Simulating the Evolution of Aggression - Lake Harding Association

Simulating the Evolution of Aggression

Simulating the Evolution of Aggression

By Micah Moen 100 Comments August 14, 2019


– [Justin] In this
video, we’re gonna start exploring conflict between creatures. To try to build some understanding here, we’re gonna use some
simulations and some ideas from a field of math called Game Theory. (light music) Okay, so in our simulation,
food will appear each day, and then blobs will appear
and go out to eat the food. We’ll use the same survival
and reproduction rules as in previous videos. Eating one piece of food lets a creature survive to the next day, and eating two pieces of
food allows a creature to both survive and reproduce. What’s different in this simulation though is that food will come in pairs. Each creature randomly picks
a pair of food to walk to, so it might get the pair all to itself and get to go home with two
food and then reproduce, or another creature might find
the pair at the same time. And when this happens, they
have to somehow figure out how to split things up. We’ll start out by having
only one possible strategy for creatures who run into each other. They’ll just share, each
taking a piece of food and going home to survive to the next day. And because this strategy is so nice, we’ll give it the name “dove.” All right, let’s let things run for a bit. (light music) All right, now let’s add a new strategy called the hawk strategy. Hawks are more aggressive. If a hawk meets a dove, the hawk will go for the same
piece of food as the dove, eat half of it, and then quickly eat the other piece of food,
taking it for itself. This half food does
complicate our survival and reproduction rules a little bit. So in this situation, a dove
ends the day with half a food, so it’ll have a 50% chance
of surviving to the next day, and the hawk ends its day
with one-and-a-half food, so it’ll survive for sure, and also have a 50% chance of reproducing. So it looks good to be a
hawk, but it’s also risky. If two hawks meet, they’ll fight, and fighting is taxing. At the very least, they
use a lot of energy, and they might also get injured. So, when hawks fight, each
one gets a piece of food, but they spend so much energy fighting that they use up all the
benefit of the food right away and effectively go home with zero food, meaning they won’t survive. So, now let’s try adding a hawk
creature to our simulation, and see what happens. Now is a good time to pause and predict what you think will happen. (light music) All right, it looks like we have a mixture that fluctuates roughly
around half and half. And, there are also
fewer creatures overall, even with the same amount of food. Here’s an example of how natural selection doesn’t necessarily act for
the good of the species. And, to cover our bases, let’s
try starting with all hawks. (light music) Okay, not too surprisingly, they’re tearing each other apart, and their max population
size didn’t even reach half of the population size of the doves. Now, if we add a dove to
the mix in the next day, what do you think will happen? Okay, so it took the doves a little while to gain a foothold here, but eventually we end up
in a similar situation, with a fluctuating mixture
of hawks and doves. So why do we care? Well, this is a situation
where survival of the fittest doesn’t help us understand
what’s going on. There isn’t one fittest strategy. We can get a better sense for why this is by translating our conflict
rules from before into a table. If two doves face each other,
they’ll each get one food. If a dove faces a hawk,
the dove gets half a food, and the hawk gets one and a
half or three-halves food. And if we reverse perspectives,
if a hawk faces a dove, they’ll get three halves and one half. And when a hawk faces another hawk, they’ll each end up with zero after they waste a lot of that
energy fighting each other. Now that we have this
table, let’s imagine blobs that can choose which
strategy they want to play. Say I control the blob on top, and you control the blob on the left. Say you know that I’m going
to play a hawk strategy, which of course I am, what should you do? Well, you’re better off just backing down and taking your half food. That might be annoying since it feels like I’m winning somehow, and you might be tempted to
challenge me and also play hawk to teach me that I can’t
just push you around. This could make sense if we
were gonna play this game against each other over and over again, as two humans might do, and that is something we’ll
talk about in future videos. But, in this situation, we’re just these simple blobs
with no social structure, interacting once, and even if
we do see each other again, we won’t remember it. So, all that matters is how much food we take home right now. And if you want to maximize
your chances of surviving and reproducing, you’ll play dove. Discretion is the better
part of valor here. Let’s record this by drawing an arrow. If we’re in the right-hand
column because I’m playing hawk, the situation in the upper-right square is the best you can do. Okay, in the other case
where I’m not so mean, you know that I’m going
to play the dove strategy. In this case, you’ll
do better playing hawk. And here again, because
you’re a very smart human, you might be tempted to
think about the future, and want to reward me for playing nice and play dove yourself, but we’re just these really
simple blob creatures who might never see each other again. So, if you want to maximize
your chance of reproducing, you’ll play hawk. And, we can record this
with another arrow. So now, to complete this table, we can reverse perspectives
and think about what I should do in response to you, which I won’t go through in
detail, it’s the same reasoning. But, we’d get similar
arrows in the rows here. These arrows all point to
more advantageous strategies, and the interesting thing to notice is that there are two stable situations: either you play hawk and I play dove, or you play dove and I play hawk. If we’re in one of those two situations, either one of us would be worse off if we pick a different strategy. And by the way, this
way of analyzing choices is called Game Theory, which is a whole field of math. In a situation where nobody benefits from changing their strategy, it’s called a Nash Equilibrium,
named after John Nash, who some would say had a beautiful mind. So, the best strategy isn’t hawk or dove. It’s to do the opposite of
what your opponent is doing. When there are a lot of doves,
it’s better to be a hawk, and when there are a lot of
hawks, it’s better to be a dove. There’s some equilibrium fraction of doves that the population is
always pulled toward. Great, so we have the main
conceptual point down, but we can deepen our understanding by calculating what that
equilibrium fraction should be. The population will be an equilibrium if doves and hawks have the same expected average score in a contest. Right? Equilibrium is when, on average, we don’t expect a change
