Hey, can you please suggest some good economics channel for clearing concepts and learning, actually I am a beginner in economics and wated to know more about engeneering Economics and econometrics
@@trendnews6761 try crash course economics if you want to go into more mathematics on modeling finance try mit topics in mathematic with applications in finance. hope it helps.
I made the numbers up. For now, the important feature of payoffs is the rank ordering of the outcomes, i.e. I prefer going first to going second to having us both sit there to causing an accident. The payoffs I used reflect that ordering. Later on (third unit), we will generalize payoffs as variables and investigate how changing the payoffs (while still preserving the rank ordering) affects Nash equilibria.
I think this is the way the traffic light is made, by looking at strategies and getting best possible outcomes. He didnt make a game about stoplights, he showed us the principle of the idea that came out of this problem.
The idea is that if both stop, then they lose a few seconds coordinating who should go first. But you'll notice that (pass, stop) and (stop, pass) are still the only pure strategy Nash equilibria even if make your suggested adjustment.
Hey, can you please suggest some good economics channel for clearing concepts and learning, actually I am a beginner in economics and wated to know more about engeneering Economics and econometrics
Hi where did you get your values such as (-5) when your problem or situation does not have numbers in it, is are there set values you use? I want to be able to create my own matrix / payoff matrix if I get into a " GAME " situation. Please help me :)
i never got how these values are determined... why is the payoff for stopping 0 if the other player goes, and -1 if the other player stops ? it's the same time lost either way, so wouldn't they payoff for stopping be the same regardless of what the other player does ?
Why is inconveniencing both, one of them actually has a stop light so either way they wouldn't go, assuming they would adhere to the law? Is it because one of them could go, regardless of who it is, so technically they are both wasting their time?
I would change the 1,0 and 0,1 to 2,1 and 1,2. The player that stops while the other player is going gets the benefit of avoiding a car crash. I feel like that is a return greater than zero. Maybe you address this in the very next video. Just rambling in to the void at this point.
Pardon my ignorance, but why is the crash -5? Where does that number come from some of these numbers I just don’t understand and some of these examples in the series so any help would be greatly appreciate it again sorry for the ignorance.
William, can you explain the connection between pure and mixed Nash Equilibriums ? They feel like two very different things, but I suspect they're named similarly for a reason.
Hey Spaniel, this is a Chinese professional benefit from your video. I'm wondering to make my own video based on yours to tell more people what it is about game theory and I will tell them how to find your video. Is it fine to you? btw, how can I contact you personally from RUclips? I can't find a Chat button. LOL
So.... what you are saying is that pedestrians and bicyclists are at a huge disadvantage because there unfortunately is no inherent incentive for drivers to STOP for them, lol
From an individual's perspective, two equilibria can't be compared (from a group's perspective, they could be; see -1 -1 vs. -8 -8 in the last video). Each player can only control half of the outcome, but equilibria only happen when both players act a certain way; so neither individual can choose all by themself what equilibrium they would prefer to bring about. That is why in the payoff matrix, he only compares 2 squares when they are adjacent (horizontally or vertically). Those are the 2 choices that you have once you've assumed what the other person will do
@@dhooth Thanks so much. But then the theory is incomplete. In reality, there is only one possible outcome. How can this be improved to predict which one will be selected ? (Maybe this exists)
Which one is better is determined by what you expect the other person to do. This is why it is described as a law everyone would want to follow: the law gives you an expectation of what the other person is likely to do, hence what you should do. And your knowledge of what you should do feeds back to encourage the other person to follow that law also. Here is another traffic law example: I (player 1) pull out of my driveway. I have a choice between driving on the left side of the road, or driving on the right side of the road. Somebody (player 2) coming towards me has also had to make a left or right decision. If we make the same decision (both left, or both right) all is good. If we make different decisions, we get a bad outcome. Even without traffic cops, I'm going to drive on the left. This is because in my country, there is a law saying I should drive on the left, giving me a strong expectation that player 2 will be driving on their left. However, when *you* pull out of *your* driveway, it is likely you're going to drive on the right, because it is likely you live in a country where the law is to drive on the right. Similarly, if you were in a country where there was a law (or societal expectation) that red meant go and green meant stop, you'd be best stopping on green and going on red. If you have no idea what the other player will do, or what the other player expects you to do, we haven't yet got the tools to analyse this situation.
