I think that the problem with the example at the end is that some people might value their reputation more than 1 or 2 points, therefore cooperating is actually the correct choice
The way I see it lowering the stakes would make it more likely for me to play to win (in a game with win/lose/neutral scenarios). If the outcome is not transcendental, it is seen as "just a game" and no one would take it personally. Many games (especially card and betting games) consist of lying or deceiving your opponent and no one thinks that playing it makes you a "liar" or a "bad person". You don't see people "losing their reputation" for being good at poker. Put it this way, if you were playing tic-tac-toe for 2 bonus points and you had the opportunity to win, would you not go for it? However if the losing meant failing the class, I'd be mainly focused on not losing, rather than winning. I think it'd be quite the dick move to go for the win in this case
So the moral of the story is that in order to prevent people from acting uncooperatively, you just have to shun them socially, thereby making the drawbacks of defection worse than the benefits.
@@leftylizard9085 Yup because being shunned by others is the harshest punishment known to humanity. And I'm serious about that, there is no harsher treatment than being shunned by others, for a social animal, in the wild, animals shunned by their supposed herd will die, either of depression, or to predators, or by being ganged up on and killed by the other members of the herd. And this is the biggest difference between the right and the left politically as well, as the left loves to shun people, who disagree with them, while the right only believes that people should only be punished by the court. I wouldn't say that either side is particularly correct, let's just say I prefer the bestial course of action over all other.
@@polokan I think the difference there doesn't really have much to do with the stakes. If I'm playing a betting game against someone I can probably assume they knew the rules and thought the risks were acceptable, or else they wouldn't agree to play the game. And the whole point of the game is to compete against your opponent, so there's no reason to feel bad for trying to win even if the stakes are really high. But in real life you shouldn't just go rob somebody, even if the amount you're taking is much less than in the high stakes poker game.
Best strategy is to always cooperate, unless your opponent defects, and then retaliate by defecting. That way if rational, neither player will defect as not to be worse off from their opponent retaliating (Defecting is worse for the other no matter what they choose), and they will both cooperate and end up gaining more.
@@marcusscience23 Tit for Tat did win the Axelrod tournament. But it works on the assumption that its opponent is trying to maximise its score; play it against a strategy which just picks at random, and it does no better than random does.
I believe that the "rationality" of defecting in the prisoner's dilemma is cultural. There is an unfounded assumption made that the most rational thing to do is to act only in your own self interest.
this might be the case in a game where your defection is broadcasted to the world, real life defection occurs in secret. That's one thing, another thing is that the points of defection could be themselves reputation points themselves, the connection of the systems of what "defection" exactly means and in what social situations involves a plethora of systems and it can get philosophical very quickly. Ill save you the trouble, defecting is always the better option
I think there's also a point to be made of empathy. Even with secret decisions, lets say everyone does 20 matches against different people and they only get to know their total gain/loss instead of that from each individual round, I think most people would go with cooperation because they generally don't want to screw someone over with something that has meaning beyond the game itself (i.e. class grade). Competitive natures however would probably result in people playing strictly for in-game rewards to be more aggressive with it. That said this is only speculation based off of the very limited information I have on the subject.
You know, if both people cooperate would be better than both defecting, but what is lacking is the trust the other person will also cooperate. Think like this: let’s say that I cooperate. Then, if there’s a 50-50 chance that the other person would pick either, then the average would be 1/2 • 3 + 1/2 · 0 = 1.5 Then if I defect, then the average is 3. Since 3 > 1.5, it’s better to defect.
What if instead of just choosing once, you and your opponent could choose over and over again times and add to your score each time? In that case, provided both players are rational and know it, a good strategy will be to always cooperate each time, unless your opponent defects, in that case you retaliate by defecting afterwards, partly to make up for your loss (though only to a certain extent), but mainly to disincentivise your opponent from defecting. You defecting is always worse off for your opponent no matter what they choose, and even if they had defected before it would still be worse for them than if you both cooperated. That way, your opponent wouldn’t defect so as not to provoke you and be worse off, and also knowing that you wouldn’t either with the same reasoning. This way, you can both end up being better off with mutual cooperation.
@@otesunki About two years ago I read a paper that used linear algebra to construct a strategy that could beat tit4tat. So it is no longer the optimal strategy known. (Wish I could remember the name of the paper.)
I think you missed the point your professor was trying to make. An iterated prisoners dilemma is an entirely different game and ties in to the evolution of cooperation. The reason we have concepts such as reputation and revenge is that life in many ways resembles game theory, and overall, tit for tat cooperation is the dominant strategy by far for the individual. We see this play out in nature and human societies all the time.
@@marcusscience23 You could only ever do that once. The next player will anticipate it and go for one more defect. You would just end up with the same scenario of trying to one-up one another on a higher level and end up inferior to cooperations between two purely tit-for-tat algorithms.
Agree :). And if you guys haven't seen, there's an amazing video by the channel 'Primer' called "Simulating the Evolution of Aggression". Especially at 5:00 and onwards, it becomes really close to this video
Defecting is a better strategy simply because there are no other objectives for agents playing, but humans, we have also social objective (bring benefit to the group), and this objective doesn't captured by solution explained.
But even if you leave out people's social instincts, group selection favors those groups who choose strategies that produce better net outcomes for all players. In fact, our social instincts probably come from such group selection. The groups that had bad social instincts died out
The classroom experiment is very interesting. To me it suggests.. punnet squares make for bad models. They just aren’t complete representations of all the decision factors.
You were going to see the other students in the class again right? The dynamics of the prisoner's dilemma change in a context of iterated play. Cheat me once, shame on you; cheat me twice, shame on me!
This game gets even more interesting (like Prisoner's Dilemma) if you play repeatedly. (Ie. allowing for learning and/or 'revenge'.) There was an experiment done years ago where the winner (winning program) (with repeated games) would cooperate till 'betrayed' by the other player, then go for 'defecting'.
Interesting that if you know that you play with the exact copy of yourself, best strategy is to cooperate. Which leads to an interesting question: if both actors know the rules and play perfectly aren't they exact copies?
Applying a little empathy and altruism to acknowledge that winning is _not_ the objective, then the winning strategy becomes not to maximise _your_ points, but to maximise _everyone's_ points. So now, 1 cooperate and 1 defect is 5 points, 2 defects is 2 points, and 2 cooperates is 6 points. Cooperating is always the better outcome as long as you're not just playing for yourself. Same as in the class since the payouts were 1, 0, and 2 for 1 of each, 2 defects, and 2 cooperates respectively.
