Game Theory

Despite its name Game Theory is a branch of mathematics which applies to many everyday situations and is very relevant in Economics. During the 19th and first half of the 20th Centuries Economic theory was largely based on the ideas of Adam Smith: that the best outcome for the group comes from each individual pursuing what is best for himself. Although this theory was used for 150 years it had one major flaw: it was incorrect in many circumstances. This was eventually spotted by John Nash in 1950, and this discovery led to him writing 4 articles from 1950 to 1953. These articles lay the foundation for Game Theory as we know it today, and he received a Nobel in Economics in 1994 for his contribution to science.

Perhaps the most famous example of Game Theory in action is in 'The Prisoners' Dilemma'. Here 2 suspects have been caught by the police, but the police only have enough evidence to charge them with trespassing but they are sure the prisoners have stolen something. They decide to offer them a deal to get them to 'rat' on each other. The police would like to get both the prisoners for theft - so they set up the deal in such a way that it is preferable for both the prisoners to rat on each other. Please consider the following table:

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Each player represents a prisoner and the numbers are how long they will each get in prison depending on what each of them do. In each little square the bottom left represents Player 1's years and the top right represents Player 2's years. So for instance if Player 1 cooperates, but Player 2 rats then Player 1 gets 12 years and Player 2 only get 2 years. Where this gets interesting is that no matter what Player 1 does, it is in the interest of Player 2 to rat - the opposite is also true. If you rat when the other cooperates you get 2 years instead of 4 if you had also cooperated. If you rat when the other rats too, then you get only 10 years instead of 12.

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Therefore 'ratting' is the dominant strategy, but does not wield the optimum result for the group - which would be if they both cooperated and each only got 4 years instead of 10 years each when they both rat.

Now from one quite complicated and serious situation to a little more fun one: you are one of three cowboys having a 'Truel', and you're turn is first to shoot - for simplicity's sake let's presume that none of you ever miss. Who should you shoot? Strangely it would be best for you to purposely miss because if you kill one of them then the other would kill you in his turn. Even more bizarrely, by everyone adopting this 'dominant strategy' then no one will ever shoot anyone else - yielding the best outcome for the group, where everyone stays alive. So in this situation the theory of Adam Smith is correct. but unfortunately this isn't always true.

I hope to by now have convinced you that mathematics, or at least parts of it, can be interesting. If I have managed to wet your appetite for more then I recommend you watch 'A Beautiful Mind' and have a read of 'Rock, Paper, Scissors' by Len Fisher.

Also please bear in mind that I am not a mathematician and only understand this whole thing to a very basic level, so if you have any complicated questions I'll try my best to answer, but can not promise that I will be able to.