@@michaelwoodhams7866 Check this one: 10,5 | 3, 2 2, 3 | 5,10 There are two Nash equilibrium, I want the top left one, he wants the bottom right one. Basically, I think that what this does is reduce the problem from elementary decisions to Nash equilibrium selections. So now there are 3 actions: agree on NE1 or agree on NE2 or blow each other up. I think there is already stuff on that. I believe that it's a matter of resolve and of capability, but now we are out of scope... I think that we could assume that besides utility we could have other quantities to incorporate, like moral integrity, resolve, etc, and then combine them. And then test the validity of the model based on whether or not it is complete (i.e. one single solution). If not, better data has to be incorporated. If this theory will be prescriptive, then it has to solve the problem. Or maybe it allows to at least eliminate options, or get a proper frame to the problem (now we are dealing with a resolve issue, when before we attacked it from a purely utilitarian point of view) Now the problem is that we both have to push a button (the same): A: 10, 5; B: 5, 10; C: -inf,-inf How would you solve this problem ? Either, you take 10 million and I take 0, or inverse or we both die. And we have limited time. I think the only way to do this is to reframe the problem. Like the players will sit there and reexplain the game but in their favor. Like "I'm ready to die actually" or "I'll share it with you later" or "money doesn't matter actually", "it's bad for you cause I got a father with cancer"... Actually, actually, actually,.. There should be a problem reformulation theory in game theory (to model possible (misleading) negotiations) (God knows better)
I think if 1 stops and 2 goes it should be ( -1 , 1 ) as 1 is obviously wasting time, so i think the table is wrong and should be -----> ( -5 , -5 ) ( 1 , -1 ) ( -1 , 1 ) ( -1 , -1 ) please tell if it's still a nash eqb or not
This is incorrect because in the event both stop, they will both be stalled longer than if one goes and one stops. Therefore, if you are stopping for sure, you would prefer the other car goes rather than stops. As a result, it should be ( -5, -5 ) ( 1, 0 ) ( 0, 1) ( -1, -1). As the stopped car, you do not want the other car to stop. Think about it, if you were at a 4 way stop sign, and the other car got there before you, you have to stop regardless. By regulation, you'd expect the other car to go before you, and the sooner that car goes, the sooner you can go. On the other hand, if that car waits for you to go first, then you both will be deadlocked, and it will be an even longer delay for both of you. Hope that makes sense.
You're trying to answer a different problem. One type of problem: Here is the game payoff matrix. Figure out what strategies each player should play. Another type of problem: Here is a real world situation. Figure out a payoff matrix which reflects that situation. We're currently learning to deal with problems of type 1. You're treating it as a problem of type 2. Both matter, but type 2 isn't the topic of this lecture. For the purpose of this lecture, the payoff matrix was handed to you by God carved in stone.
Do games exist in higher dimensions? If we have 3 people could we draw a cube payoff matrix, and for 4 players could we (theoretically, if it was possible) draw a hypercube payoff matrix?
Yes. For example, for three players, you can draw two matrices. Player 1 picks a row, player 2 picks a column, and player 3 picks the matrix. For four players you can do the same with two sets each consisting of two matrices. Player 4 picks the set.
I don't see why it would be '0' value for stopping when other goes, surely it's '-1', I guess you could argue that you stop for shorter time as you see the other person go, but still seems bit weird
If you look at it that way, than (go,go) would be (1,1) But these numbers don't indicate time, but rather how good some choice is. Stopping while someone is going is better than stopping while someone is stopping. That's why in the first case has a bigger value (0) than the other (-1).
