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    "segs": [ {
      "utf8": "We're gonna use some simulations and some ideas from a field of math called \"game theory\"."
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    "segs": [ {
      "utf8": "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"
    } ]
  }, {
    "tStartMs": 20580,
    "dDurationMs": 3060,
    "segs": [ {
      "utf8": "same survival and reproduction rules as in previous videos."
    } ]
  }, {
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    "dDurationMs": 3440,
    "segs": [ {
      "utf8": "Eating one piece of food lets a creature survive to the next day, and"
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  }, {
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    "dDurationMs": 3649,
    "segs": [ {
      "utf8": "eating two pieces of food allows a creature to both survive and reproduce."
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  }, {
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    "dDurationMs": 3600,
    "segs": [ {
      "utf8": "What's different in this simulation though is that food will come in pairs."
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  }, {
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    "dDurationMs": 5940,
    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 42300,
    "dDurationMs": 6180,
    "segs": [ {
      "utf8": "food and then reproduce or another creature might find the pair at the same time. And when this happens they have to"
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  }, {
    "tStartMs": 48640,
    "dDurationMs": 2000,
    "segs": [ {
      "utf8": "somehow figure out how to split things up."
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  }, {
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    "segs": [ {
      "utf8": "We'll start out by having only one possible strategy for creatures who run into each other."
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  }, {
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    "dDurationMs": 4520,
    "segs": [ {
      "utf8": "They'll just share, each taking a piece of food and going home to survive to the next day"
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  }, {
    "tStartMs": 60550,
    "dDurationMs": 3139,
    "segs": [ {
      "utf8": "and because this strategy is so nice, we'll give it the name \"Dove\"."
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    "segs": [ {
      "utf8": "All right, let's let things run for a bit."
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    "segs": [ {
      "utf8": "Alright now let's add a new strategy called the \"Hawk\" strategy. Hawks are more aggressive"
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    "segs": [ {
      "utf8": "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"
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  }, {
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    "dDurationMs": 2279,
    "segs": [ {
      "utf8": "quickly, eat the other piece of food, taking it for itself."
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  }, {
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    "dDurationMs": 3679,
    "segs": [ {
      "utf8": "This half-food does complicate our survival and reproduction rules a little bit"
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  }, {
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    "segs": [ {
      "utf8": "so in this situation a dove ends the day with half of food"
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    "segs": [ {
      "utf8": "so it'll have a 50% chance of surviving to the next day and the hawk ends its day with 1 and 1/2 food"
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    "tStartMs": 114910,
    "dDurationMs": 3959,
    "segs": [ {
      "utf8": "so it'll survive for sure and also have a 50% chance of reproducing."
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    "segs": [ {
      "utf8": "So it looks good to be a hawk but it's also risky. If two hawks meet they'll fight and"
    } ]
  }, {
    "tStartMs": 124910,
    "dDurationMs": 5300,
    "segs": [ {
      "utf8": "fighting is taxing. At the very least they use a lot of energy and they might also get injured"
    } ]
  }, {
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    "dDurationMs": 2819,
    "segs": [ {
      "utf8": "so when hawks fight each one gets a piece of food"
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  }, {
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    "segs": [ {
      "utf8": "but they spend so much energy fighting that the use of all the benefit of the food right away and"
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  }, {
    "tStartMs": 137300,
    "dDurationMs": 2929,
    "segs": [ {
      "utf8": "effectively go home with zero food. Meaning they won't survive."
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  }, {
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    "segs": [ {
      "utf8": "So now let's try adding a hot creature to our simulation and see what happens."
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  }, {
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    "dDurationMs": 2869,
    "segs": [ {
      "utf8": "Now was a good time to pause and predict what you think will happen."
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    "segs": [ {
      "utf8": "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"
    } ]
  }, {
    "tStartMs": 197830,
    "dDurationMs": 5699,
    "segs": [ {
      "utf8": "of food. Here's an example of how natural selection doesn't necessarily act for the good of the species."
