Simulating the Evolution of Aggression

– [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

100 thoughts on “Simulating the Evolution of Aggression”

Woa noice

Math

• Manik Sahdev Post author

I'm greeting my 6 year older self to future

• Milan Stupljanin Post author

So the whole simulations is based on random idea that "One food – Survive; Two food – Reproduce"

• ImaTreeNut Post author

Hello 19yr old boy I hope you got into a college and is till watching YouTube bc this will be recommend again soon in 6 years

very nice

• bakersmileyface Post author

Always play hawk. If you encounter another hawk, just make sure you have bigger claws.

• drugi ce Post author

Me:Doves?! Potato? Wth…

• Raikkonen 311 Post author

Shake And Take.

• what ever Post author

interesting. in real life however, it's far more complex & diverse. their are still, undoubtedly, unknown variables at play. I suspect humans aren't allowed to comprehend the whole picture. doves & hawks have a much better chance

• Rickard T Post author

This is also called ESS (Evolutionary Stable Strategy) in biology if you're interested in reading up more about it from a biological perspective rather than a mathematical one.

• yassine werdani Post author

First time i watched this stuff and i dunno how i got here but this is very intrestin

• Bulbasaur Brutal Post author

>When the final video will end up analyzing world Jewry, boiling down their global domination to their genetic biological behavior and survival strategy xD

• Ze Master Post author

How do you make your videos?

• The Cabbage Post author

This randomly showed up in my recommendations and I am glad that I watched it.

• Mr.Apriza Yutama Post author

We must share

• Agus Post author

Wish I could share my things and both get 3/4. I would not feel a prisoner at all.

Balance

• Rockerguy96 Post author

First time that the recommended section ACTUALLY has something good in it for me

• pilover314159 Post author

Very thought provoking

• Weather Isawesome Post author

Wow 508,784 subscribers already! Keep replying how many subscribers there are now.

• bakago Post author

now i wanna hug these blobs

• 1000 subs without any viedos Post author

Primer: called "Game Theory"

Me: BUT HEYYYY…
My Friend: shut up

• ava horie Post author

god wants me to watch this

• Logikael Impakt Senzory Overload Post author

My phone heard me discussing practical application of game theory with an associate.. this shows up in my youtube feed fifteen minutes later lol.

• M├бt├й P├бsztor Post author

Someone needs to make a game of this where you can just add variables and traits and see how it plays out.

BEANOS

• Atthetta Post author

Stupid hypothesis and conclusion — two hawks fighting = 1 wins and gets all the food
Whoever presented this video has not included survival of the fittest

• the master yeeter Post author

It was peaceful and then video games were created

• Galactic Bird Post author

But it's just a theory a "Game Theory"

• Joseph de Vismes Post author

nerd:this is so cool me: uh

• Cirrus H Post author

So. In essence if the entire field is hawks eventually all hawks would die because every hawk will exhaust itself getting said resources.

• Bagel monster 123 Post author

THERE SO CUTE

• A Random Passerby Post author

See, what I don't agree with is the part of the equation presented where two "hawks" fighting each other have a 0% chance of survival. I'm curious what the numbers how much the numbers would be affected, if any, if they each one had a 25% chance of living.

• MUH Geschichte Post author

how about introducing in group preference?

• Puissant Powernapper Post author

This sounds 1:1 like what Richard Dawkins talks about in his book "the selfish gene", or rather some of the sources he was referring to.

• *Starling * Post author

Rhino = Warrior Unicorn

• Anthony Smith Post author

But that's just a theory,

a game theory.

• Corbin Bernier Post author

And that's just a theory, a "Game Theory". Thanks for watching.

• duy anh hoang Post author

this series is slowly spiraling into a video that says nothing matters and our life is just a meaningless illusion.

Dove gang

• GeographicCreator Post author

god wants to know your location

• Audrey G Post author

BUT THATS JUST A THEORY

• Captain Gurdy Post author

Wonderful except for the hawk vs hawk where both die, doesn't make much sense.

• Mr. Blue Post author

Red boy be angry

• Eric Fleet Post author

I predicted a 2/3 hawk ratio. In a 2/3 ratio, 4 times out of 9, two hawks would meet and the hawks will both die. 1 out of 9, two doves would meet, again no hawks. In 4 out of 9 a hawk and a dove would meet producing 1.5 hawks or 6 hawks out of these encounters. A grand total of 9 encounters producing 6 hawks, equaling the original 2/3 ratio. I was surprised to see that the simulation didn't meet this ratio.

• Your Daily Grapes Post author

I dare you to subscribe to me!

• eis thefifthletter Post author

I like how all the blue Doves are on the left and the red Hawks on the right.

• Mista_Fur Post author

I'd play the human, kill everything and live like a king all alone for eternity.

• Alex Schmidt Post author

Alright fine there, i finally clicked on it.

• Imma Box Post author

nah its clearly from videogames

• EXPLORATORY MINDS PROJECT Post author

this is fascinating

• TheShaggyGamer Post author

The one issue I find with these calculations is the lack of taking into account randomicity and not just best-case outcome of each pairing with the best-case scenario.