Why call it a Nash equilibrium, but to draw attention to its ... inventor? Or discoverer? For if the latter, it is "universally true", a martian might grasp the concept. But if the former, than sure, give him the credit, being the craftsperson who created it. For example, the physicist Richard Feynman came up with diagrams one might use to explain interactions between subatomic particles - being nonintuitive, inventive - they are rightly called, Feynman diagrams. But when he postualted the existence of a particle that travels back through time, he did not call it a Feynmanite, but a tachyon. That makes sense. For to look upon a star in the sky and think to name it after yourself, or another person, seems idolatrous to me.
Isn't this stoplight game equivalent to a Chicken game in a particular way? en.wikipedia.org/wiki/Chicken_(game) Something like Go Swerve Go -5, -5 (1), (-1) Swerve (-1), (1) 0, 0
This video is infinitely better than my entire game theory class this semester. Thank you
true
in india that - 5,-5 is nash equilibrium
😂😂😂
Hey, can you please suggest some good economics channel for clearing concepts and learning, actually I am a beginner in economics and wated to know more about engeneering Economics and econometrics
@@trendnews6761 try crash course economics
if you want to go into more mathematics on modeling finance try mit topics in mathematic with applications in finance.
hope it helps.
Same in Vietnam. We never stop for red light
What if it’s a simultaneous example where you don’t know whether the other guy is gonna stop or go?
this made so much more sense than the five weeks where crap just poured out of my professor's mouth. thank you.
Thanks so much! I'd really appreciate a review on Amazon when you're ready.
I made the numbers up. For now, the important feature of payoffs is the rank ordering of the outcomes, i.e. I prefer going first to going second to having us both sit there to causing an accident. The payoffs I used reflect that ordering.
Later on (third unit), we will generalize payoffs as variables and investigate how changing the payoffs (while still preserving the rank ordering) affects Nash equilibria.
I have a game theory exam this morning and you helped more than the lectures, book and notes I have. thank you.
What did you get bro?
@@slowsatsuma3214 I don't think he remembers since 6 years have passed xD
@@manuelmarcelino3314 AHAHHAHAAHHAAHHA
I think this is the way the traffic light is made, by looking at strategies and getting best possible outcomes. He didnt make a game about stoplights, he showed us the principle of the idea that came out of this problem.
And then the government passed a law replacing stop lights with optimal diameter round-abouts. Great video!
+ed frank Amen.
The idea is that if both stop, then they lose a few seconds coordinating who should go first. But you'll notice that (pass, stop) and (stop, pass) are still the only pure strategy Nash equilibria even if make your suggested adjustment.
Hey, can you please suggest some good economics channel for clearing concepts and learning, actually I am a beginner in economics and wated to know more about engeneering Economics and econometrics
I must say you are amazing. You are on my daily training list now.
Yup. I'd check the playlist on the channel. Also, the end of each video sends you to the next.
Dying is only 5 times as bad as waiting for a bit in traffic
Equilibrium? More like "entertainment for the cerebrum", because that was fascinating!
So, Nash equilibrium is a state in the game, where every player will participate for their best interest? Will it be ok to say it in that way?
no, rather when they have no reason to change what they have chosen.
Hi where did you get your values such as (-5) when your problem or situation does not have numbers in it, is are there set values you use? I want to be able to create my own matrix / payoff matrix if I get into a " GAME " situation. Please help me :)
So good. Bought the book too. 🎉
i never got how these values are determined...
why is the payoff for stopping 0 if the other player goes, and -1 if the other player stops ?
it's the same time lost either way, so wouldn't they payoff for stopping be the same regardless of what the other player does ?
You are correct.
I'm assuming the are given. It's what you say. It's no concrete.
That's why I think a lot of these theories are BS.
Why is inconveniencing both, one of them actually has a stop light so either way they wouldn't go, assuming they would adhere to the law? Is it because one of them could go, regardless of who it is, so technically they are both wasting their time?
I would change the 1,0 and 0,1 to 2,1 and 1,2. The player that stops while the other player is going gets the benefit of avoiding a car crash. I feel like that is a return greater than zero.
Maybe you address this in the very next video. Just rambling in to the void at this point.