one way or the other, so we can’t have one
strategy doing better. They’re equal. Our goal is to find the fraction of doves that makes this condition true. On our way there, let’s first calculate the expected average score for a dove in a hypothetical example. Say, where the rest of the
population is 90% doves. So let’s see, a dove
will have a 90% chance of facing another dove, in which case it gets the dove versus dove payoff of one food. And a dove also has a 10%
chance of facing a hawk, right? That’s just the rest of the creatures. In which case it only gets a half a food. So overall, when a dove
runs into another creature, when the rest of the
population is 90% doves, it’ll come away with 0.95 food on average. This number is pretty
meaningless on its own. But, once we calculate
the expected hawk score, we can compare the two to see whether the equilibrium condition is met. So let’s do that; let’s find
the expected hawk score. It could be good to pause
and try to do this yourself to make sure it all makes sense. Maybe even rewinding to
watch the dove part again. Okay, just like before, the rest of the population is 90% doves, and against a dove, a
hawk gets one-and-a-half or three-halves pieces of food. And again, there’s a 10% chance of running into another hawk, in which case our hawk
goes home with zero food. And this comes out to
1.35 food on average. Now, notice that 1.35 is more than 0.95. So at 90% doves, hawks will do better, and we’d expect the fraction
of hawks to increase in the next generation. So, it’s not equilibrium. Not 90%. Now to find out what fraction of doves does meet the equilibrium condition, we can write the fractions
of doves and hawks as variables instead of just
guessing at specific numbers. And you might be saying right now, “Wow, that’s a lot of letters,” which is a fair point,
but we’re almost there, and our next step is actually to get rid of one of those letters. So, there’s a nice treat already. Doves and hawks make up all the creatures, so their fractions have to add up to one. And, this means we can replace the small h with one minus small d. And now, the expected dove and hawk scores are both written as
functions of one variable. And the same variable. So, we can graph them
on top of each other. The expected scores are equal
when the graphed lines cross. And, indeed, the equilibrium
condition is met at 50% doves. And, if we run a simulation with way more creatures than before, unfortunately too many to animate, the randomness smooths out a bit, and we can see that
the prediction is true. Okay, so, it might feel like
that was kind of a lot of work just to verify what we already thought. But, the fraction of doves isn’t always going to be one half. It depends on the numbers
in our payoff grid. The most interesting
number to play with here is the hawk-versus-hawk payoff. So far, we’ve been saying that the hawks each get one piece of food, but waste all the energy
of the food on fighting. But, what if instead, they only waste most of the energy, not all of it, and go home with a score of 1/4th? Plugging that in, we see the population move toward 1/3rd doves. And again, we can see this
borne out in the simulation. At this point, congratulations, we have a pretty detailed understanding of how populations of
hawks and doves work. And as basic as this model is, with only two simple strategies, it’s a powerful starting point for analyzing behavior in the real world. And, before we go, I want
to give you some teasers for how we’ll build on this to get closer to reality in future videos. First, creatures in the real world can play more than one strategy. So instead of having their behavior completely determined by a single gene, our creatures could have several genes affecting their behavior, causing them to have different chances of playing hawk or dove. And the Game Theory term for
this is mixed strategies. There can also be more
complex, conditional strategies that act differently
depending who they’re facing. For example, there could be a strategy that fights with hawks,
but is nice to doves. And, there could also be a strategy that tries to threaten a fight, but runs away if things get serious. And, seeing what happens with
these kinds of strategies can help us understand why some animals put on threatening displays
while rarely actually fighting, or have somewhat ritualistic fights that usually don’t harm anyone. Next, most conflicts
are actually asymmetric. So far, we’ve been
assuming that everyone has the same amount to gain and lose, and that all the creatures
are on equal footing. But when this changes, we can
start to understand things like territorial behavior
and dominance hierarchies. And last, let’s go back to our equations and see what happens as the hawk payout gets less and less bad. Say, getting to three fourths. Now the graphed lines don’t cross at all. There’s no equilibrium. At this point, even if you
know you’re facing a hawk, the three-fourths food
you get from fighting is better than the one-half
you get from being nice. So these arrows should actually flip, and, it only ever makes
sense to play hawk. We end up in this tragic situation where everyone’s fighting all the time, even though they would do better if they could just cooperate. This kind of situation has a special name. It’s called the prisoner’s dilemma. It can feel kind of grim,
but there are ways out of it, which we’ll talk about in future videos. And, I’ll see you then. Okay, so now I have some people to thank. First, thanks to you
for watching to the end. Second, thanks to everyone who’s
become a patron on Patreon. Your support is what makes me feel like people actually get
value from these videos, and gives me the confidence
that they’ll be funded into the future. Third, I want to thank
the channel 3Blue1Brown, who shared the last video and really gave this channel a kick. If you like this channel, you really should go
check out 3Blue1Brown. And finally, this video was
supported in part by Brilliant. If you like how I treat biology
as a quantitative subject and want more like it, then I really think you might like Brilliant’s computational biology course. In it, you learn things
like how to analyze genetic information, map ancestry, and predict the structure of proteins. Videos are a great way to
get excited about a topic, but to really learn deeply, you have to engage in
active problem solving. And, that’s what’s so
great about Brilliant. Their courses are built
around answering questions. And some of the exercises
even have you run code, like this script that
analyzes protein folds. Super cool. If you’d like to give Brilliant a try, you can go to brilliant.org/Primer, link in the description, to let them know you came from here. And the first 200 people to use that link get 20% off the annual
premium subscription. Check it out.