    } ]
  }, {
    "tStartMs": 204530,
    "dDurationMs": 2779,
    "segs": [ {
      "utf8": "And to cover our bases, let's try starting with all hawks."
    } ]
  }, {
    "tStartMs": 216379,
    "dDurationMs": 6830,
    "segs": [ {
      "utf8": "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."
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    "segs": [ {
      "utf8": "Now if we had a dove to the mix in the next day, what do you think will happen?"
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    "dDurationMs": 3199,
    "segs": [ {
      "utf8": "Okay, so it took the doves a little while to gain a foothold here"
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  }, {
    "tStartMs": 259959,
    "dDurationMs": 4650,
    "segs": [ {
      "utf8": "but eventually we end up in a similar situation with a fluctuating mixture of hawks and doves."
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    "segs": [ {
      "utf8": "So, why do we care? Well, this is a situation where survival of the fittest doesn't help us understand what's going on."
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    "segs": [ {
      "utf8": "There isn't one fittest strategy."
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    "segs": [ {
      "utf8": "We can get a better sense for why this is by translating our conflict rules from before into a table"
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    "segs": [ {
      "utf8": "If two doves face each other they'll each get one food"
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    "segs": [ {
      "utf8": "if a dove faces a hawk the dove gets 1/2 of food and the hawk gets one and a 1/2 or 3/2 food"
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    "segs": [ {
      "utf8": "and if we reverse perspectives, if hawk faces a dove"
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    "segs": [ {
      "utf8": "they'll get 3/2 and 1/2. And when a hawk faces another hawk"
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  }, {
    "tStartMs": 297760,
    "dDurationMs": 5360,
    "segs": [ {
      "utf8": "they'll each end up with zero after they waste all that energy fighting each other. Now that we have this table"
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    "segs": [ {
      "utf8": "let's imagine blobs that can choose which strategy they want to play"
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  }, {
    "tStartMs": 306440,
    "dDurationMs": 3649,
    "segs": [ {
      "utf8": "Say I control the blob on top and you control the blob on the left"
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  }, {
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    "segs": [ {
      "utf8": "Say you know that I'm going to play a hawk strategy which of course I am. What should you do?"
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    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 323410,
    "dDurationMs": 4049,
    "segs": [ {
      "utf8": "might be tempted to challenge me and also play Hawk to teach me that I can't just push you around"
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  }, {
    "tStartMs": 328430,
    "dDurationMs": 1520,
    "segs": [ {
      "utf8": "This could make sense"
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    "tStartMs": 329950,
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    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 335350,
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    "segs": [ {
      "utf8": "about in future videos, but in this situation"
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    "segs": [ {
      "utf8": "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"
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    "segs": [ {
      "utf8": "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"
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  }, {
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    "segs": [ {
      "utf8": "You'll play Duff"
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  }, {
    "tStartMs": 352310,
    "dDurationMs": 2000,
    "segs": [ {
      "utf8": "Discretion is the better part of valor here"
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  }, {
    "tStartMs": 354530,
    "dDurationMs": 2269,
    "segs": [ {
      "utf8": "let's record this by drawing an arrow."