Thank you! This series is helpful! ✨
Actually, both would get to their *final destination* quickest in the go+go scenario. ;-)
Pardon my ignorance, but why is the crash -5? Where does that number come from some of these numbers I just don’t understand and some of these examples in the series so any help would be greatly appreciate it again sorry for the ignorance.
Thanks
A nice clear video
thank you!!
William, can you explain the connection between pure and mixed Nash Equilibriums ? They feel like two very different things, but I suspect they're named similarly for a reason.
Thank you.
Hey Spaniel, this is a Chinese professional benefit from your video. I'm wondering to make my own video based on yours to tell more people what it is about game theory and I will tell them how to find your video. Is it fine to you? btw, how can I contact you personally from RUclips? I can't find a Chat button. LOL
Your videos are very high quality but there is an extreme lack of organization. I don't really know where to start after watching your intro videos.
So.... what you are saying is that pedestrians and bicyclists are at a huge disadvantage because there unfortunately is no inherent incentive for drivers to STOP for them, lol
How to decide which Nash Equilibrium is better ? Thank you so much for this course, may God reward you
From an individual's perspective, two equilibria can't be compared (from a group's perspective, they could be; see -1 -1 vs. -8 -8 in the last video).
Each player can only control half of the outcome, but equilibria only happen when both players act a certain way; so neither individual can choose all by themself what equilibrium they would prefer to bring about. That is why in the payoff matrix, he only compares 2 squares when they are adjacent (horizontally or vertically). Those are the 2 choices that you have once you've assumed what the other person will do
@@dhooth Thanks so much. But then the theory is incomplete. In reality, there is only one possible outcome. How can this be improved to predict which one will be selected ? (Maybe this exists)
Which one is better is determined by what you expect the other person to do. This is why it is described as a law everyone would want to follow: the law gives you an expectation of what the other person is likely to do, hence what you should do. And your knowledge of what you should do feeds back to encourage the other person to follow that law also.
Here is another traffic law example: I (player 1) pull out of my driveway. I have a choice between driving on the left side of the road, or driving on the right side of the road. Somebody (player 2) coming towards me has also had to make a left or right decision. If we make the same decision (both left, or both right) all is good. If we make different decisions, we get a bad outcome.
Even without traffic cops, I'm going to drive on the left. This is because in my country, there is a law saying I should drive on the left, giving me a strong expectation that player 2 will be driving on their left. However, when *you* pull out of *your* driveway, it is likely you're going to drive on the right, because it is likely you live in a country where the law is to drive on the right.
Similarly, if you were in a country where there was a law (or societal expectation) that red meant go and green meant stop, you'd be best stopping on green and going on red.
If you have no idea what the other player will do, or what the other player expects you to do, we haven't yet got the tools to analyse this situation.
@@michaelwoodhams7866 Check this one:
10,5 | 3, 2
2, 3 | 5,10
There are two Nash equilibrium, I want the top left one, he wants the bottom right one.
Basically, I think that what this does is reduce the problem from elementary decisions to Nash equilibrium selections. So now there are 3 actions: agree on NE1 or agree on NE2 or blow each other up.
I think there is already stuff on that.
I believe that it's a matter of resolve and of capability, but now we are out of scope...
I think that we could assume that besides utility we could have other quantities to incorporate, like moral integrity, resolve, etc, and then combine them. And then test the validity of the model based on whether or not it is complete (i.e. one single solution). If not, better data has to be incorporated. If this theory will be prescriptive, then it has to solve the problem.
Or maybe it allows to at least eliminate options, or get a proper frame to the problem (now we are dealing with a resolve issue, when before we attacked it from a purely utilitarian point of view)
Now the problem is that we both have to push a button (the same):
A: 10, 5; B: 5, 10; C: -inf,-inf
How would you solve this problem ? Either, you take 10 million and I take 0, or inverse or we both die. And we have limited time.
I think the only way to do this is to reframe the problem. Like the players will sit there and reexplain the game but in their favor. Like "I'm ready to die actually" or "I'll share it with you later" or "money doesn't matter actually", "it's bad for you cause I got a father with cancer"... Actually, actually, actually,..
