The (strange) Mathematics of Game Theory | Are optimal decisions also the most logical? - monstrousmath.com

The (strange) Mathematics of Game Theory | Are optimal decisions also the most logical?

Zach Star
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267 Comments

  1. is it weird that "me" looks like young hitler?

  2. There is a slight fault in your prisoners example. You say that "Everyone" is better off, but that can be misleading.

    With deception the total payoff combined to both players is way higher than if both players cooperate. As such, the "whole" benefits more.

  3. Assuming you have completely open communication with the other player and could strategize in any way, I would convince them that By allowing me to choose Green, I can individually win the sum of 100k and split it with them after the event takes place. If I can hammer home that I have no intention of choosing anything other than green, I can hopefully convince my partner that they have 2 options; either going green themselves and making a comparatively measly 1k, or hopefully trusting me through the relationship I have build up with them enough to take the gamble that I would split the 100k with them 50/50. My justification to my partner for why I would choose nothing except green would be because it would be the best option for me personally, no matter if I decided to split it or not. Depending on psychological hints I pick up and the personality of my partner, I should be able to determine on some level if they would be so bold as to insist they should be the one to hit the green button and if so it would turn into a game of chicken.

  4. There is a TV show called split, which is about dilemma.

  5. Before watching this video in my experience the answer is 50% of the time yes and the rest is a mix of no and maybe…

    If the "game" is long term and/or slow paced then USUALLY yes

    If it is fast paced and short then some times no…

    This is based on my experience with certain video games

  6. Omg the part where you mentioned Mr. Beast I nearly cried because of the thought of getting scammed out of 10,000 dollars as I would play red

  7. Or tell them to pick green and give you half lol 😉

  8. Another benefit to betrayel is that even if you both have the same idea, you both get 1000 bucks.

  9. In the green red, 100,000 or 10,000 game you said they could communicate before hand & then betray eachother. Wouldn't they just agree to split the 100k 50/50 and then intentionally setup a betrayal? This actually seems a lot more likely than any of the other strategies seeing as I've actually seen it employed myself. At local card tournaments when you get two players in a finals match, the winner of which will win X (the 1st place sum), and the loser wins some lesser amount Y(2nd place sum), they might just agree to split x & y, and not even play the game, or just play a friendly game.
    The idea works because each player might not have the confidence that they can win (in the case of the card game tournament it would be because they both know they are good players to have reached the final stage) and thus both assume cooperation is in their best interest (assuming after the intentional throwing they can't then betray eachother afterwards) e.g. I betray you because we agreed to split 100k 50/50 but then I just run off with the money.
    In the example of the heads up card game they might assume that winning 100k is the best, and it's an obvious option that everyone would come up with, and thus expect both to play green, so cooperation on intentional betrayal is A LOT more likely to award a high payout then hoping for the other guy to blunder with a red card. Also most people, I think, Would upon realizing that 100k is a lot more tempting than any other option just play green regardless. I'd bet a small % of people actually do play red when trying to agree upon double red. Also if you're going to agree to cheat (play double red) why not just cheat & play green / red & split 100k.
    Hell, they do this in real competition's too, which is probably why there is usually some rule against it which would see both teams forfeit the prize money.

  10. "Let me win the 100,000 dollars and I'll give you 50,000, here's a signed contract."

  11. 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 🙂

  12. 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.

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

  14. You sir, are my favorite YouTube of all time.

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

  16. 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.

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

  18. 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!

  19. 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!!

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

  21. 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)

  22. 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).]

  23. 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.

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

  25. +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.

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

  27. how did you calculate these percentages

  28. 10:15 i would show green, bc if i show green then i either get 100K or 1K, which is 50.500 avarage, but if i show red then i either get 10K or 0 so its 5K in avarage. And If i show green and get the lower price 1K is still better then nothing

  29. what's the update on that Mr.Beast collab video

  30. I would always show red if the other person says they are going to show red. I don't care if they are lying, trusting people always wins out in the long term and after all, relationships are always better than money.

  31. This sure as hell is not GTO . Not one mention on hunl.

  32. Hello internet welcome to….

  33. Can someone get Mr beast on this idea like now

  34. 9:57 there actually already is a game show like this called golden balls

  35. Your channel is too interesting. It's taking time away from my full stack web development courses.

  36. When you find out you've been using Game Theory to make decisions all your life:

  37. How deep did I see into your initial question of if we all picked a number between 0-100? I said 67 😑

  38. I'd pick 46, because I expect everyone to pick 69 and 2/3 of 69 is 46.

  39. I would suggest that my opponent picks red and I pick green and then we split 50/50 after, then when he/she inevitably thinks I'm going to just take the money afterwards I'll suggest that we skip the roles making him/her more likely to split with me after

  40. Ok. I can talk to the other guy? Insist that by bargaining I'm eliminating the possibility of the best result, IE, double red. Drop he subtle hint of a red drop, then Play green.

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