100 Comments found

User

Hugo A. Nava

If you come from 2025 (thanks to youtube recomendations) say hi

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User

Pumpkin Spice Bleach

but that's just a theory, a game theory

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User

susan olson

no

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User

Rygom

Reccomended to me?
Why was fasting taken out of our diet and made us believe we needed food every day?

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User

Jorah Mormont

Poker in a nutshell

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User

Esaelp Em llik

Is no one gonna talk about GAME THEORYYYY

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User

Benjamin Branch

what does he simulate on

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User

Chearth

plumpy bois

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User

Artemirr

Makes me wonder about the sly methods of those Italian men. surprised no one talks about it, but Italian men, will seduce/charm, women to go to dinner with them at a fancy restaurant, rack up a bill and then deke out on the foreign visiting women while pretending to go to the bathroom. lol. So would hten one state Italians like in ww2 are jsut teh same manipulators as before? Or gene sect where there is a strong desire? hmm..

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User

Death Merchant

Not impressed or interested

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User

M Tarık

I dont understand the subject very well but the blobs are cute so im gonna watch all the videos of this channel

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User

jannik joubert

Nature doesn't work like this, it doesn't have constants.

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User

《《Hobi Snickerss》》

Math? No im good

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User

Gabe Trap

But that's just a theory, A Game theory.

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User

Cahyo Amiseso

Because, for a dominant (hawk) to survive, it surely needs a submissive (dove).

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User

AlexForSale

Subbed. These simulations obviously aren’t a 1:1 comparison of reality and it’s complex natural processes, but it’s interesting and insightful in its own way.

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User

random smchuck is random

Game theory???????

INTRO INTENSIFIES

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User

Jikook Harling

So basically, when there are Doves, the Hawks do better than the Doves.

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User

Nephty

The time when a dove got added to a hawk population really got me mind blowned

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User

Cabbij

You should add jugdement to the creatures, so they interract accordingly in terms of their colour/actions

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User

xemsisx

you forgot that i will kill you, or rob you. then you will play deadbird.

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User

keso

Be back in 5 years

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User

xemsisx

don't listen to him kids, don't fight evil ppl better run, you will get yourself injured or killed. if you fight back that's the best thrill that you can have, only fight if you know you can win

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User

Dominic

I wanna know how you simulate this. do you use Processing? or do you use something else? please do a tutorial, I wanna try my own simulation too. 🙂

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User

animestop95

Just subscribed. I love this video, and I'm about to watch the Simulating Natural Selection video.

