How could it be that my professor at university cant explain the game theory and nash equilibrium in over multiple hours and only one RUclips video with 6 minutes content will provide me with everything i ever wanted
learned this in my MBA economics courses. I use it for everyday life. Great to learn. If you dive deeper into than this video does, (read a book on it), it will do you much value in life.
Your psychology teacher probably just knew that most people in the room aren’t likely to abstract at genuinely high level, making it difficult to understand for many. Mash equilibrium probably makes sense to the people who have a passing interest in it to begin with, which probably goes back to that fact that their brain is better at abstracting than others. A lot of people in an average cognitive range actually struggle with formal logic in general, so concepts like Nash Equilibrium will likely seem like nonsense to them. That’s okay too
Anna banana this is the first time I recall hearing about Nash equilibrium and I could do some help but it does sound easier to rock than I first thought. Let's see what we can do with this.
@@maddawgzzzz can you give us some suggestions? Names? Links? Where's a good place to start, the easy way and still be accurate, in understanding this equation? Your help is most valued! I think I remember who Nash was so I'm going to start there.
Just watched A Beautiful Mind and wanted to know more about Nash and his work. As someone with severe mental health disorders, and with partners who have been committed for long periods of time, Nash's story is extremely inspirational to me, I love that someone with such debilitating disabilities can still be such an influence. I love math.
Agree, is just common sense from where it seems. I hate when a light turns red when nobody is coming/is on my left or right and I thinkis a waste of time.
I never comment on videos, but I'm definitely showing and using this example in teaching my econ classes. Thank you for a great and easy to understand example.
If both players stop, it's going to take them some time to figure out who is going to go first, which is bad for both of them. If I stop and you just go, then I know I can go immediately after you pass.
But how are they going to know who is going to stop or go ? Since they would know that going may result in a serious loss wouldnt they refrain from choosing "go"?
Well, if you go deeper into this course, you will discover that there is also a mixed strategy Nash equilibrium. In it, each side sometimes yields and sometimes does not. The observable implications are pretty chaotic, just like what you described!
Bro even I am from India and while he explained even I was curious and thought such thing wouldn't work any where in India. Because we have an inflated ego. But... I analysed it a bit differently with an example I have encountered recently. And it goes like, I along with my friends were travelling in an auto. And as part of our route we had to take a narrow lane in which only one vehicle can fit at a time. So, when we are almost 90% through it, we encountered another auto in opposite direction. Now imagine the Nash equilibrium. The options we have: 1) Give into our egos and crash into each other, and get both the vehicles damaged. 2)Maintain a stand still and create a long traffic jam. 3) Let us pass through. Then the other auto can also get a clear path. 4) Give way to the opposite auto, and go back 90% of the way we just covered. The most logical and less time consuming solution was option 3. That's what we chosen that day.
@@shashanksagar1534 yes but u also have to consider the singular implications of each players possible decision making on the total outcome because if one can benefit consistently ur example doesn’t work
I have always been so intrigued by mathematcis and its theories. I wish I had the super power mind to understand it all!! Subbed your channel, planning to watch all your vids. You breakdown info the way I learn. This could be a new start for me!! *THANK YOU!*
2:36 Nash Equilibrium fails in India. Everyone will go at the same time, yet no one gets hurt! Accidents are less in India compared to the resources and population the developed world has!
So in this example, both players have perfect information of what the other is seeing. Is this a pre-requisite of Nash equilibrium? What happens if the other driver sees a green light and then he automatically think (assume) that the other one is seeing a red? Can somebody shed some light about this?
Great video! I feel Nash Equilibrium is the kind of theory that needs a complex real life problem to make it easier to absorb because it's way too fundamental and neat.
Mr. William Spaniel, thank you for all the videos for Game Theory. They helped me a lot to get my 1st class in this subject and also, to better understand the theory and how it can be applied. It is really well explained! Good job and keep the good quality of the videos !
William Spaniel "Non-Cooperative Games" is only about 30 pages. Do you think it would be too hard to read and understand for a person that doesn't know anything about math?
That paper is a fun combination of abstract math and fixed point theorems. Really important and really interesting, but not worth reading unless you have had the background classes.
But if P1 chooses stop, P2 is better off going. A nash equilibrium is only when P2's strategy doesn't change when P1's does or vice versa; in other words, it's only a nash equilibrium if someone is better off doing the same thing regardless of the other players strategy
Nature of games is that they are "turn based". Hence why it is a nash equilibrium if both players benefit from it. It has something to do with it being a dominant strategy for each player, regardless of what the other does or when he does it. But since its turn based one of them has to go first.