I read about this in a Piers Anthony Xanth book. It can be inferred that he advocates, at least in a large group, for cooperating with an individual until they defect, and then defect. I think I'd have to try that too.
The professor's game kind of reminds me about that one Tom Scott's gameshow. I believe that once there's a third party being the house (or, the one who give the prize), the best strategy is not going against other players, but going against the house, aka, cooperative.
That's because the listed "payment" isn't the REAL payment, as the game is not played in isolation. The real payment includes one's reputation in the class which outweighs these bonus points. The game's best strategy also changes in case there are repeated games for similar reasons.
Sir wouldn't it be great if you signed the contact with the opponent to co-operate with you , so both you and your opponent would get 3 points and if they betray you according to the contract you can fawn over their won points
I would always coop cuz in avarge that is 6points and the others are 5 and less I try to alway choose the bigger good instead of self good and even though my hope in humanity isn't big I still have just enough to trust the guy am playing with
Collaboration (price agreement) is forbidden in a kapitalist market. Companies are required to compete with eachother and not divide the market among the players. That's why, for example, many shops that sell similar goods in a city (clothes shops, computer shops, gas stations, banks) end up in the same streets even if they would collectively earn more if they were distributed over the whole city.
"I'm going to pick Defect every time. You should pick Cooperate, and here's why: If I'm telling you the truth, I'll pay you 2.5 points for your trouble, which is still better than you could do defecting when I've clearly stated I will defect - there is nothing you can do that gets you better than that deal, since I guarantee you I'm going to defect. But if you think I'm lying, then you should still pick Cooperate, because if I'm lying and I'm actually going to Cooperate, then we'll both win 3, which is *even better*. But I'm going to pick Defect, which you can believe because there is zero benefit to me in lying about it." Over multiple rounds of play, this produces very nearly the best possible outcome, and only 'breaks down' on the last round of a multi-round game, where I no longer have any reason to convince you I'm trustworthy to continue going along with me, and might screw you over on the bribe. How well this strategy works depends on the relationship between the 'Cooperate/Defect' payoff and the 'Defect/Defect' payoff. In the Professor's example, the 'bribe' is 1.5 points, meaning that both players gain 0.5 points of credit, which is better than they can do with both Defecting. As long as the total payout between both players in the Cooperate/Defect scenario is higher than the Defect/Defect scenario, and as long as the reward is transferable, this works.
Winning is completely subjective here, the results aren't a bit based on the prize they are 100% based on what the prize is and what the winner really gets
defecting isn't always better because the other player isn't equally likely to defect and cooperate. maybe if we consider the expected payout including those odds - then the "best strategy" will be different?
Somehow I got the idea in my head that getting only one point was not substantially more desirable than getting no points at all. So I decided that the risk of only getting one point was not worth the chance of getting five points, so I decided to cooperate and go for three, figuring he would see it the same way and cooperate as well. Looking back, I don't know what I was thinking. one point is obviously better than no points.
what _really_ ended up spooking me out was when i realised doctors and therapists were playing an unsymmetrical version of the prisoner's dilemma with me - as in, whatever my reaction would be, they were objectively better off being stubborn (and, as it turned out, making the decision worst for me) now looking for a good trauma therapist and hoping they won't do the same shit. i'm telling this story so people realise game theory actually _has_ applications in life, outside of actual games and economics.
If it was not absolute grading, adding 1 pt to each student's final score doesn't change the deviation of the distribution. Hence, all cooperating or all defecting are essentially the same.
I actually chose to cooperate, even knowing full well that you’d defect ❤️ 😇 Still though, an interesting game that requires the mastery of human prediction in order to consistently win 🤔
As humans most of us will always go with what makes us feel good and not rock the boat. Everyone that is a B personality and below will take this route. A personality will strive to win as that is how they approach life. Again it’s about winning for some and others are comfortable just breaking even. The professor should have staked the entire class grade on the outcome to see how it would change the dynamics of this test. Again some would choose the F over being confrontational. Others wouldn’t bat an eye at taking the win or A.
If let's say you played a tournament style against 5 other pairs of plates so ten total and kept your cumulative sum through all the matches, there may be an incentive that would motivate you to play Cooperative being that you score 3 each instead of one each, each turn. And then the highest score at the end amongst the individuals would win. You could do the same thing but rotate each match or rotate at some number of matches. Or you could play as pairs and as pairs you would switch off playing with your partner then with not your partner but then it would really just be when with partner play Cooperatively and when with other play defect since 2 rounds gains 3 each round so six each and a cooperative/defect sorta switch back and forth gains only 5 total for each player. It would just become that sorta thing so playing as individuals against each other but at different times is probably the only way you could incentivise the cooperative move. That sorta setup could prolly actually be used in a logic setup that allows for deceit, so would understand it better for neural network architecture. Hmmmm
If the game goes past 1 iteration, Defecting is the least optimal strategy as no one will cooperate and why should they if they know you're going to defect anyways.
The way I look at it in the first example it is just meaningless points and your only way to win is to have more points than your opponent and if you have an equal amount of points neither of you win. In the second however the more points each of you have the more extra credit you get therefore a tie is a win for both of you as opposed to just a tie.
the other problem with this game is the hidden assumption that the objective is selfish, to score for oneself as many points as possible, whereas for me and many others, the goal in life is to achieve the greatest outcome for all, and in that paradigm, it's always better to cooperate in this game.
This game has been simulated with various strategies. If you set up a game where you play multiple times against the same opponent and then switch to another person in your class while tracking your point total for all matches. The best strategy is a tit-for-tat. That is, start by cooperating and only defect after your opponent defects. If your opponent cooperates, change to cooperate on the next round.
Mr beast did something similar but w real money... you can either choose to share or to steal If both people share they get $ 5000 each If both choose to steal neither of them gets any money and if one chooses to share and other chooses to steal, the thief gets $ 10 000 and the nice guy gets nothing...
I hate what this game is teaching. First, the lack of communication is not a normal circumstance (hence the name of the dilemma). Second, the point values for the different scenarios are usually called unjust. Third, a rational player does not play for their own intrest, but for the interests of all rational players. A little poverty that means more wealth for the whole race is better for each individual, too.
In such cases (a class being an example) where you trust your classmates to a certain extent (or both players are aware that the other person cares about what the entire class will think of them) can't we add a probability that the opponent will defect? This probability being low means high trust and vice versa. Would such a modification change the winning strategy?
