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24 Comments

Zach Star

July 20, 2020

Hope you guys enjoy! So most of the 'games' mentioned in the video are in fact famous game theory examples but I changed the payouts to mainly involve money rather than something like 'years in jail' or hypothetical 'points'. If you want more info regarding the 'games' I pulled these payouts from though I've attached the wikipedia pages below.

Also if you're interested in the results of the 'iterated prisoner's dilemma' tournament I attached a link where a couple dozen programs each with a unique strategy played each other.

Battle of the Sexes: https://en.wikipedia.org/wiki/Battle_of_the_sexes_(game_theory)

Guess 2/3 of the Average: https://en.wikipedia.org/wiki/Guess_2/3_of_the_average

Prisoner's Dilemma: https://en.wikipedia.org/wiki/Prisoner%27s_dilemma

Iterated Prisoner's Dilemma Competition: https://www.lesswrong.com/posts/hamma4XgeNrsvAJv5/prisoner-s-dilemma-tournament-results

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Shane Fernandes

July 20, 2020

How did you arrive at 62.5%.?

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OwenCulleton Personal

July 20, 2020

how did you calculate these percentages

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Caleb Gosselin

July 20, 2020

i would tell the other person to let me when the $100,000 and split it with them

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mushroom0 thepro

July 20, 2020

i'd say "I'l pick green since i don't trust you so you should pick green as well"

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Justin Anonymous

July 20, 2020

+zachstar
One of my classes in University was Negotiations in business, and every class session we played a game similar to this. But a little more complex having 10 round each game with the option to "collaborate" or "compete", developed by Harvard. on the 5th and 10th round there was a BONUS if you chose to compete if everyone else collaborated (and vise versa).
100% of our class grade was based on how many points we acquired in the game throughout the semester. The element of self interest made the game extremely difficult, because when everyone agreed to "collaborate," the distributed points is much, much lower – essentially only guaranteeing a "C" for everyone in the class. For that reason, people would choose to compete and screw over everyone else and reap massive reward toward their grade on the bonus rounds. However, if everyone chose to compete, the distributed points would be 0, and the one person who collaborated would get all the points.
Statistically only 5% of the class could make an A, the majority would make B's and C's, and a few would make an F. What we learned from the professor who had a giddy excitement all through the semester as we became total savages, Is that there WAS in fact a way to play the game so that we ALL got an A. It was through strategy and negotiation. If we collaborated on HOW and WHEN we chose to "compete" on certain rounds each class period when we played the 15 minute game, then the distribution of points would be 100 for everyone come the end of the semester. the key was in the bonus rounds.
He was too cryptic and we never understood this concept until the end, and so he decided to give us all A's for trying our absolute best to understand the game. Make no mistake, we were SAVAGES to each other, and at one point we all HATED each other for betrayal, ourselves for being guilty of doing the same, and the professor for putting us in an "unfair" environment.
HAHA! It was an amazing life lesson. Everyone truly wins in capitalism if we work together!
Game theory: In a system of rules, cheaters reap the reward. On the contrary, In a system without rules, those who collaborate, create, and abide by agreed upon rules, reap the reward.

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Luis Guevara

July 20, 2020

👍🏻

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Kicksnarehat

July 20, 2020

cooperate and then all of us go have fun at a science convention :p

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Thothrax

July 20, 2020

As for the "screw over" game, my response would be: I would show red if it were someone I know, green if it was someone I didn't. My reasoning being: if I know the person it's likely I wouldn't want to screw them over, and vice versa, so by showing red we either get the best outcome for the both of us, or they're happy and might give me some money later when you can no longer enforce the no sharing thing. However if it's someone I don't know I have to assume that they are going to try and screw me over as there is no presumed trust, so I either get 1,000 and dollars which is pretty good for no work and we go our separate ways appreciating that we each have the same understanding that this is how it had to be, or I get 100,000 dollars, feel bad for them in the moment, then leave and never see or think about them again.

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Antonio Sraffa

July 20, 2020

Am I the only one who has no idea how the mind of engineers work? [Respect, by all means!]
Technically, this is an explanation of Nash Equilibria, and I've worked through these games myself numerous times prior.
And yet, I'm SO lost trying to follow concrete values in these formulations.

I'm just glad someone is translating Game Theory (& other abstract concepts) to the language of applied mathematics–definitely isn't a task I'd be up to; I have a few CS colleagues that refuse to ask for clarification for this specific reason!
[Also, I'm glad you guys are building our infrastructure; if we were building spaceships, I'm pretty sure they'd be shaped like doughnuts (less phallic).]