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FZone96

I bet this is in my recommendations because I subscribed to The Game Theorists, and YouTube's algorythm doesn't know the difference between MatPat's "(Video) Game Theory" and the evolution of aggression known as "(Survival) Game Theory."

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User

Larry

Why didn't you have the blobs that fight destroy the other blob and hence get more food. That's why they fight 😅

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User

Mernerner

yay mutual aid and tit for tat

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User

Solid Sauce

I came here expecting an AI video and came away with some more knowledge, strange how the internet is..

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User

the letter k

yeah me tooo

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User

Tobaz _Sketches

But hey, that’s just a theory
A 6:59!

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User

thunderborn 32

the problem with these 'simulations' is they only ever take the 'math' into account noone would EVER think its
'logic' to give themselves a 50% survival chance because someone stole half their food instead of trying to get it back because you know you fucking die

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User

E

Your pronunciation of hawk sounds funny xD

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User

bdcopp

Not sure the calculation is correct. You are assuming that the probability of meeting a dove is equal to their proportion within the population. This isn't true. It is equal to the remaining proportion after the current blob is accounted for.

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User

David Knaack

I'd like to see one where when there is a conflict over resources nearby creatures will join the fight.

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User

JOAO BOT

Next video: Simulating the USA

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User

Olejnik

Wow, your yt channel looks interesting I will stick for a while

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User

Silkwesir

8:25

your calculation completely misses the availability of food versus the number of blobs, or in other words, it doesn't account for the cases where they meet no one, and so will get 2 food regardless of whether they're hawks or doves.

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User

Hot Plan of Action

This is a really complicated way of saying "Don't bother wasting your energy being a jerk back to someone being a jerk to you. It's literally not worth it."

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User

thot creations

Most political activism parties suffer from the prisoners dilemma… And never actually evolve to hawks… Its like they just become doves with talons and reduce the doves… Tldr: hawks always win… Yet doves never can become hawks themselves…

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User

Jeb _

This world is dead we are all assholes

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User

peppa! what are u doing in my pfp!?!??

why did i click this and what type of crack did the comment section snort?

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User

Ry Richards

6:59 but that’s just a theory…

A game theory

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User

Hypo Dryo

when i realised i was in math class:

how dare he make me enjoy a nightmare!?

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Håvard Eriksen

9:47

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User

Jeraboa JumpingMouse

but that's just a theory… a game theory!

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User

Christopher Villarreal

looks like population control to me lol we need HAWKS

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User

DragoonKain3

Wouldn't Hawk vs Hawk be more like certain death for one blob, and maybe 50% of reproducing but 50% of dying due to injuries for the other? The victor goes the spoils, so there MUST be some reward for which hawk won the two pieces of food.

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User

Feza Gaming

I don't understand it but it looks cool

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User

drak d

Wow so rich in what im searching for, thank you, I needed that,
I believe we need more of these findings to help humanity, this subject is crucial for our well-being and even maybe our survival, and is a true mercy for our souls and existence
these matters of resources sharing/not, encouragement/discouragement and camaraderie/rivalry is extremely critical for the coexisting creatures, this psychological inference is THE ONLY THING "along with act of kindness (dove)" that'll help us live a better and happier life, its more critical than any sorts of technological advancement, although technology advancement, matters of livelihood and well-being is what we do, yet we face such absurd psychology of beings that infiltrate our maters and affairs and thrive on degenerating our society, for that reason, this indeed what comes first before elaborating in any social matters and affairs and before any sorts of relationship, this, must, be, established, and this inferences thank God is the only thing along with "Dove-ness" that'll execute and take care of that for us, so that we can rejoice in whats really important to us and what we like, love and do.
I believe that, that along with fear and lust, are the only things that is inhibiting us from our full potentials. so lets get rid of that… or make use of it where its useful 🤷‍♂️ therefore executing those issues and moving forward with true happiness, joyfulness, liveliness and true content, fulfillment and recognition. (∞)

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User

Nikita Chumachenko

This is the luckiest random recommendation from YouTube ever. Thanks dude, I loved this video

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User

Killian Harle

"Yo can you pass me some food"
No thanks, im not a commie

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Alexis Chaperon

Nooooooo it ended !

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User

Le Cobra

Accurate simulation of Capitalism.