    } ]
  }, {
    "tStartMs": 357050,
    "dDurationMs": 5210,
    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 363260,
    "dDurationMs": 2510,
    "segs": [ {
      "utf8": "Okay in the other case where I'm not so mean"
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  }, {
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    "segs": [ {
      "utf8": "You know that I'm going to play the dove strategy in this case, you'll do better playing hawk and"
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  }, {
    "tStartMs": 371540,
    "dDurationMs": 710,
    "segs": [ {
      "utf8": "here again"
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  }, {
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    "segs": [ {
      "utf8": "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"
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    "segs": [ {
      "utf8": "dove yourself, but we're just these really simple blob creatures who might never see each other again"
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    "tStartMs": 382690,
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    "segs": [ {
      "utf8": "So if you want to maximize your chance of reproducing you'll play hawk. And we can record this with another arrow"
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  }, {
    "tStartMs": 388970,
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    "segs": [ {
      "utf8": "So now to complete this table we can reverse perspectives and think about what I should do in response to you"
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  }, {
    "tStartMs": 393770,
    "dDurationMs": 1130,
    "segs": [ {
      "utf8": "-Which I won't go through in detail,"
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    "tStartMs": 394900,
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    "segs": [ {
      "utf8": "It's the same reasoning- but we get similar arrows in the rows here. These arrows all point to more advantageous"
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  }, {
    "tStartMs": 401780,
    "dDurationMs": 4429,
    "segs": [ {
      "utf8": "strategies and the interesting thing to notice is that there are two stable situations"
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  }, {
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    "segs": [ {
      "utf8": "Either you play hawk and I play dove or you play dove and I play hawk"
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  }, {
    "tStartMs": 410690,
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    "segs": [ {
      "utf8": "if we're in one of those two situations"
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  }, {
    "tStartMs": 412960,
    "dDurationMs": 2880,
    "segs": [ {
      "utf8": "Either one of us would be worse off if we pick a different strategy"
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  }, {
    "tStartMs": 415840,
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    "segs": [ {
      "utf8": "And by the way, this way of analyzing choices is called game theory, which is a whole field of math. In a situation"
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  }, {
    "tStartMs": 422680,
    "dDurationMs": 3059,
    "segs": [ {
      "utf8": "Where nobody benefits from changing their strategy is called a Nash equilibrium"
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    "segs": [ {
      "utf8": "Named after John Nash who some would say had a beautiful mind"
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    "segs": [ {
      "utf8": "So the best strategy isn't hawk or dove it's to do the opposite of what your opponent is doing"
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    "segs": [ {
      "utf8": "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"
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    "segs": [ {
      "utf8": "A dove there's some equilibrium fraction of doves that the population is always pulled toward"
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    "segs": [ {
      "utf8": "Great, so we have the main conceptual point down"
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    "segs": [ {
      "utf8": "But we can deepen our understanding by calculating what that equilibrium fraction should be"
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    "segs": [ {
      "utf8": "The population will be in equilibrium"
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    "dDurationMs": 4110,
    "segs": [ {
      "utf8": "If doves and hawks have the same expected average score in a contest."
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    "segs": [ {
      "utf8": "Right? 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."
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  }, {
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    "segs": [ {
      "utf8": "They're equal."
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    "segs": [ {
      "utf8": "Our goal is to find the fraction of doves that makes this condition true. On our way there"
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    "segs": [ {
      "utf8": "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"
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    "segs": [ {
      "utf8": "so, let's see a dove will have a"
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    "segs": [ {
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    "segs": [ {
      "utf8": "A dove also has a 10% chance of facing a hawk, right?"
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    "segs": [ {
      "utf8": "That's just the rest of the creatures in which case it only gets 1/2 of food"
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    "segs": [ {
      "utf8": "so overall when a dove runs into another creature when the rest of the population is 90 percent doves it'll come away with"
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    "segs": [ {
      "utf8": "0.95 food on average"
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    "segs": [ {
