Game Theory is Broken

welcome back to Gary's economics today we are going to teach you some Game Theory learning about Game Theory can teach us a lot about number one how modern economists think and number two I've been thinking about it a lot recently with regards to difficulties I've been having and difficulties I think we're going to have with regards to fixing our economic system so we're going to go through that today okay so first a very quick introduction of what game theory is so game theory is a very popular field of Economics well it's a field of mathematics really Which is popular nowadays in economics where you basically turn real life situations into games you say there's a certain number of players maybe you and me a two player game we make moves we play against each other and we get outcomes and through game the we can analyze what you're going to do what I'm going to do what you should do what I should do and hopefully we play the game better what I'm going to do today is I'm going to explain to you the simplest and probably most famous game in Game Theory which is called the prisoners dilemma now this is a super popular game and it's been used by a lot of economists to basically defend the idea that that people are selfish and the best way to understand is to explain the game okay so in the prisoners dilemma you've got two prisoners they've been arrested for doing something wrong it could be anything let's assume they've been arrested for running a YouTube channel that says the government is full of idiots and the police is sitting these two prisoners down in separate rooms and they've got a little bit of evidence on both of these prisoners but not enough to really really hit them put them in prison for a long time so what they're trying to do is they're trying to get both of the prisoners to Gras on each other to give information on one another and the way they do that is they say listen if you grass on your friend the other prisoner then will reduce your prison time and the way that they set this game up is like this okay so there's two players in this game right let's assume it's you and me so you and me and basically we only have it's a very very simple game we only have one choice to make each which is whether or not we grass on each other and that means there are four possible outcomes in this game which is either we both grass or we both stay silent or you grass and I stay silent or I grass and you stay silent so I'm drawing out a diagram here which basically covers all the four situations in the game and we can view it as basically a move from you so in this diagram your two options are listed here on the top grass on the left stay silent on the right my two options are listed down the side grass on the top stay silent on the bottom so this covers all the four situations and the police have set it up so that they want you to grass so they say to you if you grass and your friend doesn't grass so I don't grass we will let you go away completely free and we'll send your friend to jail for 10 years so this is the situation here where you grass and I stay silent so it's this bottom left situation and in that case they give you zero years and they give me 10 years and they make the same offer to me so if I Gras and you stay silent you'll get 10 years and I'll get zero years if we both stay silent then they don't have much evidence on us at all so they can only give us one year each so that's this bottom right corner we both stay silent you one year me one year if we both Gras then they've got a lot of evidence on both of us and they'll put us both in jail for 5 years that's this top left corner we both grass okay so now we've got the basic setup of the game we can start to analyze it from a game theory perspective and what game through will tell us to do is consider your situation now you could be in one of two situations situation number one is I'm grasing on you and Situation Number Two is I'm silent and I'm not grasing on you so you analyze what you should do in both situations now consider I'm grasing on you now you have a choice either you Gras on me and you get 5 years or you don't grass on me and you get 10 years so what game theory will say is now we've we've really simplified this game if Gary grass is on you your choice is 5 years in prison or 10 years in prison obviously 5 years is better so if I grass on you you should grass that's your strategy if Gary grasses you should grass Now situation number two what if Gary stays silent well now you have a choice either you grass on me and you get zero years in prison you get to go free or you don't Gras on me and you get one year in prison now you have a choice zero years in prison or one year in prison zero years in prison is obviously better than one year in prison so again you should grass so in both situations whether I grass on you or I don't grass on you you should grass on me because you will get less time in prison so that means we have what game theorists would call a dominant strategy whatever I do you should Gras on me grasing on me is the best outcome for you regardless of my action so according to economists game theorists you should definitely grasp on me that is your dominant strategy now of course this game is is totally symmetrical so if we analyze the game from my perspective it will be exactly the same analysis as what we just went through now so that means obviously I also have a dominant strategy whatever you do I should grass on you and whatever I do you should grass on me now this means that we have what in Game Theory they call a Nash equilibrium which is named after the insane mathematician