Everybody plays games, but did you know there is a whole area of maths dedicated to the theory of playing games? You can have a look at the Wikipedia entry for it here, but be warned, it gets quite complicated!
One of the most famous (and easiest to follow) examples of Game theory is called "The Prisoners Dilemma", and it goes a bit like this...
There are two prisoners, that the police strongly suspect of both being guilty of a serious crime, but they cannot quite prove it. In order to get to the bottom of things, they keep the two prisoners seperate, there is no way for them to communicate.
They then get the two prisoners to confess, by offering them a deal. The offer goes..
"If you confess, you will get a lighter sentence of 1 year. Your partner in crime will get the maximum sentence of 5 years, as they have not confessed". The criminal knows that if they both keep quiet, they will get a much lighter 2 year sentence as the police will not be able to pin anything on them. He also know that if he keeps quiet and his friend confesses, then he will get 5 years while his friend only gets 1, and that if they both confess then they can both look forward to 3 years in prison!
So, what should he do?
This problem has implications beyond prisoners in cells. I've been reminded of this problem twice in the recent past...
1. In the "Hunger Games" there is a choice that Katniss and Peeta have to make, near the end. I'm not posting spoilers, but it involves some berries!
2. When there was a possible fuel strike we saw lots and lots of queuing at petrol stations on the news. This was a great example of this problem. Should you panic buy or not? The best solution would have been for no-one to panic buy, and everyone would have just bought as normal until the situation was resolved (which it was without there even being a strike).
Once one person started panic buying, and pumps started to run dry, there was a danger that those who hadn't filled there tanks would be left unable to use their cars, and so it became in everyone's interest to fill up!
Next time you have a decision to make, think about how the actions of other people impact that decision and how what you decide impacts on them.
One of the most famous (and easiest to follow) examples of Game theory is called "The Prisoners Dilemma", and it goes a bit like this...There are two prisoners, that the police strongly suspect of both being guilty of a serious crime, but they cannot quite prove it. In order to get to the bottom of things, they keep the two prisoners seperate, there is no way for them to communicate.
They then get the two prisoners to confess, by offering them a deal. The offer goes..
"If you confess, you will get a lighter sentence of 1 year. Your partner in crime will get the maximum sentence of 5 years, as they have not confessed". The criminal knows that if they both keep quiet, they will get a much lighter 2 year sentence as the police will not be able to pin anything on them. He also know that if he keeps quiet and his friend confesses, then he will get 5 years while his friend only gets 1, and that if they both confess then they can both look forward to 3 years in prison!
So, what should he do?
This problem has implications beyond prisoners in cells. I've been reminded of this problem twice in the recent past...
1. In the "Hunger Games" there is a choice that Katniss and Peeta have to make, near the end. I'm not posting spoilers, but it involves some berries!
2. When there was a possible fuel strike we saw lots and lots of queuing at petrol stations on the news. This was a great example of this problem. Should you panic buy or not? The best solution would have been for no-one to panic buy, and everyone would have just bought as normal until the situation was resolved (which it was without there even being a strike).
Once one person started panic buying, and pumps started to run dry, there was a danger that those who hadn't filled there tanks would be left unable to use their cars, and so it became in everyone's interest to fill up!
Next time you have a decision to make, think about how the actions of other people impact that decision and how what you decide impacts on them.
Very interesting this! Glad to have stumbled across it.
ReplyDeleteGreat economic application of game theory is global warming. There are 2 countries which can either pollute or not pollute. The optimal outcome for society is for neither to pollute but the Nash Equilibrium (John Nash won nobel prize for economics i might add!) is for both to pollute as even if they could agree between themselves to not pollute there will always be an incentive for both of them to cheat ie pollute which would potentially leave them better off and obviously come at the expense of the other country! This basically explains why world as of yet has been unable to reach an agreement between all countries that limits emissions. Had an economic policy exam today where we had to talk about this!