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

Not Mr Beast but someone has done this game with money Once I find it I’ll edit my comment Edit: jubilee have done it it’s called human theory

well thanks for keeping your words. Hope you do the same with AI

I have been waiting for this video. Thank.

Nice video, a traditional matrix is easier to understand the strategies though. I found the reordering confusing

There is a TV show called Split or Steal, and the game is basically the same!

Source on this? I would love to read about it.

@@RedYakshaEntertainment web.archive.org/web/20140421055745/www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml

You wrote: "It's true that "Tit for Tat" was initially the most successful strategy. However, subsequent tournaments showed that stronger strategies exist. For example, there was a tournament in which two A.I. players would be matched for 100 repetitions of the game. Matches were organized in a "Round Robin" fashion, where every algorithm played against every possible opponent for the same 100 rounds. Each bot would get a score based on the outcomes it achieved in each round. The winning strategy was really clever. [...]" What you are describing doesn't showed that stronger strategies exist than "Tit for Tat". It just showed that in a different kind of game "Tit for Tat" isn't the strongest strategie. And that shouldn't be surprising, imho, because if you change the rules of a game significant, than the strongest strategie has to change also. Say, the main goal of a chess changes from killing the king to one must kill all enemy figures. If the best player in the world wouldn't change they strategy, they would be easy to beat. "Tit for Tat" seems to be the best strategy if two single player compete in a competition of several rounds in a row. The competition you are describing is a team gameplay in a "Round Robin" structure. That is a different kind of game. It would be very surprising if "Tit for Tat" would work here. It would show, that team work is a bad thing. And that sounds very unlikely for me. _ Disclaimer: I neither studied mathematics nor game theory. It's not unlikely that I'm wrong. So if you see an error in my conclusion please tell me.

@@andarted The original finding that "Tit for Tat" was a strong strategy originated from exactly this kind of tournament. It grabbed headlines by defeating many other strategies in this same context, a few decades ago. In some sense you are kind of right, though, because "Tit for Tat," like almost all other strategies, was focused on winning the match rather than winning the tournament. The team that succeeded in 2004 did so by taking a broader view of the rules of the game. As far as your conclusion about chess, it's probably true with regard to the current best players. However, there probably does exist an optimal chess strategy which never loses even if the opponent knows it perfectly (his strategy would have to involve many contingency plans for different situations). Predictability is no disadvantage in a game with perfect information. And in theory, chess has perfect availability of information, although in practice no player (human or machine) actually has access to the whole of that information, nor has the kind of memory or intelligence necessary to understand it fully.

​@@CricketStyleJ I wasn't aware, that the "Tit for Tat" originated from this kind of tournament. The video didn't explained the whole ruleset. A short mention that the maker simplifies it for the sake of intelligibility, would have been nice. Thank you for adding this information!

Da Aaron no, it’s better. It’s actual Mathematics.

ive been trying to find a game theory video without matpat.

I was waiting for something about matpat for the whole video

NO thats JUST a theory, A MATH THEORY

A MAT THEMATIC

This is a good point. I thought this was a competitive game, where the goal is to outscore the opponent. In this case, I would prefer 0-0, as we're still tied, over 1-2, which puts me 'behind' by one in ranked scoring.

Same, pretty much nope-d out of the video.

Sorry about that! Will keep this in mind for future videos, just wasn't thinking.

I thought you guys can make your screen change the color palette to fit your specific type of color blindness. Or is that not how it works?

as a person with no eyesight whatsoever, I find the use of video and motion pictures highly offensive

@You’re right because my dear god! just think of the atrocities committed against those persons without a brain! how could any youtuber with a modicum of self-respect and thus the acknowledgement of those less fortunate, dare to even discriminate against the diverse population of brain-less individuals! math should be accessible to every individual, including those without a well developed nervous system! I shall be reporting this channel to Google HQ promptly for crimes committed against humanity!

This was my first response to a strategy as well and kind of searched for this comment :D He even allowed making a strategy!

This should be super exploitable. If you alternate non-randomly, they can arrange their choice so they will get 100k or 10k meanwhile you get 10k or 0k.

@@joegreen4959 Doesnt really work over a large period of repetitions. Obviously, if you see that they aren't going to play nice, then you shift away and adopt another strategy.

​@@joegreen4959 not that one, the one with 2 dollars and 1 dollar

Golden Balls, iirc

@@cryme5 And the optimal outcome was to tell your opponent you were going to steal and then give them half after the show.

