How could it be that my professor at university cant explain the game theory and nash equilibrium in over multiple hours and only one UA-cam 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.
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"?
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.
This is a thought I had for most of my reading through it. They found a way to codify common sense, took them bare years to but I respect that it was done regardless.
@@Bugoy_ADHD You don't understand why Nash received the Nobel Prize. Even Einstein. Anyone can have a "Theory" about anything. But the fact that they proved it with mathematics is what makes them different than just "anyone" Because turning it into mathematical formula make it predictable and applicable. That process is what I'm interested in.
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!*
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
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 !
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.
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.
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.
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
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.
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!
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.
So think of it like this: If both cars go they crash and die, if both cars wait they're late (Likely both will never reach their destination), and if they take turns they both get there on time. Games Theory automatically assumes we're out looking for ourselves and this is a perfect example of that.
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.
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 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.
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
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.
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
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
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.
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 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?
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.
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)
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.
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?
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
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.
Can you give me an example of a law no one would want to break? I think you have described the empty set. You seem to be confusing specific examples with universal definitions.
Why would there be a yellow light when the other light is green? That doesn't make any sense unless one car was going to make a right turn, but in this case both go straight so they would be driving perpendicular to one another.
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?
How could it be that my professor at university cant explain the game theory and nash equilibrium in over multiple hours and only one UA-cam 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
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
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
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
This is a thought I had for most of my reading through it. They found a way to codify common sense, took them bare years to but I respect that it was done regardless.
@@Bugoy_ADHD You don't understand why Nash received the Nobel Prize. Even Einstein. Anyone can have a "Theory" about anything. But the fact that they proved it with mathematics is what makes them different than just "anyone" Because turning it into mathematical formula make it predictable and applicable. That process is what I'm interested in.
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!*
The whole clip along with comments "make my day again"
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.
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
Great explanation! Always is possible to explain difficult concepts with simple examples
Still come back to this from time to time years later when I'm in an economics mood, great video!
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 !
This was a brilliant explanation. Thanks so much
I've been a fan of your geopolitics content for a while now and now I'm watching this for my microecon class lol
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.
1:38 the gulp is unreal
been 9 years and still the single best explanation on youtube
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.
The best video out there by miles (no pun intended). This definitely beats Khan Academy & those youtube videos from 2009!
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.
thanks for the explanation man, i've never clearly understood this concept before
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
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
I love concise explanations!
many thanks!
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.
But hey, that's just a theory. A game theory. Thanks for watching.
Go-Go decisions occur all too often, so many places have decided that roundabouts are more pareto-optimal.
This explanation really helped, thank you!
thanks u explain so good and easy to understand
Nice and easy to understand example 👍
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
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.
Thanks so much for this , I need to understand this concept but my degree
Thanks for making it so easy.
How I would love to understand but my genetic makeup makes it hard lol
So think of it like this: If both cars go they crash and die, if both cars wait they're late (Likely both will never reach their destination), and if they take turns they both get there on time. Games Theory automatically assumes we're out looking for ourselves and this is a perfect example of that.
@Philosopher K its an example not literal
Philosopher K I think the example only applies to rational people.
@@merrillgeorge1838 but if you throw kants categorical imperative into the mix, then the prisoners dilemma does not reach the same equilibrium
@@merrillgeorge1838 Nothing is equal to something else in reality, only ideally. Thinking is all we can do.
Really well explained! Thanks
so insightful. thanks! really helpful.
Thank you Thank you. Makes this much more clear.
thankyou so much!! hope i will do great on my quiz on Friday
Crazy how you explain it and ironically R.I.P Mr. Nash and his wife died in a car crash.
So in this case, there is no dominant strategy, but there are multiple nash equilibriums (2)?
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.
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.
So how do you use this in economics?
That's mostly right. The stoplight game also has a MSNE which is Pareto-dominated, but I didn't cover it here/
MSNE?
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.
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
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.
Why is it -1 and not 0? Or vice versa? Shouldn’t the “stop” action have the same value for the participants?
Thank you for your explanation, but i couldn't understand why you've chosen (1,0) instead of (0,1).Please, help me
Sir!So in this example of the 2 drivers,it is unknown whether the signal is green for player 1 or player 2?
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.
I don't understand why "-5"?
because a crash is worse than an unnecessary stop
Fantastic video! Thank you so much!
Thanks! Very clear explanation.
To clarify, in the stoplight game the equilibria are pareto-optimal, but in the hunting game only the stag-stag option is?
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
Thank you, my professor wasn't clear in lecture but this helped immensely
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
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.
Great explanation
Why would both stopping be worse for one player than stopping while the other goes?
What does dominance solveable mean
So is a Nash equilibrium basically a suggestion to follow for the benefit of everyone ?
How would this be applicable in operating systems / time sharing.
That made this _way_ easier!
6:00
What other examples of laws illustrate Nash's Equilibrium? Great Channel. Subbed.
¡Thank you for this explanation!
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.
So is it the last one
I need answers now
Good explanation...thanks!
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.
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
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.
How do i know a conflict is ruled by a matrix?
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)
Is there any way NE fails to predict behivor???
The drivers obviously had to have knowledge of each other. How would this work if they didn't have that knowledge.
Filipinos are constantly trying to negotiate with the Nash equilibrium :P
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
thanks very efficient way to explain
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?
you're a legend
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
What is the Pareto optimality in here? the same as Nash equilibrium, right?
What a first-mover advantage in the stoplight equilibrium :)
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.
Can you give me an example of a law no one would want to break? I think you have described the empty set. You seem to be confusing specific examples with universal definitions.
Why would there be a yellow light when the other light is green? That doesn't make any sense unless one car was going to make a right turn, but in this case both go straight so they would be driving perpendicular to one another.
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
Isn't the traffic light example actually an example of a correlated equilibrium?
Who camr here from beautiful mind?
:") Its 2019 what am I doing !?
Nur Al Ahsan lmao i literally watched it today and im very deep into reasearching into John Nash, im watching this and i dont even take maths😂
Lmao same idk what I clicked on
Thanks for clearing things up in a few minutes!
@TinBryn I'd like to see you try!
If I hypothetically have a redlight ticket, could I use this as an argument to get out of it?
What would be the opposite of a nash equilibrium? A law that everyone benefits for breaking?
It would be nash equilibrium.