John Nash which means I definitely know what I'm going to do because I'm going to grass on you whatever you definitely know what you're going to do you're going to grass on me whatever so we will both definitely grass on each other I can't change what you do you can't change what I do it's a stable equilibrium we will both Gras on each other and we will end up here in the top left box where we both get 5 years in prison now what is interesting about this game is there's another box this bottom right corner where if we both stay silent it would have been better for both of us I would have got one year you would have got one year as it is we're both grassing we're both getting five years so we're ending up in a pretty bad situation so it's interesting right why why does it happen that we end up in this bad situation why can't we just both not grass and and be in a better situation the reason for that is we've done the analysis if I know you're not grassing it's better for me to grass so I'm going to Grass anyway and and you're in the same situation if you know I'm not grassing you're going to grass so basically we can't trust each other because we're both selfish we're both going to grass and the end result is we're going to get a bad outcome for both of us now this is the most famous game in Game Theory and it's often used by game theorists microeconomists to basically justify the idea that that people are selfish and that basically us up because we're selfish but there's nothing you can do about it because people are selfish and I think this analysis and people who are very good at game three probably shouldn't be making this analysis I think it's really interesting and and I want to explain to you why so we are ending up in the bad outcome because we both selfishly chose the grass and there's nothing we can do about that because because people are selfish right but actually the reason this happened is because we when we did the game theory we assumed that and we never spoke about this assumption I never mentioned this assumption when we went through the game we assumed that both players act in such a way that the only thing they care about is reducing their prison time so actually when we went through the analysis we kind of assumed that the players were selfish in reality if you were in the situation with your friend you might say well you know I don't want to betray my friend or I I trust that my friend is not going to grasp me up so I'm I'm not going to I'm not going to betray him because you know he's my friend and I trust him but we didn't talk about this at all in in our analysis right there are many situations where this game has been tried out in game shows or in Economist experiments and what you find is actually a lot of people in this kind of situation they won't betray their friend they will they will stick with their friend because they like them or because they trust them or because they think they can get the better outcome by sticking together so actually the people who have kind of proved themselves to be selfish in this analys in this analysis are the economists themselves it was the economists that said you will definitely betray your friend because the only thing you care about is your prison time and that analysis is correct if the only thing you care about in the whole world is reducing your prison time in this game you should definitely betray your friend that is true but the analysis that we did that we will both grasp that answer that equilibrium that response only becomes correct if we make the Assumption so if we assume selfishness we get selfish outcomes which may be bad in reality this game does nothing to tell us whether people are selfish or not it only tells us that here is a game where the correct strategy if the only thing you care about is reducing your prison time is to be selfish so this is my first conclusion here anyone who ever says that game theory suggest that people are selfish um basically doesn't understand Game Theory a game theory can tell you what to do if we know exactly what you want if we know what you want we can tell you what to do if we know that you're selfish we can tell you which outcome sorry which strategy is is probably going to give you the best selfish outcome if you're not selfish if you care about other people then you can probably work together and you can probably get towards this good outcome of only getting one year in prison each but that only works if if you have a degree of non-selfish now I want to get on to the reason I've been thinking about this a lot recently now the reason for that is as you know I've been running this YouTube channel for three more than three years now and the main idea behind this YouTube channel is that the economy as it is is in a really bad situation um living standards for ordinary families are getting worse and worse quite quickly and they will continue to get worse and what I continually say on this channel is that if we get together and force politicians to tax the rich more aggressively to force wealth to flow to Ordinary People rather than away from Ordinary People we can make inequality come down we can make the economy better and we can make living standards better for ordinary people and yet when I speak to politicians about this idea including politicians who are on the left like politicians in the labor party very often they say to me you know we can't publicly support these kinds of ideas because they're not popular because they're not vote winners and when I publicly speak about these ideas I very often get people push back against me and say oh we basically we don't want to