Ye but the golden balls got "solved" and got canceled soon after. If we would solve it like in the show I would say "I pick green no matter what you do. So you can choose red and I will share 50% of the money with you after the show or you can take green and we go home with a miserable 1000 $ both. " In the show the host says than there is no binding contract and he does not have to share the money in any way after. but any reasonable person would then still go for the chance of 50k instead of going with 1000 home. The show because the numbers worked out had a switch back in the end def worth a watch: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-S0qjK3TWZE8.html (I know Skyline prob watched it but that is for others)

@@Utoko yeah but the guy stated in this video you couldn't share the money afterwards, so that strategy won't work. I figured it was in direct reference to that gameshow.

Kintama

You're right except there's generally an odd number of rounds then, for such a game. The incentive goes away on the last round!

@@vishwalohana6404 Actually, simply announcing the last round is the last will make the incentive go away, if you're trying to maximize own gain. Because whoever has to win nothing in the last case will betray the strategy to get something, knowing it is the last chance to do so.

I think people are missing the point of prisoners dilemma. The name of the game is "non cooperative games" which means that they can only choose the best strat one time, and they cant talk. Alternating because of communication would become cooperative game, which goes into a whole different area of game theory, and prisoners dilemma is exactly not that, hence ur theory make sense, but will never happen

It’s not Nash equilibrium though.

@@Shikogo But cooperation is allowed. The only different thing is there is no signed contract. So, would you believe the other person if she/he told you "i win then i divide it"? she could totally just take the 100,000 dollars and leave you without a penny.

I feel like I saw a video of this with a guy and girl and the dude screwed the girl over

@@ethanschaefer8327 Yh I saw it. I feel like I got major trust issues from that video alone

@@Shikogo The actual game is the prisoner's dilemma so you can't exactly split the prison sentences.

I WILL GIVE YOU 10 TO 1 ODDS!!! U IN?!

This is such an interesting anecdote, and that observation at the end might explain why corruption tends to arise in bureaucratic organizations that become overly bogged down with rules and red tape

BRUH, your class was literally an anime plot 💀💀

That game is known as the Win as Much as You Can Game. The payoff structures are designed to prevent collaboration. Other versions of the payoff structures will promote more collaboration.

Two years late, but I'd like to point out that everyone does not win in capitalism if we work together, as, if we all work together, it's no longer Capitalism, and it's, instead, Socialism. Capitalism is a system of economics where businesses hold the "power of the product" (i.e. they are the ones who get to make most, if not all of the decisions on what happens). Socialism is where the power of the product is given to the people THEMSELVES. Lastly, Communism is where the power of the product is given to the state (aka the government).

@@deadersurvival4716 I hope your last line was intended as a joke, though it does not come off as one.

The search is ruined by pretty much dumbest show on the internet.

yeah, but what the hell os he doing there? hahahaha just randomly moving player markers from place to place

I noticed that too. TM is a great game.

Well that isn't usually the case with this game cuz its a one off

No betraying gives you a better payout than cooperating with another player who's cooperating. Otherwise there wouldn't be an incentive to betray if you were both cooperating and mutual cooperation would be an efficient nash equilibrium.

@@joshuafury5353 In the classic prisoners dilemma, the lowest total prison time comes from both sides cooperating.

@@cookiecakeeater6340 ​ @cookiecakeeater6340 No that's not the prisoner's dilemma. While mutual cooperation is better than mutual defection and usually in how it's written mutual cooperation is less prison time between both players overall than 1 person betraying it is not the case that mutual cooperation is the best outcome to land on, betraying someone who is cooperating gives you less prison time or else there's no point in betraying. In a game matrix player 1 picks a row and player 2 picks a column, player 1 receives the payoffs on the left. This is the prisoner's dilemma each player can cooperate or defect. Sorry for the shitty drawing but here: A>B>C>D c d c B,B | D,A -------------- d A,D | C,C Player 1 would like to play Defect as regardless of his opponents choice A>B and C>D Player 2 would like to play Defect as regardless of her opponents choice A>B and C>D Payoffs are good and prison time is bad so maybe it's more intuitive to think of the payoffs as the negative amount of years they spend in prison (so it's clear that more prison time is worse). In the game you're describing we would likely see mutual cooperation. B>A>C>D c d c B,B | D,A -------------- d A,D | C,C There are actually 3 Nash equilibrium in this game but mutual cooperation is the only one that would make sense for you to play as it gives a better and actually the best possible payoff for both players than the other equilibria, a payoff of B every time. A Nash equilibrium is a set of strategies for each player such that neither player has a profitable deviation given the other player's strategy. Mutual cooperation and mutual defection are both equilibria in this game. if you are cooperating and the other player is cooperating you would not want switch to defect as B>A. This also applies to the other player. if you are defecting and the other player is defecting you would not want to switch to cooperate as C>D. This also applies to the other player. There is also a mixed strategy Nash equilibrium where each player is using the strategy that makes the other player indifferent between his choices. A Nash equilibrium by definition, as neither player can profitably deviate given the opponents strategy. These other equilibria don't really matter though because it is in both players interest to play into the equilibrium where they both cooperate.