Not by itself no. Because even if let's say that there is a 90% chance that your classmate will cooperate, that leaves your choices as Cooperate: having a 90% chance of you getting 3 points, and a 10% chance of getting 0 (so an expected value of 2.7 points) and Defecting having a 90% chance of you getting 5 points and a 10% chance of you getting 1 (so an expected value of 4.6 points), so defecting is still the best choice for you. And flipping the odds the other way doesn't change things either (if there's a 90% chance of them defecting then cooperation ends up with an expected value of 0.3 points, and defecting having an expected value of 1.4 points, so defecting is still the better choice. The issue here is that it doesn't matter what the odds of the opponent's choice are, regardless of their choice, defecting will always give you more points than cooperating, even if they were guaranteed to cooperate, then defecting would just give you a guaranteed 5 points which is the max payout (and if they were guaranteed to defect, then obviously defecting would be the only way you could get any points). The only way to make cooperating worth choosing is, as others have pointed out, is to effectively attach other consequences and benefits to the choices. Such as playing repeatedly in which the best strategy becomes cooperating unless/until your opponent defects. This effectively causes the choices to not only affect this game, but later games as well. In other words, the deciding factor isn't your opponents trustworthiness, it's your own that causes cooperation to become optimal.
Defecting is only the best strategy if your opponent is guaranteed never to learn from their past experience and therefore guaranteed never to act on their past experience, which is a situation that never actually happens in real life. Also, defecting is only the best strategy if the given rewards and punishments in the game are the only rewards and punishments that exist, which is also a situation that never actually happens, because the human mind is ridden with all manner of conflicting drives and desires. For example, cooperating is very often intrinsically rewarding to the human psyche.
With the assumption that you could trust each other not wanting to be 'the jerk that defects' you start looking more at the mutual gain than purely your own. By taking the sum of the individual points and considering that you get 2 points as a pair for both coöperating, 1 point (2 - 1 or -1 + 2) for one defecting and the other cooperating, and 0 points for defecting each other. This way the game turns more into a Stag Hunt, and the trust that you'd rather risk the other betraying you for getting a win-win and, in way, beating the teacher who put you in this game together.
The problem is that maths doesn't consider emotions, values such as morals and empathy and other human traits. The best strategy according to maths isn't always the best strategy in reality whenever it is about human interaction.
It's actually very easy to model these emotions with the math: simply add the points given to both players into 1 value. Then cooperating will always give the best outcome in both scenarios since 5 > 2 and 6 > 5.
This only applies in a zero sum game. If your goal is to defeat your opponent, then you should defect; the amount you win by is irrelevant, and cooperating will never let you win. If your goal is to gather as many points as soon as possible, you should cooperate. If the other defects then their a dumbass that can't be trusted, prioritizing short term gain over the long term.
I think the non-intuitive result comes from two assumptions: 1. You have no knowledge of your opponent's strategy (so you assume either choice is equally probable) 2. There is only a single payout. In the single-payout scenario, you have no incentive to cooperate, but I think a lot of people think about these games as being repeatable, and if you are playing over and over with the same person, the best strategy would be to cooperate. But if you were playing with strangers every time, then you should always defect.
Is there any reason for the rules to benefit defectors over cooperators? It seems there is not. So, what if the reward were the reverse? I'm unsure as to whether this is a true mathematical game instead of a one of socio-economics. Our capitalistic way of thinking doesn't promise a sure reward for defectors, but the possibility of it, and this is what suffices for people to ignore what seems to be the logical goal of living in society, to cooperate, by starting the all out competition (did I say war?) of everyone against everyone else that we still don't tire of living through day after day. This is perhaps why young people are prone to challenge such rules by choosing cooperation, maybe by 'instinct' (one would say 'innocence'), maybe from the received - moral, religious - education (through which we pretend we try to assuage somehow the de facto scenario of generalized enmity): they wouldn't still be prepared to live their lives through with the weight of such an incoherence, as it seems obvious that living in a group is a choice for cooperating. This is also not to say that the capitalist system, which stems from that apparently harmless operation of exchanging goods according to their presumed relative value, has been a choice for self-inflicted perversity that we've been making for generations in a row, but one that at a first look appears to be quite just. In quite good faith we just didn't foresee the most immediate consequences of this simple game whose rules everyone is capable of grasping, and to which we ended up adapting, as expected. However, we at least have learned that the hell is plenty of the best intentions.
Because defecting gets you a bad reputation. And many people care a lot about their reputation. If people were playing this game over and over, the strategy cooperate with those who cooperate with you is a good one. A bunch of people who know defection will get them points this round, but loose more points next round. Of course, this can only happen in big brained animals that can track who cooperates. Which is why a lot of complicated working together behavior only appears in big brained animals.
There is a difference between playing once - where your analysis that always defecting is the best strategy - and playing multiple times - where your current choice affects the future choices of your opponent. With three points for both cooperating you only need to get the other player to cooperate more that one in three turns to get a better return. Axelrod in his book "The Evolution of Cooperation" details an experiment where the game was played multiple times. There the best strategy was determined empirically to be "tit for tat". Your first move is cooperation and for subsequent turns you make the same choice that your opponent made in the previous game.
U can't call the guys who choose to defect 'Jerks'. Because mathematically it is the best and most correct strategy to choose as you acknowledge here & remember this is a test under the game theory also. Further, the guys who choose the 'Defect' option might have trust issues with society or with the opponent due to various previous reasons. So they are not 'Jerks'. The only 'Jerk' here is the professor himself.
Why is it frustrating? Individual choices being different than collective choices is baked in the problem, given that there's incentive to not cooperate on individual choice pov. The fact that you ignore what the other is doing shouldn't surprise you to the fact that you aren't always cooperating. In fact if you exchange 5 and 0 in your example, your answer will be to always cooperate. In fact, if you changed 5 to 7 you'd win more if you alternated cooperation and betrayal to maximize your outcome with the other participant. So if the result you wanted was to cooperate, you'd have exchanged the 5 and the 0. If you guys simply couldn't communicate, you'd always choose defect, for the worst outcome is nothing changes.
actually, the other player would probably defect, so you should really play multiple times and keep cooperating until they also do(they have morals) and then it would be better than if both players defected each time
Не смотрел видео, так что вначале отвечу, как я бы сделал :) Я бы нажал на дефект, и сказал бы тебе, "я скооперировался, кооперируйся тоже!". А сам нажму на дефект. Если ты поверишь мне и решишь скооперироваться, то я получу 5 баллов, а ты ноль. Если бы я кооперироовался в этот момент, то получил бы меньше очков. Если же ты не поверишь или захочешь предать, то я получу больше (1 балл), чем получил бы в случае нажатия на кооперэйт. Проблема этой стратегии дьявола в том, что если и ты будешь таким же умненьким, то мы гарантировано получим 1, что невыгодно для обоих. Куда более лучшей и надёжной стратегией было бы та же, но только с условием того, что мы - хорошие друзья, и ты мне веришь (правда терять дружбу из-за такой игры довольно глупо, хехех). Однако этого, увы, уже подкрутить не могу¯\_(ツ)_/¯.