I guess there's something wrong here! I am not sure if i am the only one who is noticing it! In the game of the red-green light, the outcomes should be for ONE situation when player 1 has the green light and player 2 has the red light! You seem to be saying that cell [0,1] is when one has green light and cell [1,0] is when the other has the green light! This is incorrect! We have one situation and we write the outcome for it. To say it in another way: we have one situation: player 1 has red and player 2 has green. So there two options for player 1, either stop or go and two options for player 2, either stop or go and in then we have a matrix and the cells [0,1] and [1,0] will not be equivalent because player 2 is expected to go and thus should be able to go, if stopped then his payout should be less. . . i propose the following outcome cell[0,0] = (-5,-5), cell[0,1] = (1,-2), cell[1,0] = (0,1) and cell[1,1] = (-1,-1) and it has no Nash equilibrium! clearly this game has no Nash equilibrium or you don't need to police to monitor people!
Why would cell[0,1] have a harsher punishment for stopping than cell[1,1]? Player 2 is still getting to the destination in [0,1] faster than in [1,1] because while he is stopping in both cases, in [0,1] he is avoiding the awkward game of who goes first with the other car. Even if you adjust [0,1] to be (1,-2), cell [1,1] should be further adjusted to something like (-1, -3) since it's worse to both have to stop at a green, and then also play who goes first.
That's an intuitive example in theory, but one that quickly breaks down in practice. There would be no justification for stoplight cameras if that were true. Worse still is that fact that running the light doesn't guarantee that the outcome will be a crash every time, so there's an incentive to play the odds. I'm a total novice at game theory, but in real life the stoplight scenario seems more like a prisoner's dilemma than a Nash equilibrium. The incentive is to always go, but the disincentive is a wreck or a ticket. If you both follow the law, you run zero risk, but if one person runs the red light they have good odds that they will escape the consequences. If they both break the law, they both get a ticket (assuming they get caught)- one for running a light and the other for obstructing traffic. Ignoring the green light only benefits you if the other person runs the red light at the same time. Running the red light has the highest risk but also the highest rewards. That sounds to me like the Prisoner's dilemma, but I could be wrong.
But did you come up with this thought experiment out of the blue? This is the simplest possible explanation that makes it seem commonsense. This is applicable when there are N number of players. Then you need a formula and not just commonsense
Interestingly enough, the stoplight example doesn't work for each and every case in real life, but on big numbers it becomes clear that it is indeed a good example of Nash equilibrium. So we're talking not about absolute law, but statistically correct law
So, according to your interpretation of the Nash Equilibrium. nobody would ever run a red light. Or anyone who did, would not be by definition, a rational person.
The problem, which separates theory from reality, is that humans are terrible at doing risk assessment. Going despite the red light is a -5 situation, because the other guy will crash into you. Going over the green light is a 1 situation, because you reach you destination faster. Now people are naturally optimistic, meaning those who go over the red light can only see "reach the destination faster" not the "other guy will crash into you" situation. TL;DR this theory doesn't work with us, because we suck at math.
@@xellos5262 Well, if it is a world without law enforcement, what if you've got a red light but you're driving a 12 wheeler truck and the other guy is driving a mini cooper. Is it irrational to go over the red light or just douchbaggery? Is douchbaggery a synonym for irrationality? This situation is a Nash Equilibrium only if you assume which types of vehicle are possible, not just the rule. If you also assume eventual damages to the mini cooper driver are also negative to the truck driver, you're assuming the psychology of players to fit your moral standards and that feels like a failure in risk assessment.
@@XxKnuckleSOverlorDxX Both the vehicle type and the psychology of the driver are additional parameters, each of which gets its new dimension in the matrix. This therefore creates a new equilibrium.
@@xellos5262 I mean in this theoretical world I would also benefit if I honk my horn and make it clear I'm not going to stop, forcing the other player to stop.
@@lukasg4807 if you honk, and therefore demonstrate you will not stop, the other player can still choose to not stop. There is always a choice, and when there is a choice, parameters are taken in. If this stuff were this easy, even Elon Musk could build a real self-driving car. It isn't, and because it isn't, true self-driving is impossible with the type of AI we have.
Stoplight isn't the best traffic analogy. Four-way stop sign is better. The stoplight isn't a simultaneous game. It is a leader-follower situation. At a 4-way, it is possible for both drivers to stop at the intersection at the same time.
It's not an analogy though, it is an actual example of Nash Equilibrium. Of course it may not work as such in all countries. I do think that 4-way stop may be an even more clear example.