• TimeTraveler Post author

around 7 minute you say, its smart to do the opposite strategy of what the other is doing, but this is just plain stupid, if the other is a dove and i pick to be a dove too, we can build a great community or a greater society as you just said earlier when everyone is a dove we had more population, your logic only makes sense when you think 100% egoistic and if you would have the slightest bit of wisdom you would see the choice between being a hawk or a dove is just about what kind of world do you want to live in, do you want to live in a peacefull world or in an old testament like world, an eye for an eye, where you treat aggression with aggression.

Also, im sad to say this as you put quite a bit of work into this, but this video has no connection to reality because in reality there is more than enough food and more than enough of anything to get everyone in a comfortable situation, just our "glorious" capitalism is preventing a fair distribution of resources of any kind, regarding food its very easy to find out, there are plenty of example where for example the USA had destroyed tonnes of wheat and corn to keep the price stable and at the same time we still had ten of thousands people dying from starvation daily!

How can there be billionaires while 1/3 of the population is suffering from poverty. This is insane.

• PERPLEXUSZ Post author

But's thats just a theory an AIM THEORY, THANKS FOR WATCHING

• Kinnik Kinnick Post author

Dear god (natural selection? ЁЯШЙ this series is addictive.. Someone give this person a feature length documentary series! I could seriously watch these for hours.. First YT channel I've ever clicked the bell for. Make more soon! I'm Jonesing!!!

• KINGWOLF Post author

my brain hurts

• Justin Greene Post author

Explains my sex life….

• EnraEnerato Post author

Nice, but there is another thing that is an important strategie, social behavoir.
When a blob meets a blob, that it has encountered before, it might remember it's the previous choices (say 0.75 chance, more when it encouters the blob more times) and it would react by changing it's style to get the best result out of it. In theory after enough encounters they should play nice with each other. Things get even more complicated when the blobs can negotiate each other and or make use of deception.
I believe if someone could craft a modell like that they might see the result which is eriely similiar to us humans.

• bastardtubeuser Post author

If you look at the real life simulation, it goes from dark to light, with light being at the top. all around the world. a savage dark majority and the light minority of virtue.

• Claude Armstrong Post author

Attempting to synthesize creation is useless, since it never adds the single most influential factor; Creator. This is the reason evolution theory never can stand on its own merits, if there can be found any merit in it at all.

• Sim Won Post author

All blobs become breatharians
Problem solved

• this boi Post author

I just wanna take a second and remind y'all that you're watching a video about blobs

And want to watch more

• Mystery Monk Post author

Try hawk/dove hybrid.

• Darth Biomech Post author

So, how are you actually making these sims? You write each of them from scratch, or is there a program of some kind that lets you do that?

Of course, judging that there are 6500 comments, I feel like whispering at a rock concert…

• Emre Can Sa─Яl─▒k Post author

Did you just call me "Blob"? for instant aggression

• Grammar Police Post author

I just saw two blobs and clicked, I didnтАЩt even look at the title until I was 10 seconds into the video.

• killerrabbit gaming Post author

I clicked this and was gonna click off till I heard game theory

• Names Last Post author

Check out Nicky Case's website!

• D C D Post author

There is one seriously wrong thing about this, you added one dove to the hawk filled test, now IтАЩm no sex expert but how the fuck did that dove procreate? Unless we are talking about a baby Jesus dove

• Wurminator Post author

Dove's of the world unite!
You have nothing to lose but the risk of losing half of your food, you have one food to win!

• DRTosh Post author

/pol would love this

• ccrawfissh last name Post author

One food you will survive two food you will replicate imagine two slices of pizza and then a clone appears

• Shane McIntosh Post author

Why am I watching this for fun lmao it feels like school… but I'm so engaged anyway

• Connor Is My Waifu Post author

I'm dying by the cuteness of these avocado blob things

• WeeWDiedrich Post author

fine ill watch

• Hugo A. Nava Post author

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

• Pumpkin Spice Bleach Post author

but that's just a theory, a game theory

no

• Rygom Post author

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

• Jorah Mormont Post author

Poker in a nutshell

• Esaelp Em llik Post author

Is no one gonna talk about GAME THEORYYYY

• Benjamin Branch Post author

what does he simulate on

plumpy bois

• Artemirr Post author

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..

• Death Merchant Post author

Not impressed or interested

• M Tar─▒k Post author

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

• jannik joubert Post author

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

• J hope Is mine Post author

Math? No im good

• Gabe Trap Post author

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

• Cahyo Amiseso Post author

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

• AlexForSale Post author

Subbed. These simulations obviously arenтАЩt a 1:1 comparison of reality and itтАЩs complex natural processes, but itтАЩs interesting and insightful in its own way.

• random smchuck is random Post author

Game theory???????

INTRO INTENSIFIES

• Jikook Harling Post author

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

• Nephty Post author

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

• Cabbij Post author

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

• xemsisx Post author

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

• keso Post author

Be back in 5 years

• xemsisx Post author

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