      "utf8": "This number is pretty meaningless on its own"
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    "segs": [ {
      "utf8": "But once we calculate the expected hawk score, we can compare the two to see whether the equilibrium condition is met"
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    "segs": [ {
      "utf8": "So let's do that. Let's find the expected hawk score"
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  }, {
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    "segs": [ {
      "utf8": "It could be good to pause and try to do this yourself to make sure it all makes sense"
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  }, {
    "tStartMs": 524199,
    "dDurationMs": 2450,
    "segs": [ {
      "utf8": "Maybe even rewinding to watch the tough part again"
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    "segs": [ {
      "utf8": "Okay, just like before the rest of the population is 90% doves and against a dove a hawk gets 1 and a 1/2 or 3/2"
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    "tStartMs": 534040,
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    "segs": [ {
      "utf8": "pieces of food. And again, there's a 10% chance of running into another hawk"
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    "segs": [ {
      "utf8": "In which case our hawk goes home with zero food. And this comes out to 1.35 food on average"
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    "dDurationMs": 4039,
    "segs": [ {
      "utf8": "Now notice that 1.35 is more than 0.95"
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    "segs": [ {
      "utf8": "So at 90% doves hawks will do better and we'd expect the fraction of hawks to increase in the next generation"
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    "segs": [ {
      "utf8": "So it's not equilibrium. Not ninety percent"
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    "segs": [ {
      "utf8": "Now to find out what fraction of doves DOES meet the equilibrium condition"
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    "segs": [ {
      "utf8": "We can write the fractions of doves and hawks as variables instead of just guess again specific numbers"
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    "segs": [ {
      "utf8": "And you might be saying right now,"
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  }, {
    "tStartMs": 571050,
    "dDurationMs": 2759,
    "segs": [ {
      "utf8": "\"Wow, that's a lot of letters,\" which is a fair point"
    } ]
  }, {
    "tStartMs": 573809,
    "dDurationMs": 5070,
    "segs": [ {
      "utf8": "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"
    } ]
  }, {
    "tStartMs": 579459,
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    "segs": [ {
      "utf8": "doves and hawks make up all the creatures so their fractions have to add up to one and"
    } ]
  }, {
    "tStartMs": 584170,
    "dDurationMs": 4010,
    "segs": [ {
      "utf8": "This means we can replace the small H with one minus small D"
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    "segs": [ {
      "utf8": "And now the expected dove and hawk scores are both written as functions of one variable-"
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    "segs": [ {
      "utf8": "And the same variable. So we can graph them on top of each other"
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    "segs": [ {
      "utf8": "The expected scores are equal when the graphed lines cross, and indeed the equilibrium condition is met at 50% doves"
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    "segs": [ {
      "utf8": "And if we run a simulation with way more creatures than before"
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  }, {
    "tStartMs": 608709,
    "dDurationMs": 5330,
    "segs": [ {
      "utf8": "unfortunately, too many to animate the randomness smooths out a bit and we can see that the prediction is true"
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    "tStartMs": 615339,
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    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 621059,
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    "segs": [ {
      "utf8": "doves isn't always going to be 1/2"
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  }, {
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    "segs": [ {
      "utf8": "It depends on the numbers in our payoff grid. The most interesting number to play with here is the hawk versus hawk payoff"
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    "segs": [ {
      "utf8": "So far we've been saying that the hawks each get one piece of food, but waste all the energy of the food"
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  }, {
    "tStartMs": 633839,
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    "segs": [ {
      "utf8": "on fighting. But what if instead they only waste most of energy, not all of it and go home with a score of 1/4"
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    "tStartMs": 640550,
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    "segs": [ {
      "utf8": "Plugging that in we see the population moved toward 1/3 doves"
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    "segs": [ {
      "utf8": "And again, we can see this born out in the simulation at this point, congratulations"
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  }, {
    "tStartMs": 648549,
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    "segs": [ {
      "utf8": "we have a pretty detailed understanding of how"
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    "tStartMs": 650660,
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    "segs": [ {
      "utf8": "populations of hawks and doves work. And as basic as this model is with only two simple strategies"
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    "tStartMs": 656290,
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    "segs": [ {
      "utf8": "it's a powerful starting point for analyzing behavior in the real world."