I think to sum up most of he criticism in the comment section on the stoplight analogy is that nash equilibirium assumes that both parties are aware of the consequences of not following the rules (assuming no police exists), but in the real world people are either no. 1 they are not aware of consequences or no. 2 they are immune to the consequences or no. 3 they dont.care about the consequnces.
This Nash Equilibrium example is apt if people participating can assume that others will follow traffic light. In parts of the world, there is the expectation that no one else will follow the rules and therefore if you follow the rules, you will never get to your destination in reasonable time. This leads to every one trying to cross the intersection to maximize their transit time with the hope that others will yield--it's really a game of chicken in display--never mind that it increases the traffic time for every one involved.
Interesting and clear explanation. And yet... People run red lights every day. Why? My guess would be because there's never just one game going on at a time. e.g., bank robber fleeing police, rush to the hospital with a dying loved one in the back seat, etc
Where are the numbers in the matrixes from? I don't understand how there are set (determined)? Otherwise thank you for explanation on the nash equilibrium, I understood well thanks to the light example.
Ok but what if you decided that the only negative outcome is a crash then both players would want to stop because in that case the smartest choice for both players to make would be to stop because now their outcomes don’t rely on the other players decisions meaning that each player is making the smartest possible decision
Does the Nash equilibrium account for ANY chance of a player changing strategy? Say even a .000001% chance?? Or does if require 100% obedience for it to remain valid?
Nash equilibrium does not, but a refinement called "trembling hand perfect" equilibrium does. Not all Nash equilibria are trembling hand perfect, but the examples in this video are.
I know the utility values here aren't meant to be entirely accurate but why is the outcome of both of them stopping -1, -1 while the outcomes of only one of them stopping are 0, 1 and 1, 0? Shouldn't all "Stop" strategies result in -1, effectively changing (Stop, Go) = -1, 1 and (Go, Stop) = 1, -1?
Think of it like this. If we both wait, then we are back to square one at the next moment. Should I go? Should you go? That outcome is worse for me than if you clear the intersection from the start, because I know to just go immediately afterward.
It's a bit under 300 pages. It will keep you busy. If you eventually want to become an "expert" on the subject, you are pretty much stuck buying the $75 textbook from Fudenberg and Tirole. But that's written more as a reference manual than an actual teaching book.
Doesn't this depend on the value judgements we assign to each outcome, which could be highly subjective depending on the players involved? Eg. I may value getting to work on time more/be more prepared to take a risk of damage because I have a really important meeting to get to?
I recently watched the movie and was touched emotionally....and start searching all about Nash. Could anyone help me with something I dont understand. What is the purpose of this theory. How it can be applied? Can it help in resolving important issues . At first it looked so simple but then it is actually very complicated for someone like me who is not mathematician but I tend to have strange ideas others cant see or understand quickly
Because it is assumed that the cars will crash into each other, the consequences of which (damaged car/s) are far worse (-5) than the inconvenience of stopping/waiting (-1)
The game is not a correct representation of a traffic lights situation. there must be a probability assigned to all the outcomes. Going through red led will not always have a bad outcome. And according to the comments the probability depends on the country you’re in. So for instance in India the probability of a bad outcome by “go” will be so low that it pays off to drive through red. Also the action each player had to chose from at the same time is different. When player 1 have red, player 2 will have green. And When player 2 have red, player 1 will have green.
I have a small query; you say that no one would want to break the law of obeying the traffic light, but what if, for example, they were on the run for the police? Is there an example of a Nash equilibrium containing an action that no one would want to break under ANY circumstances?
William, actually, I quite don´t understand why Stop-Stop -1/-1 is not the Nash Equilibrium. It says: Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy. let me give you an example to your example ;-) : Player1 follows Stop, then he gets 0 or -1. If he follows Go, he gets -5 or 1. f I sum that up, the outcome of stop is better then the one of Go. So why is Stop Stop not the Equilibrium? The GO-strategy is also not stable. If both Players say go, then we get -5/-5 Thank you in advance
Stop-stop is not a Nash equilibrium because one of the players can do a unilateral strategy change to do better. Instead of stop-stop, one player can decide to go instead and change the payout from -1 to 1 for him/her.
But here they have, in the stoplight example, a indication telling them what they "should" do! What if they don't? What if there's no stoplight at all, and there's these 4 outcomes, and they don't know what the other will choose? I see lots of exercices where that seems to appear...who would know if they were supposed to go or stop?