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User

Rannos22

The chart when you can choose has major prisoners dilemma vibes

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Ghostie

I might get ridiculed for this, but I was only able to complete year 8(The first year in highschool back when i went) and it shows that there's parts of society I never got to learn about. little really interesting educational videos like these really make me feel like a smarter, more indepth person and I have to thank you for that.I know a lot of information, most self taught even while I was attending school, but these help more than you can imagine. it may sound small, but don't stop the amazing work this channel does ^~^

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User

Unknown Division

Bruh I learned some math without realizing it

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User

Weston Paschall

I think the hawks will take half the population and stay at tgat

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User

Layerty

What did I stumble upon in this cursed land

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User

Papi Harpy

I've never been so interested in something my entire life

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User

W0ngnim

3:43
"Now if we add a Dove to the mix, what do you think will happen?"
Dove meets Hawk on it's first day, only gets half food, then dies.
"uhh, let's try that again…"

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User

Mr. Accurate

Uhhh, thanks Youtube recommendations!

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User

Crazyswag 21

Primer: Now we add a new variable, POPULATION CONTROL.

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Gijs Meulen

Now what if hawks would only be agressive to dove's and share when together?

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Ofedia

I really like how you tied everything together and how you explained it. Great video!

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kevin caicedo

i love your content :3 greetingd from Colombia!

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User

Culted

when he said "pause"
a fucking amber alert when off

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Gunslinger

This video raised my IQ to 72, which is 72 higher than my original IQ.

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User

Plasma100

Idea: Age
A blob will die after 20 days

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User

Konrad Leyk

What the fuck am I watching

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User

Raf galvão

That's the why someone have to do anal

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User

isaac

Watching this so YouTube algorithm chills out

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User

Jonathan Mafi

the "good" of the species. And what is good?

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T. Mitchell

10:45 caught my eye. The graph looks like an underdamped response to a step input.

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login scooter

I dont understand a single thing of this

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KnucklesWTD

This is how humanity exists. I wonder what cycle are we on

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devon marcus

The stated R.O.E. seem set to support a desired outcome.

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Mixinnitup

Thing is a society purely made of doves seem to do much better than a society full of hawks. Hawks can only really thrive in a world with doves

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User

Maple Foox

She's such a snake- I mean hawk.

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User

Caleb Friesen

hi future me

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User

Planet Gamer

Lesson Learned: Peace is better than war.

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Boomblox5896

I actually play this roulette game in a Discord server where you claim characters from various TV shows and games, but once a certain character is claimed, then nobody else can have that character unless they trade or gift it to somebody else.

This model might just help me understand strategies in this game because I've gained valuable allies that help me get the characters I want in return for being nice and helping them, but there are aggressive players who like to steal characters I want for their own enjoyment, which leaves me at a disadvantage, and if they're feeling nice, might bargain with me, but I must sacrifice a valuable character from my collection to appease them and get what I want.

This model sort of illustrates those two play styles, although maybe not in-depth.

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User

R

It's only advantageous to be a hawk, when the other is a dove, when one is self-centered. If one is most concerned with the well-being of the population as a whole, then it is most advantageous for everyone to be a dove.

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User

Davis the memer man

And they say video games make us mad

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User

Simonmonkey z

Who are u?! u just popped up in my feed. i like ur vid very much!

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Zimmermann Márk

I also want to have a same group blub change strategy against another group and a running average of changing strategy ( if wellfare goes good then more dove)

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Cat Chris

Maybe you could explore the interaction and relationship between carnivores and herbivores in the next video, since every creature we've seen so far that eats something appears to behave like herbivores, eating food provided by the environment itself, while nature tends to have many carnivorous creatures that hunt for prey as well as many herbivores.

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User

Daniel kim

I learned this in life science class and its really cool how the simulation perfectly simulates what happens in actual nature

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AnyShape

The first thing I thought when I saw you were trying to say playing the Hog is a bad strategy over time was that the Hog could eat both of the pieces and normally that's what happens in real life with the humankind. Other creatures are smart enough to eat half of the food and give their "enemy" a chance to survive for the egoistic purpose of surviving in an easier environment themselves. Other than that a great video! I love the concept. It may help some of us change their way of thinking because visual representation is a powerful tool.

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Creative- Name

Interesting stuff, thanks for making this video.

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User

Fulton Films

Survival of the fittest has been the rule of life since the first multicellular organism spawned.

This smells like some beta male shit.

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User

Guille Arana

Yesss new video 😀

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Operator 801

Good stuff.

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Mike Wu

Life explained in 14mins.

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RC 17g

All I can think of is how much these blobs are so cute .

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Bill Evans

Humanities student here, feel very grim about humanity's fate lately. At the very least I'll get an understanding of why things work the way they do. Keep up the brilliant work!

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User

One-Soul-a-Time

We don't bully by choice, it is natural. 🙂

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User

Nazz Akon

What is this

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User

ray Williams

This channel seems to have a Very bright future

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User

ROTO47

Ok yt, I finally watched it 🙄🙄🙄

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