There should be a problem reformulation theory in game theory (to model possible (misleading) negotiations)
(God knows better)
If there was no traffic light they'd both stop. Similar to the hare thing it's like a secret true equilibria over the nash equilibrias
I think if 1 stops and 2 goes it should be ( -1 , 1 ) as 1 is obviously wasting time, so i think the table is wrong and should be -----> ( -5 , -5 ) ( 1 , -1 ) ( -1 , 1 ) ( -1 , -1 )
please tell if it's still a nash eqb or not
This is incorrect because in the event both stop, they will both be stalled longer than if one goes and one stops. Therefore, if you are stopping for sure, you would prefer the other car goes rather than stops. As a result, it should be ( -5, -5 ) ( 1, 0 ) ( 0, 1) ( -1, -1). As the stopped car, you do not want the other car to stop.
Think about it, if you were at a 4 way stop sign, and the other car got there before you, you have to stop regardless. By regulation, you'd expect the other car to go before you, and the sooner that car goes, the sooner you can go. On the other hand, if that car waits for you to go first, then you both will be deadlocked, and it will be an even longer delay for both of you. Hope that makes sense.
You're trying to answer a different problem.
One type of problem: Here is the game payoff matrix. Figure out what strategies each player should play.
Another type of problem: Here is a real world situation. Figure out a payoff matrix which reflects that situation.
We're currently learning to deal with problems of type 1. You're treating it as a problem of type 2. Both matter, but type 2 isn't the topic of this lecture. For the purpose of this lecture, the payoff matrix was handed to you by God carved in stone.
I forgot to like some other videos so here's a comment
Rational actors should be mentioned along or in place of self interest.
if they both went, they would get in an accident which is really bad (-5), and if both are stopped, they are wasting time (-1)
Do games exist in higher dimensions? If we have 3 people could we draw a cube payoff matrix, and for 4 players could we (theoretically, if it was possible) draw a hypercube payoff matrix?
Yes. For example, for three players, you can draw two matrices. Player 1 picks a row, player 2 picks a column, and player 3 picks the matrix.
For four players you can do the same with two sets each consisting of two matrices. Player 4 picks the set.
@@Gametheory101 And for 5 players, player 5 would pick a set of sets, out of the two sets of sets of matrices, and so on?
@@nicolastorres147 Exactly.
Is this the nash from the movie "a beautiful mind"
Yep!
Here min(max(Mij))row-wise!=max(min(Mji)) yet we have a Nash equilibrium. How?
Because u forgot that the traffic light exists and it allows for a "sequence" to be chosen.
View's to comment ratio doesn't make sense
I don't see why it would be '0' value for stopping when other goes, surely it's '-1', I guess you could argue that you stop for shorter time as you see the other person go, but still seems bit weird
If you look at it that way, than (go,go) would be (1,1) But these numbers don't indicate time, but rather how good some choice is. Stopping while someone is going is better than stopping while someone is stopping. That's why in the first case has a bigger value (0) than the other (-1).
Thats not the point here...
Why call it a Nash equilibrium, but to draw attention to its ...
inventor? Or discoverer? For if the latter, it is "universally true",
a martian might grasp the concept. But if the former, than sure,
give him the credit, being the craftsperson who created it.
For example, the physicist Richard Feynman came up with diagrams
one might use to explain interactions between subatomic particles -
being nonintuitive, inventive - they are rightly called, Feynman diagrams.
But when he postualted the existence of a particle that travels back through
time, he did not call it a Feynmanite, but a tachyon. That makes sense.
For to look upon a star in the sky and think to name it after yourself, or
another person, seems idolatrous to me.
John Nash was the man who developed Game Theory
2019 haha
Isn't this stoplight game equivalent to a Chicken game in a particular way? en.wikipedia.org/wiki/Chicken_(game)
Something like
Go Swerve
Go -5, -5 (1), (-1)
Swerve (-1), (1) 0, 0