IF you take it as nobody would want to make a different move/choice, does that mean that given the nash equilibrium that all players are getting equal results?
great video, very well explained. But the one thing i don't understand is : How is this theory useful to us in our real life and what are its applications?
Wouldn't the outcome if both players stop be -1 for the player with green light and 0 for the player with red light since she was going to stop anyway?
This is probably the origin for the name of the 1950's Nash Rambler... for it's-not-properly an equilibrium-rather the equilibrium point or fulcrum would be the saddlepoint between four-corner-twistings, the local minimum 'betweenish' the here odd corners which are co-maxima standoffs not equilibria... easier to see on a continuum gameboard; better in 3D.
Well answer me this: did John Nash's Equilibrium Theory lead to the development of deregulation? Simply put, is his theory responsible for the deregulation of the power industry, the trucking industry, and the great breakup of Ma Bell?
@@pmtips4482 Ok agree. To your main point, idk if Nash was used to justify deregulation, but it is logical. Possibly it was used as an excuse without actually doing the math.
@@nmarbletoe8210 It is an interesting subject no doubt. I have read where the Nash Equilibrium did not include factors for greed, corruption, and fraud but I can't really verify that. Even if it was factored in, to what degree ?
How could it be that my professor at university cant explain the game theory and nash equilibrium in over multiple hours and only one RUclips video with 6 minutes content will provide me with everything i ever wanted
Exactly
2:22 I like how the car crash is considered only 5 times as painful as waiting at the red light lmao
Hey man I’m in a hurry here!
My psychology teacher said that Nash's equilibrium was hard to understand, but this is actually easier to understand than I thought it would be
learned this in my MBA economics courses. I use it for everyday life. Great to learn. If you dive deeper into than this video does, (read a book on it), it will do you much value in life.
Your psychology teacher probably just knew that most people in the room aren’t likely to abstract at genuinely high level, making it difficult to understand for many. Mash equilibrium probably makes sense to the people who have a passing interest in it to begin with, which probably goes back to that fact that their brain is better at abstracting than others. A lot of people in an average cognitive range actually struggle with formal logic in general, so concepts like Nash Equilibrium will likely seem like nonsense to them. That’s okay too
@@nicholasmatthew9687 Your introspection without lessening "others" who don't understand, simply is respectable
Anna banana this is the first time I recall hearing about Nash equilibrium and I could do some help but it does sound easier to rock than I first thought. Let's see what we can do with this.
@@maddawgzzzz can you give us some suggestions? Names? Links? Where's a good place to start, the easy way and still be accurate, in understanding this equation? Your help is most valued! I think I remember who Nash was so I'm going to start there.
Just watched A Beautiful Mind and wanted to know more about Nash and his work.
As someone with severe mental health disorders, and with partners who have been committed for long periods of time, Nash's story is extremely inspirational to me, I love that someone with such debilitating disabilities can still be such an influence.
I love math.
Game Theory and Behavioral Economics are amazing fields of study
same here
This sounds more like common sense. But what most people would be interested to learn is how Nash converted common sense into a mathematic equation.
Agree, is just common sense from where it seems.
I hate when a light turns red when nobody is coming/is on my left or right and I thinkis a waste of time.
Ironic how something seemed common sense is not so obvious all the time.
You'd be surprised with how uncommon "common sense" is
If only more people took a moment to understand this. RIP John Nash.
Epic
So deep
James Beningfield
January 7, 2018
Yes, James, it is soooo deep! Because, it actually flowed from the Mind of GOD first! WOW!
Is it basically unwritten rules we instinctively need to follow?
Good one Nash Equilibrium well understand
I never comment on videos, but I'm definitely showing and using this example in teaching my econ classes. Thank you for a great and easy to understand example.
Thats too bad. I hope you include some real world facts along with this limited theory.
@@MSpeedThree if both players go, then that would cause a crash, or if they both stop, then they will hold up traffic, which is a problem.
If both players stop, it's going to take them some time to figure out who is going to go first, which is bad for both of them. If I stop and you just go, then I know I can go immediately after you pass.
But how are they going to know who is going to stop or go ? Since they would know that going may result in a serious loss wouldnt they refrain from choosing "go"?
@@tanercaslaman I guess that would be the job of traffic lights
Still come back to this from time to time years later when I'm in an economics mood, great video!
The whole clip along with comments "make my day again"
1:38 the gulp is unreal
Cme to India buddy... Here no Nash but 'rash' equilibrium...
Well, if you go deeper into this course, you will discover that there is also a mixed strategy Nash equilibrium. In it, each side sometimes yields and sometimes does not. The observable implications are pretty chaotic, just like what you described!
