Name: Simulating the Evolution of Aggression
Uploaded: 2025-11-19T01:57:59.000Z
Duration: 13 min 17 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

In this video, we're going to start exploring conflict between creatures to try to build some understanding.

Here, we're going to use some simulations and some ideas from a field of math called game theory.

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, but

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.

Alright, now let's add a new strategy called the hawk strategy.

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 then, 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, Sam.

Alright, 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.

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.

Well, this is a situation where survival of the fittest doesn't help us understand what's going on.

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 all 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.

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 going to play this game against each other over and over again, as true 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.

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

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.

And a situation where nobody benefits from changing their strategy is called a Nash equilibrium, named after John Nash, who some would say had a beautiful mind.

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 has 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 in equilibrium if doves and hawks have the same expected average score in a contest.

Equilibrium is when, on average, we don't expect to change one way or the other.

So we can't have one strategy doing better.

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 HOX score, we can compare the two to see whether the equilibrium condition is met.

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

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Simulating the Evolution of Aggression

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