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    "segs": [ {
      "utf8": "And before we go"
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    "segs": [ {
      "utf8": "I want to give you some teasers for how we'll build on this to get closer to reality in future videos"
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  }, {
    "tStartMs": 665870,
    "dDurationMs": 3590,
    "segs": [ {
      "utf8": "First creatures in the real world can play more than one strategy"
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    "tStartMs": 669470,
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    "segs": [ {
      "utf8": "So instead of having their behavior completely determined by a single gene"
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    "tStartMs": 673180,
    "dDurationMs": 2460,
    "segs": [ {
      "utf8": "Our creatures could have several genes affecting their behavior"
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  }, {
    "tStartMs": 675980,
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    "segs": [ {
      "utf8": "Causing them to have different chances of playing hawk or dove. And the game theory term for this is mixed strategies"
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  }, {
    "tStartMs": 681710,
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    "segs": [ {
      "utf8": "There can also be more complex conditional strategies that act differently depending who they're facing"
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  }, {
    "tStartMs": 686870,
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    "segs": [ {
      "utf8": "for example"
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  }, {
    "tStartMs": 687730,
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    "segs": [ {
      "utf8": "there could be a strategy that fights with hawks but is nice to doves"
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  }, {
    "tStartMs": 691700,
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    "segs": [ {
      "utf8": "And there could also be a strategy that tries to threaten a fight but runs away if things get serious"
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  }, {
    "tStartMs": 696980,
    "dDurationMs": 7100,
    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 704080,
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    "segs": [ {
      "utf8": "Somewhat ritualistic fights that usually don't harm anyone"
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  }, {
    "tStartMs": 707870,
    "dDurationMs": 2659,
    "segs": [ {
      "utf8": "Next, most conflicts are actually asymmetric"
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  }, {
    "tStartMs": 710870,
    "dDurationMs": 5599,
    "segs": [ {
      "utf8": "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"
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  }, {
    "tStartMs": 716600,
    "dDurationMs": 5179,
    "segs": [ {
      "utf8": "but when this changes we can start to understand things like territorial behavior and dominance hierarchies"
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  }, {
    "tStartMs": 722480,
    "dDurationMs": 7010,
    "segs": [ {
      "utf8": "And last, let's go back to our equations and see what happens as the hawk payoff gets less and less bad say getting to three-fourths"
    } ]
  }, {
    "tStartMs": 729890,
    "dDurationMs": 2000,
    "segs": [ {
      "utf8": "Now the graph lines don't cross at all"
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  }, {
    "tStartMs": 732040,
    "dDurationMs": 3090,
    "segs": [ {
      "utf8": "There's no equilibrium. At this point even if you know"
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  }, {
    "tStartMs": 735130,
    "dDurationMs": 5130,
    "segs": [ {
      "utf8": "you're facing a hawk the 3/4 food you get from fighting is better than the 1/2 you get from being nice"
    } ]
  }, {
    "tStartMs": 740260,
    "dDurationMs": 3750,
    "segs": [ {
      "utf8": "So these arrows should actually flip and it only ever makes sense to play hawk"
    } ]
  }, {
    "tStartMs": 744080,
    "dDurationMs": 5809,
    "segs": [ {
      "utf8": "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"
    } ]
  }, {
    "tStartMs": 750440,
    "dDurationMs": 3739,
    "segs": [ {
      "utf8": "This kind of situation has a special name. It's called the prisoner's dilemma"
    } ]
  }, {
    "tStartMs": 754459,
    "dDurationMs": 4280,
    "segs": [ {
      "utf8": "It can feel kind of grim, but there are ways out of it, which we'll talk about in future videos"
    } ]
  }, {
    "tStartMs": 759520,
    "dDurationMs": 2000,
    "segs": [ {
      "utf8": "And I'll see you then"
    } ]
  }, {
    "tStartMs": 762300,
    "dDurationMs": 4649,
    "segs": [ {
      "utf8": "Okay, so now I have some people to thank first thanks to you for watching to the end"
    } ]
  }, {
    "tStartMs": 767740,
    "dDurationMs": 6470,
    "segs": [ {
      "utf8": "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"
    } ]
  }, {
    "tStartMs": 774210,
    "dDurationMs": 3479,
    "segs": [ {
      "utf8": "And gives me the confidence that would be funded into the future."
    } ]
  }, {
    "tStartMs": 777690,
    "dDurationMs": 5280,
    "segs": [ {
      "utf8": "Third, I want to thank the channel 3Blue1Brown who shared the last video and really gave this channel a kick. If you like"
    } ]
  }, {
    "tStartMs": 782970,
    "dDurationMs": 2880,
    "segs": [ {
      "utf8": "this channel you really should go check out 3Blue1Brown."
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  } ]
}