Bro even I am from India and while he explained even I was curious and thought such thing wouldn't work any where in India. Because we have an inflated ego.
But... I analysed it a bit differently with an example I have encountered recently. And it goes like, I along with my friends were travelling in an auto. And as part of our route we had to take a narrow lane in which only one vehicle can fit at a time.
So, when we are almost 90% through it, we encountered another auto in opposite direction. Now imagine the Nash equilibrium. The options we have:
1) Give into our egos and crash into each other, and get both the vehicles damaged.
2)Maintain a stand still and create a long traffic jam.
3) Let us pass through. Then the other auto can also get a clear path.
4) Give way to the opposite auto, and go back 90% of the way we just covered.
The most logical and less time consuming solution was option 3. That's what we chosen that day.
@@shashanksagar1534 interesting implication
@@shashanksagar1534 yes but u also have to consider the singular implications of each players possible decision making on the total outcome because if one can benefit consistently ur example doesn’t work
lmao! rASH equilibrium,... badass
I have always been so intrigued by mathematcis and its theories. I wish I had the super power mind to understand it all!! Subbed your channel, planning to watch all your vids. You breakdown info the way I learn. This could be a new start for me!! *THANK YOU!*
I've been a fan of your geopolitics content for a while now and now I'm watching this for my microecon class lol
2:36 Nash Equilibrium fails in India. Everyone will go at the same time, yet no one gets hurt!
Accidents are less in India compared to the resources and population the developed world has!
Possibly they are using the Nash Equilibrium but for a different game, none that ignores signs and laws.
So in this example, both players have perfect information of what the other is seeing. Is this a pre-requisite of Nash equilibrium? What happens if the other driver sees a green light and then he automatically think (assume) that the other one is seeing a red? Can somebody shed some light about this?
The stoplight just tells players what to do. We don't have to follow it if we don't want to. The point is that we should.
Great video! I feel Nash Equilibrium is the kind of theory that needs a complex real life problem to make it easier to absorb because it's way too fundamental and neat.
Great explanation! Always is possible to explain difficult concepts with simple examples
been 9 years and still the single best explanation on youtube
Mr. William Spaniel, thank you for all the videos for Game Theory. They helped me a lot to get my 1st class in this subject and also, to better understand the theory and how it can be applied. It is really well explained! Good job and keep the good quality of the videos !
Crazy how you explain it and ironically R.I.P Mr. Nash and his wife died in a car crash.
This was a brilliant explanation. Thanks so much
Why was John Nash's paper so much longer than this video?
***** Nash showed that such equilibria exist for a broad class of games, which is what's really remarkable.
William Spaniel "Non-Cooperative Games" is only about 30 pages. Do you think it would be too hard to read and understand for a person that doesn't know anything about math?
That paper is a fun combination of abstract math and fixed point theorems. Really important and really interesting, but not worth reading unless you have had the background classes.
But if P1 chooses stop, P2 is better off going. A nash equilibrium is only when P2's strategy doesn't change when P1's does or vice versa; in other words, it's only a nash equilibrium if someone is better off doing the same thing regardless of the other players strategy
Nature of games is that they are "turn based". Hence why it is a nash equilibrium if both players benefit from it. It has something to do with it being a dominant strategy for each player, regardless of what the other does or when he does it. But since its turn based one of them has to go first.
I guess there's something wrong here! I am not sure if i am the only one who is noticing it! In the game of the red-green light, the outcomes should be for ONE situation when player 1 has the green light and player 2 has the red light! You seem to be saying that cell [0,1] is when one has green light and cell [1,0] is when the other has the green light! This is incorrect! We have one situation and we write the outcome for it. To say it in another way: we have one situation: player 1 has red and player 2 has green. So there two options for player 1, either stop or go and two options for player 2, either stop or go and in then we have a matrix and the cells [0,1] and [1,0] will not be equivalent because player 2 is expected to go and thus should be able to go, if stopped then his payout should be less. . . i propose the following outcome cell[0,0] = (-5,-5), cell[0,1] = (1,-2), cell[1,0] = (0,1) and cell[1,1] = (-1,-1) and it has no Nash equilibrium! clearly this game has no Nash equilibrium or you don't need to police to monitor people!
Why would cell[0,1] have a harsher punishment for stopping than cell[1,1]? Player 2 is still getting to the destination in [0,1] faster than in [1,1] because while he is stopping in both cases, in [0,1] he is avoiding the awkward game of who goes first with the other car. Even if you adjust [0,1] to be (1,-2), cell [1,1] should be further adjusted to something like (-1, -3) since it's worse to both have to stop at a green, and then also play who goes first.
