior. But it is the essence of our value-oriented decision making and really quite sad that a better world is actually? quite easy to make. I think software has the potential to create that world. I propose the creation of a formal group dedicated to exactly such a purpose.

trhway 9y ago

From Netflix's "Sense8" : What is the advantage of the Homo Sapiens over the Homo Sensorium (the telepathic humans)? Homo Sapiens is capable of lying.

egonschiele 9y ago

This is super impressive. I have been asking myself these questions for years, it is awesome to see such a nice visualization of the answers. The "30 minutes to play" almost made me click away but you got me hooked at the next screen.

minademian 9y ago

this is incredibly fascinating and insightful. side question: who composed the music? the guitar track is excellent. :)

dentarg 9y ago
there's a list of music/sound credits on the github page: https://github.com/ncase/trust/#play-it-here-httpncasemetrust https://github.com/ncase/trust/#play-it-here-httpncasemetrus...

freeflight 9y ago

This is great and really fun. 10 rounds with changed payoffs has some really interesting results. Punishing cheating from both sides, regardless of how high, still leads to the cheaters taking over. But if you increase the payoffs for both sides cooperating, even if it's just by +1, you already eliminate all the cheaters very quickly and even the copycats are gone pretty quick, leaving a population of only cooperate. Sure that's for the 10 round game without any of the other players, it's still very interesting how even in that setting it seems more beneficial to reward good behavior vs punishing bad behavior.

crawfordcomeaux 9y ago

"Nonviolent Communication" by Marshall Rosenberg teaches a structured framework enshrining the takeaways from this lovely bit of art.

hellbanner 9y ago

27 points, how'd you do HN?

roflc0ptic 9y ago

More reading on this: There is a paper by David Axelrod and W.D. Hamilton called "The Evolution of Cooperation". There is also a book by Axelrod of the same name. https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation

hftf 9y ago

The execution of this visualization was rather disappointing. I didn’t like the overly cute text (the description of the Simpleton algorithm was almost incomprehensible), the low-contrast captions and colorblind-unfriendly color scheme, and the limited navigation (there was no way to go to the previous slide within a chapter, for example). But more importantly: If you are going to design an entire interactive exercise like this, graphs are a much better way to explore the effects of varying different parameters. Trying to experiment (as instructed) with different parameters by watching animations in the various chapters and the "sandbox mode" included in this simulation was not only tedious, but prevented effective comparisons. If you just run each iterated tournament (from chapter 4 and onwards) by pressing the "Start" button, there is too much going on simultaneously at a high speed to follow along – I would recommend a sorted table or bar chart rather than many multi-digit numbers arranged in a circle – while stepping through is too slow to keep everything in your head. I noticed that some of the other "explorable explanations" by the same creator include graphs; I think omitting them from this visualization was a mistake. http://explorableexplanations.com/ http://explorableexplanations.com/

cryptonector 9y ago

This blew up on reddit: https://www.reddit.com/r/philosophy/comments/6q1i1e/game_theory_and_the_golden_rule/ https://www.reddit.com/r/philosophy/comments/6q1i1e/game_the...

udkl 9y ago

As a co-incidence, I just read this relevant article today - http://www.economist.com/news/economics-brief/21705308-fifth-our-series-seminal-economic-ideas-looks-nash-equilibrium-prison http://www.economist.com/news/economics-brief/21705308-fifth... Edit : to say - This site was a beautiful insightful experience.