I just wished they had used actual gameplay footage. The way the blue cubes are being moved makes no sense.

@@holgerchristiansen4003good catch! I did not see this before.

I believe these feelings are going to change when you compare your progress with your oponent after each lap.

@@alexeysaphonov232 that is flawed thinking. Its not a zero sum game. You're just trying to win money.

The problem with this is that if you know your opponent will pick red, you get more money by playing red than by playing green.

@Pluto N. Uranus Of course I did. I did not talk against the video, all I said was what I would do. And just picking green always gives me money, there's no need to gamble for me :)

@@yonatanbeer3475 if you know your opponent will pick red, then picking green gets you 90,000 more than if you pick red.

Making a graded assignment rely on the outcome of a literal game sounds psychotic. Imagine narrowly losing a scholarship because your teacher thinks they're clever.

@@JhettJones Small assignment with minimal grade implication, if your scholarship depended on that then you didn’t deserve it in the first place 🤷🏼‍♂️😂

So the thing that went wrong is that the solution Zach put up is optimal *for direct payouts* (where you don't care what your opponent makes), not for the competitive scenario. I can't say anything about the mini-max tho, since with the adjusted payoffs the mixed nash equilibrium is exactly what you described (although I found it the traditional way by making the opponent indifferent).

Hate that show, it makes me lose faith in humanity.

Never heard of that show! Thanks for the heads up.

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-S0qjK3TWZE8.html check out this episode

@@skartdo that is an awesome episode but this one is even more messed up ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-p3Uos2fzIJ0.html

Chaosh isn't a pit. Chaosh is a laddah.

Was it in KOTOR 2? I don't remember that part.

@@raves8451 Sorry, KOTOR 1 not 2. It was on Kashyyyk, on the surface at the foot of all the trees. You had to answer a terminals questions to gain access to the star map and one of them was the Prisoner's Dilemma.

Certainly not HAHAHA

I went through coursera's "game theory" course in preparation for this video and thought it was pretty good (some parts can get really technical but that's often if you just want more of the 'proofs' and rigorous mathematical explanation, the class is meant for beginners overall). I put a link in the description and it's a free course so you don't have to enter any payment information for this one. I'll also attach two youtube lecture series below. Yale Game Theory Lectures: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-nM3rTU927io.html William Spaniel Lectures: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-NSVmOC_5zrE.html

Thanx man

His numbers are bad. The same logic applies to the Nash equilibrium if you replace 100k by any number larger than 1000. Thus we can pick 1500 which is still a decent incentive to betray, but makes alternating betrayal a suboptimal strategy.

Alternating works if you could play the game multiple times and cooperate, but for that example we are assuming you only play once and cannot split up the money afterwards.

@@zachstar Ah ok, I thought we were addressing a strategy for multiple games Love Forsberg but if the [roze was only 1500 not 100k then wouldn't you just both choose red? there is no incentive to betray since the pay is now only 1500, instead of the 10k you would get for both picking red

Hey, not that far off!

However, wouldn’t earning the most amount possible inherently require beating the other person in this case?

This game is zero sum, though, so it's equivalent.

The rules stated that splitting was NOT allowed. Yes, that is an arbitrary rule, but that is true for the whole game, so what can you do?

@@holgerchristiansen4003 The you cannot divide the money afterwards rule is not just arbitrary but unneeded, there is a game like this but slightly different and yet it is a strategy and legitimate to split your winnings if you steal. There is no reason that a green steal should have a lot bigger payout since there are many reasons why letting someone steal by playing red in a roundabout way if you trust your opponent is more beneficial than splitting like asking for them to donate $10,001 to your charity of choose. In all honesty you can even tell them I will choose red have red already choose and if you trust the other player to spend that money in a way that is beneficial to you than loosing like this is the best outcome. In all fairness the order of magnitude more a solo win nets the community it is what these two players should conspire to achieve.

@@holgerchristiansen4003 also if my last comment seems confusing the whole point is in reality you don't trust the player outside the configs of the game so for all you know they would never split those winnings even if they said they would, my point was if you could convince the other player to do so you could convince them to benefit you in other ways that is straight or direct monetary compensation.