The mistake in this "best strategy" argument is that it assumes the actions of both players to be independent, i.e. you can make your decision while the other has already committed to a decision. But if you actually run this experiment, particularly if you repeat the game with the same pairings (so that trust plays a role) you will probably find a strong correlation between both players' choices. So unless you're playing this one-shot with a person you have never met and never will again, even though you changing your strategy doesn't CAUSE the other to change their strategy, they will still be correlated, so it's kind of easier going diagonally in the diagram (correlated strategy change) than horizontally / vertically (uncorrelated strategy change).
Experiment of prisoners dilemma done and for genders for men and women not just mathematicians. “Big Five” personality traits. Agreeableness and Conscientiousness. Experiment done on women and men women are more related with Agreeableness - The agreeableness trait reflects individual differences in general concern for social harmony. Agreeable individuals value getting along with others. They are generally considerate, kind, generous, trusting and trustworthy, helpful, and willing to compromise their interests with others. Agreeable people are quite considerate and are willing to compromise. They want to keep social harmony and results are secondary to them. They demand inclusivity and care. Agreeable people do not like conflict, the do not want fights to break-out, they do not want anything to disturb the relative peace. And men are dickish adsholes:) flexible slickers thugs, thus conscientiousness is a tendency to display self-discipline, act dutifully, and strive for achievement against measures or outside expectations. It is related to the way in which people control, regulate, and direct their impulses. High conscientiousness is often perceived as being stubborn and focused. Low conscientiousness is associated with flexibility and spontaneity but can also appear as sloppiness and lack of reliability. [2] Conscientious people judge others on results and accomplishments, they do not care about people’s feelings. They demand high level performance and results. Mathematician have more agreeableness tendency mathematicians knows odds but more mathematicians choose irrational non stoic decision not betrayal partner in crime, even it will have consequences. I think more mathematicians want to keep social harmony and results are secondary to them.
Your professor's dilemma is not equivalent, because in the standard scenario the two players are only competing against each other, but in your class they were also competing against the other pairs. In that circumstance, agreeing to cooperate is a more valid strategy.
I don't think it's right to call always defecting "the correct strategy" and "the way you should play the game" in contrast to the way your class played. It *is* the correct strategy if your only goal is to maximize your own gain, but once you add in empathy, morality, or social repercussions, that's not longer true.
Did you leave out some of the rules? What if the point is to have the least points? What do the points even do? Are we competing against another team somehow? See who gives up first after realizing there is no point? I'm not understanding how the game first described is a complete game, based on the stated rules.
Personally, I think it's a safe assumption that more points is better, judging by the majority of sports that have more points as the goal, though I'm biased by previous game theory videos.
@@cameronbigley7483 could be more points is better, but the game still seems pointless, since you both get the same amount of points if you choose the same and more for not cooperating, seems like the only point would be to trick someone who didn't understand the rules ( a bar game to swindle someone possibly).
@@cameronbigley7483 I'm teying to give him the benefit of the doubt here since I'm sure he got more math under hos belt than I do, but from what little I know about game theory, this is not a mathematically complete game, let alone functional somehow based on the rules given. Or it is, and I would like to be enlightened on how it is so.
@@onradioactivewaves I get what you mean, but the way he talks about the theoretical "game" in the first example is as if getting more points is better. Betrayal or "defecting" is usually seen as a thing you do to get an advantage. In the second example he gives you a clearer example of points in the class being something to strive for. Anyway, the point of the first "game" is not to be an actual game on its own yet. It's more like a theoretical framework to explain a concept.
@@Vezur-MathPuzzles I get what you are saying, but without some additional explanation, it doesn't make much sense. Usually there is a payoff for taking a risk. In the first example, theres no additional payoff for taking the risk of cooperating. Im struggling to find a way there would be a reason to do so, maybe thats why it keeps him up at night? Thankfully for me, I've learned to not driving myself insane by trying to make sense of nonsense.
Sinceramente, la Teoría de Juegos es tan patética que hace verse mal al resto de las Matemáticas en comparación. No es más que teoría económica que hace suposiciones arbitrarias acientíficas, como gran parte de la Economía.
🎓Become a Math Master With My Intro To Proofs Course! (FREE ON RUclips)
ruclips.net/video/3czgfHULZCs/видео.html
I think that the problem with the example at the end is that some people might value their reputation more than 1 or 2 points, therefore cooperating is actually the correct choice
The way I see it lowering the stakes would make it more likely for me to play to win (in a game with win/lose/neutral scenarios). If the outcome is not transcendental, it is seen as "just a game" and no one would take it personally. Many games (especially card and betting games) consist of lying or deceiving your opponent and no one thinks that playing it makes you a "liar" or a "bad person". You don't see people "losing their reputation" for being good at poker. Put it this way, if you were playing tic-tac-toe for 2 bonus points and you had the opportunity to win, would you not go for it? However if the losing meant failing the class, I'd be mainly focused on not losing, rather than winning. I think it'd be quite the dick move to go for the win in this case
So the moral of the story is that in order to prevent people from acting uncooperatively, you just have to shun them socially, thereby making the drawbacks of defection worse than the benefits.
@@leftylizard9085 Yup because being shunned by others is the harshest punishment known to humanity. And I'm serious about that, there is no harsher treatment than being shunned by others, for a social animal, in the wild, animals shunned by their supposed herd will die, either of depression, or to predators, or by being ganged up on and killed by the other members of the herd.
And this is the biggest difference between the right and the left politically as well, as the left loves to shun people, who disagree with them, while the right only believes that people should only be punished by the court. I wouldn't say that either side is particularly correct, let's just say I prefer the bestial course of action over all other.
