How math brought revolution to evolution : Evolutionary Game Theory (Eng Sub) #SoME3

This video is about how math revolutionized biology.
It is about Evolutionary game theory. You can call it introduction to evolutionary game theory.
And I am building the famous Hawk Dove Retaliator Game from complete scratch.
It includes fundamentals of game theory and theory of evolution.

It is the first part of my plan and just minimum fundamental for following theoretical biology and population genetics videos.
It happened to be a Summer of Math Exposition 3 submission since it is an amazing event!

00:00 Intro
00:48 Game Theory
13:04 Theory of EvolutIon
16:04 Evolutionary Game Theory
21:37 Replicator Dynamics
37:45 HDR Game

#evolutionarybiology
#populationgenetics
#gametheory
#some3
#3blue1brown

Resources:
Game Theory and Evolutionary Dynamics by JK Choi
The Selfish Gene by Richard Dawkins
Mathematical Models of Social Evolution by Richard McElreath, Robert Boyd
Adaptation and Natural Selection by George C. Williams
The Evolution of Cooperation by Robert Axelrod

Patreon and buymeacoffee link can be found on my channel ABOUT page :)
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[mikip]

The topic choosen: 10/10
The animations: 9/10
The rigour of the explanation: 10/10
The way it was explained: 6/10

Let me explain that last bit. This was a very very dense topic packed in a punch. There is no time to digest. You finish a phrase and start the other one immediately. I finally ended up slowing the video a bit just to have some air. Some meditations could have helped in that regard, making smoother conceptual transitions, spacing the specifics with some philosophical realisation or simply taking a bit of time to admire the beauty of some result. I think many would rather prefer a 2 hour long video (or two 1 hour videos) than a 1 hour video at such speeds. This topic is awesome and profound but no-one will ever grasp the complete meaning of what you are saying if one have to pay full attention to the next sentence before the last one is understood. Each sentence is essential so if one takes 5 seconds to think about any of it, the rest of the explanation would not be understood.

Overall this is an awesome video. In fact, for now, I think is the best one of the #SoME3. Thank you for doing it. As I said, this topic is fascinating and deserves all the attention. But next time, please don't be in such a rush. There is delight in tasting each idea (3blue1brown masters time perfectly in that regards).

[Natures-Game]

Corrections:

The thumbnail has a typo...😂

30:49 the last line should be p_t = 1/ (1+(n_B, 0/n_A, 0)(V(B)/V(A))^t)

8:40 alexanderbrady5486 pointed out that "Mixed strategies are valid Nash Equilibria. In
Rock Paper Scissors, the strategy where a player chooses each option 1/3 of the time is a Nash equilibrium. Some papers specify Nash equilibria into "pure" and "mixed, " in which case RPS has a "mixed" Nash equilibrium but not "pure" one."

I think I left out this since the rps game appeared before mixed strategy was introduced. My memory is a bit fuzzy but his comment is totally right. 😊

[eddie.z]

What a video! This has got to be the best video on evolutionary game theory out there. Please upload more, this video was amazing :)

[MysteriousSlip]

This was a fantastic video on the topic. I am really glad you went into some more detail past a simple Nash Equilibrium, since many YT videos about game theory and it's applications seem to stop at a very introductory level. I look forward to seeing more from you. :)

[LithiumFusion]

I subbed in the first minute then realized this is your first video. Welcome to YouTube. Channels like yours are the reason I'm here!

[gbm]

I'm already hitting that subscribe button for the first video on this channel! Excited to see what's next!

[louisnemzer]

16:50 Good illustration of frequency-dependent fitness

[paulreadel]

This is such a cool topic to have in the YouTube video lesson format! I really enjoyed watching this however the pacing was just a bit too fast for my brain to keep up.

I think it would be really great to break this exact same content down into a small video series with the pacing and content delivery slowed. Call it the “director’s cut” to this already amazing video. 🙂

[pacificll]

Great video! Thank you for this wonderful introduction, I’ll look more into the subject!

[dorol]

Interesting video! Got it on SOME3's voting process. Rated it a 32/40. I can give you a more comprehensive review if you want it.

[federicomagnani]

Great video!
I think it would be highly appreciated to show in the description the main resources you used, for who wants to deepen some topics.

[AB-wfek]

Life is an entropy rachet, this concept is the key to progression.

[bloomingyouth]

You did a great job😊
I'll wait new videos from you :D

[raunaquepatra]

really good explanation and thanks for not stopping at an introductory level.
somethings I had to pause to let the notations sink in😅

[welldefchalk]

멋진 주제와 흥미로운 영상이네요, 재미있게 잘 봤습니다!
앞으로도 영상을 만드실 예정이라면 응원합니다!!

[amadzarak]

Great vid. Can’t wait for your next upload

[Jgrau]

I've never seen such a great video about this topic! Keep it up, you are doing great.

[Iridiumalchemist]

There's a mistake at ~8:45. Rock, paper, scissors it's just not a deterministic one. You calculate Nash equilibrium so you just use the definition of expectation value in conjunction with the optimal probability distribution. Here, that probability distribution is to play either rock, paper, or scissors with probability 1/3. If you deviate from that strategy then your expectation value will diminish as you will admit distributions that beat yours. One can show no such distribution dominates the aforementioned uniform probability distribution. Even if you change the pay out of rock paper scissors (like winning with paper is 2 points and everything else is 1 point), then this is just reflected in relative adjustments in the underlying probability distribution you choose. MOST Nash equilibriums are represented in terms of distributions. Few are deterministic. Technically speaking, you get no benefit from using nash equilibrium in completely deterministic games anyway- you could represent them in other, simpler ways (game trees, ect). It is entirely the point of nash equilibrium to deal with problems that require probability distribution type solutions.

[nickstebbens]

what is called a 'pure strategy' in this video should more appropriately be called a 'simple strategy' - a 'pure' strategy being one whereby all contingencies are fully strategized, which means that the example of 100% fastballs given is an overlap of both simple strategy (singular, monic) and pure strategy (as in, not relying upon any non-strategic operation) - so an accordant example of a pure but not simple strategy would be for the pitcher to always alternate between a fastball and a curveball in a predetermined manner - because, think about the meaning of the term 'purely strategic'

[kylewood]

Wonderful! I wonder what else can be analyzed through the lens of game theory? Do you plan on continuing video production on the topic?