Its jist an example dudes the graph is correct the words dont matter just the graph
That's an intuitive example in theory, but one that quickly breaks down in practice. There would be no justification for stoplight cameras if that were true. Worse still is that fact that running the light doesn't guarantee that the outcome will be a crash every time, so there's an incentive to play the odds. I'm a total novice at game theory, but in real life the stoplight scenario seems more like a prisoner's dilemma than a Nash equilibrium. The incentive is to always go, but the disincentive is a wreck or a ticket. If you both follow the law, you run zero risk, but if one person runs the red light they have good odds that they will escape the consequences. If they both break the law, they both get a ticket (assuming they get caught)- one for running a light and the other for obstructing traffic. Ignoring the green light only benefits you if the other person runs the red light at the same time. Running the red light has the highest risk but also the highest rewards. That sounds to me like the Prisoner's dilemma, but I could be wrong.
Common sense - mathematically explained.
Thats actually a genius explanation. I've always been wonderimg *why* this is consodered so import
Common sense may not be so common. In my country, they would have crashed the cars in most scnerios.
But did you come up with this thought experiment out of the blue? This is the simplest possible explanation that makes it seem commonsense. This is applicable when there are N number of players. Then you need a formula and not just commonsense
But hey, that's just a theory. A game theory. Thanks for watching.
Interestingly enough, the stoplight example doesn't work for each and every case in real life, but on big numbers it becomes clear that it is indeed a good example of Nash equilibrium. So we're talking not about absolute law, but statistically correct law
thanks for the explanation man, i've never clearly understood this concept before
So, according to your interpretation of the Nash Equilibrium. nobody would ever run a red light. Or anyone who did, would not be by definition, a rational person.
The problem, which separates theory from reality, is that humans are terrible at doing risk assessment. Going despite the red light is a -5 situation, because the other guy will crash into you. Going over the green light is a 1 situation, because you reach you destination faster. Now people are naturally optimistic, meaning those who go over the red light can only see "reach the destination faster" not the "other guy will crash into you" situation.
TL;DR this theory doesn't work with us, because we suck at math.
@@xellos5262 Well, if it is a world without law enforcement, what if you've got a red light but you're driving a 12 wheeler truck and the other guy is driving a mini cooper. Is it irrational to go over the red light or just douchbaggery? Is douchbaggery a synonym for irrationality? This situation is a Nash Equilibrium only if you assume which types of vehicle are possible, not just the rule.
If you also assume eventual damages to the mini cooper driver are also negative to the truck driver, you're assuming the psychology of players to fit your moral standards and that feels like a failure in risk assessment.
@@XxKnuckleSOverlorDxX Both the vehicle type and the psychology of the driver are additional parameters, each of which gets its new dimension in the matrix. This therefore creates a new equilibrium.
@@xellos5262 I mean in this theoretical world I would also benefit if I honk my horn and make it clear I'm not going to stop, forcing the other player to stop.
@@lukasg4807 if you honk, and therefore demonstrate you will not stop, the other player can still choose to not stop. There is always a choice, and when there is a choice, parameters are taken in.
If this stuff were this easy, even Elon Musk could build a real self-driving car. It isn't, and because it isn't, true self-driving is impossible with the type of AI we have.
Stoplight isn't the best traffic analogy. Four-way stop sign is better. The stoplight isn't a simultaneous game. It is a leader-follower situation. At a 4-way, it is possible for both drivers to stop at the intersection at the same time.
It's not an analogy though, it is an actual example of Nash Equilibrium.
Of course it may not work as such in all countries. I do think that 4-way stop may be an even more clear example.
The best video out there by miles (no pun intended). This definitely beats Khan Academy & those youtube videos from 2009!
How did you score each decision? What's the criteria?
I think that's totally subjective. We're interested in the relative payoffs of the response to the actions. correct me if I'm wrong
Thanks so much for this , I need to understand this concept but my degree
I think to sum up most of he criticism in the comment section on the stoplight analogy is that nash equilibirium assumes that both parties are aware of the consequences of not following the rules (assuming no police exists), but in the real world people are either no. 1 they are not aware of consequences or no. 2 they are immune to the consequences or no. 3 they dont.care about the consequnces.
most people know what happens when cars collide
This Nash Equilibrium example is apt if people participating can assume that others will follow traffic light. In parts of the world, there is the expectation that no one else will follow the rules and therefore if you follow the rules, you will never get to your destination in reasonable time. This leads to every one trying to cross the intersection to maximize their transit time with the hope that others will yield--it's really a game of chicken in display--never mind that it increases the traffic time for every one involved.