Moreover, you would be seen as an a hole for craving a point so much so as to make the other lose one. I Don’t feel it’s a fair comparison either
@@polokan I think the difference there doesn't really have much to do with the stakes. If I'm playing a betting game against someone I can probably assume they knew the rules and thought the risks were acceptable, or else they wouldn't agree to play the game. And the whole point of the game is to compete against your opponent, so there's no reason to feel bad for trying to win even if the stakes are really high. But in real life you shouldn't just go rob somebody, even if the amount you're taking is much less than in the high stakes poker game.
There is a huge difference between Prisoner's Dilemma and the repeated prisoner's dilemma with memory.
Best strategy is to always cooperate, unless your opponent defects, and then retaliate by defecting. That way if rational, neither player will defect as not to be worse off from their opponent retaliating (Defecting is worse for the other no matter what they choose), and they will both cooperate and end up gaining more.
@@marcusscience23 Tit for Tat did win the Axelrod tournament. But it works on the assumption that its opponent is trying to maximise its score; play it against a strategy which just picks at random, and it does no better than random does.
@@KusacUK Playing against random, best startegy is always defect
I believe that the "rationality" of defecting in the prisoner's dilemma is cultural. There is an unfounded assumption made that the most rational thing to do is to act only in your own self interest.
In your example, defecting incurs a hidden social cost as well. So the points don't necessarily correspond to utility!
this might be the case in a game where your defection is broadcasted to the world, real life defection occurs in secret. That's one thing, another thing is that the points of defection could be themselves reputation points themselves, the connection of the systems of what "defection" exactly means and in what social situations involves a plethora of systems and it can get philosophical very quickly. Ill save you the trouble, defecting is always the better option
I think there's also a point to be made of empathy. Even with secret decisions, lets say everyone does 20 matches against different people and they only get to know their total gain/loss instead of that from each individual round, I think most people would go with cooperation because they generally don't want to screw someone over with something that has meaning beyond the game itself (i.e. class grade). Competitive natures however would probably result in people playing strictly for in-game rewards to be more aggressive with it. That said this is only speculation based off of the very limited information I have on the subject.
You chose to defect too, didn't you? Be honest.
Ye 😔
You know, if both people cooperate would be better than both defecting, but what is lacking is the trust the other person will also cooperate.
Think like this: let’s say that I cooperate. Then, if there’s a 50-50 chance that the other person would pick either, then the average would be 1/2 • 3 + 1/2 · 0 = 1.5
Then if I defect, then the average is 3.
Since 3 > 1.5, it’s better to defect.
no and i was hurt
I would refuse to play this game until i know other's player very well.
No🥲
What if instead of just choosing once, you and your opponent could choose over and over again times and add to your score each time? In that case, provided both players are rational and know it, a good strategy will be to always cooperate each time, unless your opponent defects, in that case you retaliate by defecting afterwards, partly to make up for your loss (though only to a certain extent), but mainly to disincentivise your opponent from defecting. You defecting is always worse off for your opponent no matter what they choose, and even if they had defected before it would still be worse for them than if you both cooperated. That way, your opponent wouldn’t defect so as not to provoke you and be worse off, and also knowing that you wouldn’t either with the same reasoning. This way, you can both end up being better off with mutual cooperation.
Strongly recommend that you check out The Evolution of Trust.
It has a more in-depth discussion regarding multiple rounds.
congrats, you rediscovered the optimal strategy: tit4tat
@@otesunki About two years ago I read a paper that used linear algebra to construct a strategy that could beat tit4tat. So it is no longer the optimal strategy known. (Wish I could remember the name of the paper.)
@@ericdculver o dang.
I think you missed the point your professor was trying to make. An iterated prisoners dilemma is an entirely different game and ties in to the evolution of cooperation.
The reason we have concepts such as reputation and revenge is that life in many ways resembles game theory, and overall, tit for tat cooperation is the dominant strategy by far for the individual. We see this play out in nature and human societies all the time.
You make an excellent point.
What if you did tit for tat but always defecting on the last time?
@@marcusscience23 You could only ever do that once. The next player will anticipate it and go for one more defect. You would just end up with the same scenario of trying to one-up one another on a higher level and end up inferior to cooperations between two purely tit-for-tat algorithms.
Agree :). And if you guys haven't seen, there's an amazing video by the channel 'Primer' called "Simulating the Evolution of Aggression". Especially at 5:00 and onwards, it becomes really close to this video
Defecting is a better strategy simply because there are no other objectives for agents playing, but humans, we have also social objective (bring benefit to the group), and this objective doesn't captured by solution explained.
But even if you leave out people's social instincts, group selection favors those groups who choose strategies that produce better net outcomes for all players. In fact, our social instincts probably come from such group selection. The groups that had bad social instincts died out
The classroom experiment is very interesting. To me it suggests.. punnet squares make for bad models. They just aren’t complete representations of all the decision factors.
You were going to see the other students in the class again right? The dynamics of the prisoner's dilemma change in a context of iterated play. Cheat me once, shame on you; cheat me twice, shame on me!
I'm thinking of it as a psychopath detector test.
This game gets even more interesting (like Prisoner's Dilemma) if you play repeatedly. (Ie. allowing for learning and/or 'revenge'.) There was an experiment done years ago where the winner (winning program) (with repeated games) would cooperate till 'betrayed' by the other player, then go for 'defecting'.
Interesting that if you know that you play with the exact copy of yourself, best strategy is to cooperate. Which leads to an interesting question: if both actors know the rules and play perfectly aren't they exact copies?
Folks, it's Golden Balls.
Thanks so much
Applying a little empathy and altruism to acknowledge that winning is _not_ the objective, then the winning strategy becomes not to maximise _your_ points, but to maximise _everyone's_ points. So now, 1 cooperate and 1 defect is 5 points, 2 defects is 2 points, and 2 cooperates is 6 points. Cooperating is always the better outcome as long as you're not just playing for yourself. Same as in the class since the payouts were 1, 0, and 2 for 1 of each, 2 defects, and 2 cooperates respectively.
I read about this in a Piers Anthony Xanth book. It can be inferred that he advocates, at least in a large group, for cooperating with an individual until they defect, and then defect. I think I'd have to try that too.
The professor's game kind of reminds me about that one Tom Scott's gameshow. I believe that once there's a third party being the house (or, the one who give the prize), the best strategy is not going against other players, but going against the house, aka, cooperative.
That's because the listed "payment" isn't the REAL payment, as the game is not played in isolation. The real payment includes one's reputation in the class which outweighs these bonus points.
The game's best strategy also changes in case there are repeated games for similar reasons.