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Enomiel Lanidrac

July 20, 2020

Nice game of terraforming Mars going at around 13:11.

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Serlo Tam

July 20, 2020

The first game is based on mixed strategy nash equilibrium. The prisoners dilemma is base on something call "strictly dominant strategy," which means that a specific strat is always worst than the other choice in a non coopetative games. These are rally basic stuff, nash equilibrium goes into stuff like weak sequential equilibria and complex games that uses trees. And he isnt using von-neuman morgenstern payoff, which means that these are monetary valyes that dont really reflect the actual payoffs players have in mind. The games he did also disregarded players risk behavior, which have 3 different ones. Game theory is really complicated, and if u are in a prestigious university, i do not recommend u taking it. (Or maybe just that my profrssor sucked)

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TRiG (Ireland)

July 20, 2020

Have you seen Tom Scott's "Money" series on Nebula?

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Phillip Norton

July 20, 2020

12:20 so wouldnt player 1 have done better than player 2 here?

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andrew Infante

July 20, 2020

Regarding the red and green cards, where it's 100k vs 10k vs 1k vs bust, what does game theory say to players who take an even bigger risk through cooperation to "game" the game? What's to stop them from going for one person winning the 100k and then splitting the reward and both walking away with 50k?
And then there's trolls who just want everybody else to lose, and they don't care about winning. How does game theory address that?
I HAVE SO MANY QUESTIONS!!

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Zanonymous Ruiz

July 20, 2020

For the modified prisoners dilemma I think there’s a clear best answer! If you’re allowed to cooperate with the person you’re playing against, tell them that you’ll pick green, and you’ll split the money with them if they pick red. That way you reach a Nash equilibrium: The other person will always make more money picking red than green, and you’ll always make more money picking green than red.

You can even split it unevenly (say, you take 80,000 and give them 20,000) and there’s no logical reason to refuse. Although that COULD end up with some mind games and stuff fighting over who’ll get the 80,000, so I’d just stick to 50-50.

Of course, this solution doesn’t work for the original prisoners dilemma bc you can’t “split” jail time once you’ve been sentenced, but there’s no reason given that you can’t exchange money outside the framework of the game!

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Jordan Schriver

July 20, 2020

When I saw "Game Theory" in the title, I thought about MatPat.

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Gameeustrupter

July 20, 2020

0

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Carter Yott

July 20, 2020

It’d be best to agree for one person to take the 100k and split it. 50k each is the best and you already established the two people can talk beforehand.

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David Jones

July 20, 2020

Green would have been my strategy, everybody wins and no benefit to betray

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Robin Karlsson

July 20, 2020

You sir, are my favorite YouTube of all time.

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Demerion

July 20, 2020

Honestly, I would just pick green everytime, because that way I get money for sure. I don't care what the other person gets.

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David Davison

July 20, 2020

I'm going to pick green, and I'll give you $10,000 if you pick red. There's nothing in the rules that says that I can't give money to my opponent.

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Tirave

July 20, 2020

So I may be a little late to the Party. I've just been introduced to this channel today and I have been watching all videos in pretty rapid succession. But this reminds me of an Anime called Kakegurui. Its about gambling and games and the like. But on the second season episode 7 there's a game that I think is similar or related to the topic discussed here its called "The Greater Good Game" Spoiler Warning Here . I'll try to show the rules
There are 5 players. Each turn 1 player will be escorted to a room with 2 Boxes. A Personal Fund Box and a Tax Contribution Box. Each player is given 5 Silver Coins. Each player can choose the amount to put in each box. Once all turns have been taken the coins will then be counted and distributed as follows. The coins put into the personal fund box are theirs to keep. But the coins in the tax contribution box will be doubled and then distributed equally amongst the 5 people whether any player put any coins in the tax box or not. Before each round there is time for all players to be in a single room to discuss amongst themselves. But if at any time 3 or more playes agree, one player can be eliminated. The eliminated player will be excluded from the game and their coins confiscated. The goal is to acquire 40 silver coins in 5 rounds. If you reach 40 you win "Votes" (a type of desired currency in the show) depending how many coins they have collected. Obviously if they only put coins in the personal box all 5 rounds they won't have enough to win "Votes". And those who do not accumulate 40 silver coins by the end of the game lose all of their "Votes" that they had earned from previous games. There's a lot more to it if you watch the show but the limit of the winnings if you are the only one to get 40 silver coins is 133 Votes and if everyone gets 40 coins equally it turns into about 26 coins each. Im not sure what kind of mathematical equation or anything like that can be used to determine the Nash Equilibrium for this scenario and i might be missing some info but I thought it would be cool to mention 🙂

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