I love concise explanations!
many thanks!
Go-Go decisions occur all too often, so many places have decided that roundabouts are more pareto-optimal.
Interesting and clear explanation.
And yet... People run red lights every day.
Why?
My guess would be because there's never just one game going on at a time.
e.g., bank robber fleeing police, rush to the hospital with a dying loved one in the back seat, etc
Nice and easy to understand example 👍
Sir!So in this example of the 2 drivers,it is unknown whether the signal is green for player 1 or player 2?
So in this case, there is no dominant strategy, but there are multiple nash equilibriums (2)?
Why is it -1 and not 0? Or vice versa? Shouldn’t the “stop” action have the same value for the participants?
Where are the numbers in the matrixes from? I don't understand how there are set (determined)?
Otherwise thank you for explanation on the nash equilibrium, I understood well thanks to the light example.
they are arbitrary. as long as a crash is worse than waiting, and going is better than waiting, i think the equilibrium is the same.
Thanks for making it so easy.
This explanation really helped, thank you!
Ok but what if you decided that the only negative outcome is a crash then both players would want to stop because in that case the smartest choice for both players to make would be to stop because now their outcomes don’t rely on the other players decisions meaning that each player is making the smartest possible decision
Thank you for your explanation, but i couldn't understand why you've chosen (1,0) instead of (0,1).Please, help me
Does the Nash equilibrium account for ANY chance of a player changing strategy? Say even a .000001% chance?? Or does if require 100% obedience for it to remain valid?
Nash equilibrium does not, but a refinement called "trembling hand perfect" equilibrium does. Not all Nash equilibria are trembling hand perfect, but the examples in this video are.
I know the utility values here aren't meant to be entirely accurate but why is the outcome of both of them stopping -1, -1 while the outcomes of only one of them stopping are 0, 1 and 1, 0? Shouldn't all "Stop" strategies result in -1, effectively changing (Stop, Go) = -1, 1 and (Go, Stop) = 1, -1?
Think of it like this. If we both wait, then we are back to square one at the next moment. Should I go? Should you go? That outcome is worse for me than if you clear the intersection from the start, because I know to just go immediately afterward.
thanks u explain so good and easy to understand
How would this be applicable in operating systems / time sharing.
It's a bit under 300 pages. It will keep you busy. If you eventually want to become an "expert" on the subject, you are pretty much stuck buying the $75 textbook from Fudenberg and Tirole. But that's written more as a reference manual than an actual teaching book.
That's mostly right. The stoplight game also has a MSNE which is Pareto-dominated, but I didn't cover it here/
MSNE?
So how do you use this in economics?
Doesn't this depend on the value judgements we assign to each outcome, which could be highly subjective depending on the players involved? Eg. I may value getting to work on time more/be more prepared to take a risk of damage because I have a really important meeting to get to?
Yes, if you change the values it's not a Nash-equilibrium anymore
I recently watched the movie and was touched emotionally....and start searching all about Nash. Could anyone help me with something I dont understand. What is the purpose of this theory. How it can be applied? Can it help in resolving important issues . At first it looked so simple but then it is actually very complicated for someone like me who is not mathematician but I tend to have strange ideas others cant see or understand quickly
What other examples of laws illustrate Nash's Equilibrium? Great Channel. Subbed.
Might be late, but why value -5, -5, as opposed to -1, -1? Why did you choose to go beyond 1 for the value of the outcome?
Because it is assumed that the cars will crash into each other, the consequences of which (damaged car/s) are far worse (-5) than the inconvenience of stopping/waiting (-1)
The drivers obviously had to have knowledge of each other. How would this work if they didn't have that knowledge.
So is a Nash equilibrium basically a suggestion to follow for the benefit of everyone ?
Really well explained! Thanks
Thank you, my professor wasn't clear in lecture but this helped immensely
Why would both stopping be worse for one player than stopping while the other goes?
I don't understand why "-5"?
because a crash is worse than an unnecessary stop
My microeconomics final is tomorrow. Let's hope I can retain this knowledge long enough...
so insightful. thanks! really helpful.
That made this _way_ easier!
6:00
To clarify, in the stoplight game the equilibria are pareto-optimal, but in the hunting game only the stag-stag option is?
What is the Pareto optimality in here? the same as Nash equilibrium, right?
How do i know a conflict is ruled by a matrix?
Thank you Thank you. Makes this much more clear.