Prisoners Dilemma
Sir wouldn't it be great if you signed the contact with the opponent to co-operate with you , so both you and your opponent would get 3 points and if they betray you according to the contract you can fawn over their won points
I would always coop cuz in avarge that is 6points and the others are 5 and less
I try to alway choose the bigger good instead of self good and even though my hope in humanity isn't big I still have just enough to trust the guy am playing with
defecting just means the opponent can never come out on top
Collaboration (price agreement) is forbidden in a kapitalist market. Companies are required to compete with eachother and not divide the market among the players. That's why, for example, many shops that sell similar goods in a city (clothes shops, computer shops, gas stations, banks) end up in the same streets even if they would collectively earn more if they were distributed over the whole city.
imagine the stakes, if you change the parameters to 2 countries , and the options are : peace/truce and war
"I'm going to pick Defect every time. You should pick Cooperate, and here's why: If I'm telling you the truth, I'll pay you 2.5 points for your trouble, which is still better than you could do defecting when I've clearly stated I will defect - there is nothing you can do that gets you better than that deal, since I guarantee you I'm going to defect. But if you think I'm lying, then you should still pick Cooperate, because if I'm lying and I'm actually going to Cooperate, then we'll both win 3, which is *even better*. But I'm going to pick Defect, which you can believe because there is zero benefit to me in lying about it."
Over multiple rounds of play, this produces very nearly the best possible outcome, and only 'breaks down' on the last round of a multi-round game, where I no longer have any reason to convince you I'm trustworthy to continue going along with me, and might screw you over on the bribe. How well this strategy works depends on the relationship between the 'Cooperate/Defect' payoff and the 'Defect/Defect' payoff. In the Professor's example, the 'bribe' is 1.5 points, meaning that both players gain 0.5 points of credit, which is better than they can do with both Defecting. As long as the total payout between both players in the Cooperate/Defect scenario is higher than the Defect/Defect scenario, and as long as the reward is transferable, this works.
Reminded me of this, they used your strategy some as I recall ruclips.net/video/FJSI7QTAt_o/видео.html
Winning is completely subjective here, the results aren't a bit based on the prize they are 100% based on what the prize is and what the winner really gets
defecting isn't always better because the other player isn't equally likely to defect and cooperate.
maybe if we consider the expected payout including those odds - then the "best strategy" will be different?
Somehow I got the idea in my head that getting only one point was not substantially more desirable than getting no points at all. So I decided that the risk of only getting one point was not worth the chance of getting five points, so I decided to cooperate and go for three, figuring he would see it the same way and cooperate as well.
Looking back, I don't know what I was thinking. one point is obviously better than no points.
I choose cooperate 😤
Ah, good times, earning yomi in universal paperclips
isn't this just like that show on TV split or steal except if both sides steal they end up with nothing
what _really_ ended up spooking me out was when i realised doctors and therapists were playing an unsymmetrical version of the prisoner's dilemma with me - as in, whatever my reaction would be, they were objectively better off being stubborn (and, as it turned out, making the decision worst for me)
now looking for a good trauma therapist and hoping they won't do the same shit.
i'm telling this story so people realise game theory actually _has_ applications in life, outside of actual games and economics.
you can't just leave us like that, i want to know why would they be objectively better off remaining stubborn
@@proloycodes so you go to them longer, therefore sucking all the stonks out of you
We had this at microeconomics lol
If it was not absolute grading, adding 1 pt to each student's final score doesn't change the deviation of the distribution.
Hence, all cooperating or all defecting are essentially the same.
John Forbes nash was a brilliant guy
I actually chose to cooperate, even knowing full well that you’d defect ❤️ 😇
Still though, an interesting game that requires the mastery of human prediction in order to consistently win 🤔
Same by doing so in real life we can prove our benevolent nature and prove honestly
As humans most of us will always go with what makes us feel good and not rock the boat. Everyone that is a B personality and below will take this route. A personality will strive to win as that is how they approach life. Again it’s about winning for some and others are comfortable just breaking even. The professor should have staked the entire class grade on the outcome to see how it would change the dynamics of this test. Again some would choose the F over being confrontational. Others wouldn’t bat an eye at taking the win or A.
That thumbnail is such clickbait.
My man speak facts
It’s not though
@@ahsaasinator2840 come on my guy. You have to know that people on the internet can tell jokes. This is too absurd to be serious.
If let's say you played a tournament style against 5 other pairs of plates so ten total and kept your cumulative sum through all the matches, there may be an incentive that would motivate you to play Cooperative being that you score 3 each instead of one each, each turn. And then the highest score at the end amongst the individuals would win. You could do the same thing but rotate each match or rotate at some number of matches. Or you could play as pairs and as pairs you would switch off playing with your partner then with not your partner but then it would really just be when with partner play Cooperatively and when with other play defect since 2 rounds gains 3 each round so six each and a cooperative/defect sorta switch back and forth gains only 5 total for each player. It would just become that sorta thing so playing as individuals against each other but at different times is probably the only way you could incentivise the cooperative move. That sorta setup could prolly actually be used in a logic setup that allows for deceit, so would understand it better for neural network architecture. Hmmmm
If the game goes past 1 iteration, Defecting is the least optimal strategy as no one will cooperate and why should they if they know you're going to defect anyways.
The way I look at it in the first example it is just meaningless points and your only way to win is to have more points than your opponent and if you have an equal amount of points neither of you win. In the second however the more points each of you have the more extra credit you get therefore a tie is a win for both of you as opposed to just a tie.
I think the superratinal thing to do is cooperate
welcome to the shortest 1 facet personality test
the other problem with this game is the hidden assumption that the objective is selfish, to score for oneself as many points as possible, whereas for me and many others, the goal in life is to achieve the greatest outcome for all, and in that paradigm, it's always better to cooperate in this game.
This game has been simulated with various strategies. If you set up a game where you play multiple times against the same opponent and then switch to another person in your class while tracking your point total for all matches. The best strategy is a tit-for-tat. That is, start by cooperating and only defect after your opponent defects. If your opponent cooperates, change to cooperate on the next round.
Mr beast did something similar but w real money...
you can either choose to share or to steal
If both people share they get $ 5000 each
If both choose to steal neither of them gets any money
and if one chooses to share and other chooses to steal, the thief gets $ 10 000 and the nice guy gets nothing...
I hate what this game is teaching.
First, the lack of communication is not a normal circumstance (hence the name of the dilemma).
Second, the point values for the different scenarios are usually called unjust.
Third, a rational player does not play for their own intrest, but for the interests of all rational players. A little poverty that means more wealth for the whole race is better for each individual, too.