believe that's true and when I get these kind of responses what I often feel is especially when I'm talking to better off people these are people who are busy people good jobs good salaries and they basically have a choice to make when they hear my theories which is do I believe this guy do I agree with this guy and do I start to devote some of my time some of my energy towards basically help helping him achieve his goals or do I ignore it and say listen that's nonsense I don't really care about that and just let him him do his thing and when I see this player in front of me I'm often reminded of the prisoner's dilemma because that person is in a similar situation right whatever I do whether my project is a success or not whether we manage to reduce inequality or not this guy has to decide whether to devote some of his time some of his resources some of his energy towards reducing inequality and the truth of the matter is you as an individual every individual in this country whether they choose to support this or not probably won't make a difference to whether we're successful or not so that person basically has the choice of supporting and making some sort of guaranteed loss of time or just ignoring it and using his time in in a selfish way and whatever Choice he makes he will probably well Society will probably end up in the same situation we will either succeed and the economy will get better or we will fail and the economy will get worse so we once again we're in this kind of interesting situation where basically if enough people are willing to act unselfishly which means devoting a little bit of time a little bit of energy towards watching our videos understanding what's happening sharing the videos telling your friends and family trying to build a big movement so that a majority of this country understands if we don't fix inequality the economy will get worse if enough people do that then we can solve this problem if not enough people do that then you will continue to see what what we are seeing which is living conditions continue to fall relatively quickly there's big increases in poverty life gets worse and worse for people in this country and I think it's an interesting kind of essentially it's a prisoners dilemma for not just two players but the country as a whole every individual person in this country can be a little bit better off just not bothering about it basically just just do what you can for yourself for your family just only worry about you and the people closest to you and if enough people make that decision the economy will collapse and ordinary families will be poor or people make that sacrifice a guaranteed sacrifice of of their time and their energy and people and protect the Ordinary People of the country avoid the collapse of the economy and I think it's it's a really interesting kind of philosophical dilemma right because you know I grew up in this country and I grew up in a culture which was very much sort of get rich or die trying and um you know I believe it's important to look after your family and and I understand the desire to try and be selfish and to try and get rich but it's created this really interesting situation where if if ordinary people can be convinced in large enough number to be greedy then we know with certainty ordinary people's kids and grandkids will be poor it's interesting why because you would think being greedy would would make you rich but we've created this game where if we can convince enough people poor people and Ordinary People to be greedy enough then we can absolutely bankrupt the kids of poor and Ordinary People so in a sense it's kind of a it's kind of a test really it's it's a test for the people of this country basically are enough people willing to make that sacrifice of time and effort to educate themselves to educate each other that the only way we can reduce inequality is together or basically are we too selfish to do that and are we going to drive ourselves into poverty so listen Game Theory teaches us not that people are selfish but that if enough people are selfish basically we can completely them over and I think this is kind of the situation that we are in as a country um I think the culture of our country has sort of moved in a direction in the last 40 50 years where people have been trained to be selfish and the big problem with this is if everyone is selfish and everybody fights selfishly then it becomes easy for the very powerful and the very rich to to take everything from the ordinary and from the weak and and that is what is happening essentially I believe in the economy and that is why life is getting worse and the only Power that all ordinary people have to protect themselves from the rich and the powerful is that there's a lot of them and they only use that power if they act unselfishly and work together so listen I believe we can fix the economy we can only do it by dealing realistically with inequality um the rich are not going to support that and they're going to oppose it and they do oppose it but we can stop that by working together um I'm going to do that I'm going to keep working on it that's why we these videos out every week and um I hope you do too so please watch these videos share these videos and um help us bring people together and fix this economy by understanding it better thank you

Channel: Garys Economics

Views: 169,002

Keywords: Wealth Inequality, Enough is Enough, Tax Wealth Not Work, Economics of Covid, Rich get Richer, Poor get Poorer, Economics Explained, Tax the Rich, End Austerity, Billionaire, Poverty

Id: HezHJKZ47Ck

Length: 19min 14sec (1154 seconds)

Published: Sun Feb 25 2024