The game is not a correct representation of a traffic lights situation. there must be a probability assigned to all the outcomes. Going through red led will not always have a bad outcome. And according to the comments the probability depends on the country you’re in. So for instance in India the probability of a bad outcome by “go” will be so low that it pays off to drive through red.
Also the action each player had to chose from at the same time is different. When player 1 have red, player 2 will have green. And When player 2 have red, player 1 will have green.
So is it the last one
I need answers now
I have a small query; you say that no one would want to break the law of obeying the traffic light, but what if, for example, they were on the run for the police? Is there an example of a Nash equilibrium containing an action that no one would want to break under ANY circumstances?
Ewan M Gillings GTA getting ⭐️⭐️⭐️⭐️⭐️The more the rules break the more it trys to correct itself.
thankyou so much!! hope i will do great on my quiz on Friday
Thanks. I'm new to this and so I guess I was looking at it as a pure simultaneous game where both players make their decisions at the same time.
People want to go, they just dont a lot of times. And most people dont care about much until it directly "affects" or "effects" them.
Thanks! Very clear explanation.
William, actually, I quite don´t understand why Stop-Stop -1/-1 is not the Nash Equilibrium. It says: Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy.
let me give you an example to your example ;-) : Player1 follows Stop, then he gets 0 or -1. If he follows Go, he gets -5 or 1. f I sum that up, the outcome of stop is better then the one of Go. So why is Stop Stop not the Equilibrium?
The GO-strategy is also not stable. If both Players say go, then we get -5/-5
Thank you in advance
Stop-stop is not a Nash equilibrium because one of the players can do a unilateral strategy change to do better. Instead of stop-stop, one player can decide to go instead and change the payout from -1 to 1 for him/her.
Tijn van Boekel
Thank you very much!
Filipinos are constantly trying to negotiate with the Nash equilibrium :P
What would be the opposite of a nash equilibrium? A law that everyone benefits for breaking?
It would be nash equilibrium.
What does dominance solveable mean
Omg man thanks so much, this makes way more sense then what my lecturer says.
+Calvin John I find that a lot as well. These five-ten minutes are so much easier to understand than some teachers can explain
Is there any way NE fails to predict behivor???
Hey William! Excellent job!
Can you add in your videos something about the Price of Anarchy (in matrices and networks)? It would be great!
But here they have, in the stoplight example, a indication telling them what they "should" do! What if they don't? What if there's no stoplight at all, and there's these 4 outcomes, and they don't know what the other will choose?
I see lots of exercices where that seems to appear...who would know if they were supposed to go or stop?
then that is a different game, and needs a new analysis
I would like to add that there is a Nash equilibrium if there is a clear punishment
Fantastic video! Thank you so much!
IF you take it as nobody would want to make a different move/choice, does that mean that given the nash equilibrium that all players are getting equal results?
Great explanation
great video, very well explained. But the one thing i don't understand is : How is this theory useful to us in our real life and what are its applications?
Aashay Desai - it's basis is the essence of common Sense. You practice this daily. You just didn't realize it. Your welcome. Lol
Aashay Desai porn
What a first-mover advantage in the stoplight equilibrium :)
Isn't the traffic light example actually an example of a correlated equilibrium?
@TinBryn I'd like to see you try!
Wouldn't the outcome if both players stop be -1 for the player with green light and 0 for the player with red light since she was going to stop anyway?
This is probably the origin for the name of the 1950's Nash Rambler... for it's-not-properly an equilibrium-rather the equilibrium point or fulcrum would be the saddlepoint between four-corner-twistings, the local minimum 'betweenish' the here odd corners which are co-maxima standoffs not equilibria... easier to see on a continuum gameboard; better in 3D.
So far off the mark with this
Well answer me this: did John Nash's Equilibrium Theory lead to the development of deregulation?
Simply put, is his theory responsible for the deregulation of the power industry, the trucking industry,
and the great breakup of Ma Bell?
but Ma Bell's breakup was an example of regulation, not de-regulation, right?
@@nmarbletoe8210 Ma Bell was not a good example.
Ma Bell's (AT&T) breakup was initiated due to the United States vs AT&T anti-trust lawsuit.
@@pmtips4482 Ok agree. To your main point, idk if Nash was used to justify deregulation, but it is logical.
Possibly it was used as an excuse without actually doing the math.
@@nmarbletoe8210 It is an interesting subject no doubt.
I have read where the Nash Equilibrium did not include factors for greed, corruption, and fraud but I can't really verify that.
Even if it was factored in, to what degree ?