In such cases (a class being an example) where you trust your classmates to a certain extent (or both players are aware that the other person cares about what the entire class will think of them) can't we add a probability that the opponent will defect? This probability being low means high trust and vice versa. Would such a modification change the winning strategy?
Not by itself no. Because even if let's say that there is a 90% chance that your classmate will cooperate, that leaves your choices as Cooperate: having a 90% chance of you getting 3 points, and a 10% chance of getting 0 (so an expected value of 2.7 points) and Defecting having a 90% chance of you getting 5 points and a 10% chance of you getting 1 (so an expected value of 4.6 points), so defecting is still the best choice for you. And flipping the odds the other way doesn't change things either (if there's a 90% chance of them defecting then cooperation ends up with an expected value of 0.3 points, and defecting having an expected value of 1.4 points, so defecting is still the better choice.
The issue here is that it doesn't matter what the odds of the opponent's choice are, regardless of their choice, defecting will always give you more points than cooperating, even if they were guaranteed to cooperate, then defecting would just give you a guaranteed 5 points which is the max payout (and if they were guaranteed to defect, then obviously defecting would be the only way you could get any points).
The only way to make cooperating worth choosing is, as others have pointed out, is to effectively attach other consequences and benefits to the choices. Such as playing repeatedly in which the best strategy becomes cooperating unless/until your opponent defects. This effectively causes the choices to not only affect this game, but later games as well. In other words, the deciding factor isn't your opponents trustworthiness, it's your own that causes cooperation to become optimal.
@@phiefer3 oh yeah that makes sense. Guess I didnt really give my comment much thought.
if the stakes were high it could've gone the other way
Defecting is only the best strategy if your opponent is guaranteed never to learn from their past experience and therefore guaranteed never to act on their past experience, which is a situation that never actually happens in real life.
Also, defecting is only the best strategy if the given rewards and punishments in the game are the only rewards and punishments that exist, which is also a situation that never actually happens, because the human mind is ridden with all manner of conflicting drives and desires. For example, cooperating is very often intrinsically rewarding to the human psyche.
With the assumption that you could trust each other not wanting to be 'the jerk that defects' you start looking more at the mutual gain than purely your own. By taking the sum of the individual points and considering that you get 2 points as a pair for both coöperating, 1 point (2 - 1 or -1 + 2) for one defecting and the other cooperating, and 0 points for defecting each other. This way the game turns more into a Stag Hunt, and the trust that you'd rather risk the other betraying you for getting a win-win and, in way, beating the teacher who put you in this game together.
The problem is that maths doesn't consider emotions, values such as morals and empathy and other human traits. The best strategy according to maths isn't always the best strategy in reality whenever it is about human interaction.
It's actually very easy to model these emotions with the math: simply add the points given to both players into 1 value. Then cooperating will always give the best outcome in both scenarios since 5 > 2 and 6 > 5.
Defect
This only applies in a zero sum game.
If your goal is to defeat your opponent, then you should defect; the amount you win by is irrelevant, and cooperating will never let you win.
If your goal is to gather as many points as soon as possible, you should cooperate. If the other defects then their a dumbass that can't be trusted, prioritizing short term gain over the long term.
I think the non-intuitive result comes from two assumptions: 1. You have no knowledge of your opponent's strategy (so you assume either choice is equally probable) 2. There is only a single payout. In the single-payout scenario, you have no incentive to cooperate, but I think a lot of people think about these games as being repeatable, and if you are playing over and over with the same person, the best strategy would be to cooperate. But if you were playing with strangers every time, then you should always defect.
Is there any reason for the rules to benefit defectors over cooperators? It seems there is not.
So, what if the reward were the reverse?
I'm unsure as to whether this is a true mathematical game instead of a one of socio-economics.
Our capitalistic way of thinking doesn't promise a sure reward for defectors, but the possibility of it, and this is what suffices for people to ignore what seems to be the logical goal of living in society, to cooperate, by starting the all out competition (did I say war?) of everyone against everyone else that we still don't tire of living through day after day.
This is perhaps why young people are prone to challenge such rules by choosing cooperation, maybe by 'instinct' (one would say 'innocence'), maybe from the received - moral, religious - education (through which we pretend we try to assuage somehow the de facto scenario of generalized enmity): they wouldn't still be prepared to live their lives through with the weight of such an incoherence, as it seems obvious that living in a group is a choice for cooperating.
This is also not to say that the capitalist system, which stems from that apparently harmless operation of exchanging goods according to their presumed relative value, has been a choice for self-inflicted perversity that we've been making for generations in a row, but one that at a first look appears to be quite just.
In quite good faith we just didn't foresee the most immediate consequences of this simple game whose rules everyone is capable of grasping, and to which we ended up adapting, as expected.
However, we at least have learned that the hell is plenty of the best intentions.
Because defecting gets you a bad reputation. And many people care a lot about their reputation.
If people were playing this game over and over, the strategy cooperate with those who cooperate with you is a good one. A bunch of people who know defection will get them points this round, but loose more points next round.
Of course, this can only happen in big brained animals that can track who cooperates. Which is why a lot of complicated working together behavior only appears in big brained animals.
There is a difference between playing once - where your analysis that always defecting is the best strategy - and playing multiple times - where your current choice affects the future choices of your opponent. With three points for both cooperating you only need to get the other player to cooperate more that one in three turns to get a better return. Axelrod in his book "The Evolution of Cooperation" details an experiment where the game was played multiple times. There the best strategy was determined empirically to be "tit for tat". Your first move is cooperation and for subsequent turns you make the same choice that your opponent made in the previous game.
I dont get it ...co-op is the best win-win situation...
yeah but its mentioned that players can't talk to each other so no way to strategize like that
It's just among us
If I really know that you will cooperate, I will also cooperate. Not doing so would be a jerk move.
U can't call the guys who choose to defect 'Jerks'. Because mathematically it is the best and most correct strategy to choose as you acknowledge here & remember this is a test under the game theory also. Further, the guys who choose the 'Defect' option might have trust issues with society or with the opponent due to various previous reasons. So they are not 'Jerks'.
The only 'Jerk' here is the professor himself.
it is better to defect because I trust no one... and there is still a probability that they will betray you... 1 is still a win tho
Why is it frustrating? Individual choices being different than collective choices is baked in the problem, given that there's incentive to not cooperate on individual choice pov. The fact that you ignore what the other is doing shouldn't surprise you to the fact that you aren't always cooperating. In fact if you exchange 5 and 0 in your example, your answer will be to always cooperate. In fact, if you changed 5 to 7 you'd win more if you alternated cooperation and betrayal to maximize your outcome with the other participant. So if the result you wanted was to cooperate, you'd have exchanged the 5 and the 0.
If you guys simply couldn't communicate, you'd always choose defect, for the worst outcome is nothing changes.
actually, the other player would probably defect, so you should really play multiple times and keep cooperating until they also do(they have morals) and then it would be better than if both players defected each time
hi, can you tell me what software
you use to make such a video? thank you
Did we just get SAWed?
choose to defect.
Не смотрел видео, так что вначале отвечу, как я бы сделал :)
Я бы нажал на дефект, и сказал бы тебе, "я скооперировался, кооперируйся тоже!". А сам нажму на дефект. Если ты поверишь мне и решишь скооперироваться, то я получу 5 баллов, а ты ноль. Если бы я кооперироовался в этот момент, то получил бы меньше очков. Если же ты не поверишь или захочешь предать, то я получу больше (1 балл), чем получил бы в случае нажатия на кооперэйт. Проблема этой стратегии дьявола в том, что если и ты будешь таким же умненьким, то мы гарантировано получим 1, что невыгодно для обоих. Куда более лучшей и надёжной стратегией было бы та же, но только с условием того, что мы - хорошие друзья, и ты мне веришь (правда терять дружбу из-за такой игры довольно глупо, хехех). Однако этого, увы, уже подкрутить не могу¯\_(ツ)_/¯.
The mistake in this "best strategy" argument is that it assumes the actions of both players to be independent, i.e. you can make your decision while the other has already committed to a decision. But if you actually run this experiment, particularly if you repeat the game with the same pairings (so that trust plays a role) you will probably find a strong correlation between both players' choices. So unless you're playing this one-shot with a person you have never met and never will again, even though you changing your strategy doesn't CAUSE the other to change their strategy, they will still be correlated, so it's kind of easier going diagonally in the diagram (correlated strategy change) than horizontally / vertically (uncorrelated strategy change).
I hate when people try to apply this thought experiment to the real world as an argument against social altruism.
I defected lmfaoooo
Butta listen to this at 23:32
Competition, hah? 🙁
Very much Liberalism.
Dominant? Lion Spirit? 🦁
Dracula or what? 😜
This is exactly what is happening to marriage nowadays.
Experiment of prisoners dilemma done and for genders for men and women not just mathematicians. “Big Five” personality traits. Agreeableness and Conscientiousness. Experiment done on women and men women are more related with Agreeableness - The agreeableness trait reflects individual differences in general concern for social harmony. Agreeable individuals value getting along with others. They are generally considerate, kind, generous, trusting and trustworthy, helpful, and willing to compromise their interests with others. Agreeable people are quite considerate and are willing to compromise. They want to keep social harmony and results are secondary to them. They demand inclusivity and care. Agreeable people do not like conflict, the do not want fights to break-out, they do not want anything to disturb the relative peace.
And men are dickish adsholes:) flexible slickers thugs, thus conscientiousness is a tendency to display self-discipline, act dutifully, and strive for achievement against measures or outside expectations. It is related to the way in which people control, regulate, and direct their impulses. High conscientiousness is often perceived as being stubborn and focused. Low conscientiousness is associated with flexibility and spontaneity but can also appear as sloppiness and lack of reliability. [2]
Conscientious people judge others on results and accomplishments, they do not care about people’s feelings. They demand high level performance and results.
Mathematician have more agreeableness tendency mathematicians knows odds but more mathematicians choose irrational non stoic decision not betrayal partner in crime, even it will have consequences. I think more mathematicians want to keep social harmony and results are secondary to them.
I chose to cooperate because I've heard of this game before
Edit: wrong game sorry
Your professor's dilemma is not equivalent, because in the standard scenario the two players are only competing against each other, but in your class they were also competing against the other pairs. In that circumstance, agreeing to cooperate is a more valid strategy.
your professor was a psychopath
A classic demonstration about how philosophical musings are just armchair nonsense that doesn't translate into the complexity of the real world
I don't think it's right to call always defecting "the correct strategy" and "the way you should play the game" in contrast to the way your class played. It *is* the correct strategy if your only goal is to maximize your own gain, but once you add in empathy, morality, or social repercussions, that's not longer true.
wow that was great! Its an interesting dilemma
1
Did you leave out some of the rules? What if the point is to have the least points? What do the points even do? Are we competing against another team somehow? See who gives up first after realizing there is no point? I'm not understanding how the game first described is a complete game, based on the stated rules.
Personally, I think it's a safe assumption that more points is better, judging by the majority of sports that have more points as the goal, though I'm biased by previous game theory videos.
@@cameronbigley7483 could be more points is better, but the game still seems pointless, since you both get the same amount of points if you choose the same and more for not cooperating, seems like the only point would be to trick someone who didn't understand the rules ( a bar game to swindle someone possibly).
@@cameronbigley7483 I'm teying to give him the benefit of the doubt here since I'm sure he got more math under hos belt than I do, but from what little I know about game theory, this is not a mathematically complete game, let alone functional somehow based on the rules given. Or it is, and I would like to be enlightened on how it is so.
@@onradioactivewaves I get what you mean, but the way he talks about the theoretical "game" in the first example is as if getting more points is better. Betrayal or "defecting" is usually seen as a thing you do to get an advantage.
In the second example he gives you a clearer example of points in the class being something to strive for.
Anyway, the point of the first "game" is not to be an actual game on its own yet. It's more like a theoretical framework to explain a concept.
@@Vezur-MathPuzzles I get what you are saying, but without some additional explanation, it doesn't make much sense. Usually there is a payoff for taking a risk. In the first example, theres no additional payoff for taking the risk of cooperating. Im struggling to find a way there would be a reason to do so, maybe thats why it keeps him up at night? Thankfully for me, I've learned to not driving myself insane by trying to make sense of nonsense.
This problem is like communism 🔥
People promise to co-operate but they defect 😂😂
Sinceramente, la Teoría de Juegos es tan patética que hace verse mal al resto de las Matemáticas en comparación. No es más que teoría económica que hace suposiciones arbitrarias acientíficas, como gran parte de la Economía.
😂 1>👅🤗
it's this fucking game again. why do yters have to still upload basically the exact same video about the same topic?
There is no reason to pick cooporate at any point or in any version of this game. The goal of the game is to collect points.
1