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:

### WARNING: DULL AND COMPLICATED - JUMP IF YOU WISH ###

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.

### END OF WARNING ###

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.

Portal 2

To me the game industry is getting overly generic and repetitive; every big game compromises of shooting waves after waves of enemies for no apparent reason. Now I like shooting things as much as the next guy, but when something truly original comes out - like Portal 2 - it really shows how fun a game can be.
The problem with shooting games is not actually the shooting - that part is great. The problem is the week plot that keeps the whole thing together. They concentrate too much on big, cinematic story lines, rather than on simple, good stories with character development. I would rather shoot one person who I want to kill, instead of having to mow through hundreds of people I don't care about. I understand this reflects the nature of war, but not every game has to focus on it.
So it's in this state of mind that I go and buy Portal 2 from one of the few remaining HMVs in London, not really knowing what to expect, not having played the first game. I come home, put the game into my PS3 and I am pleasantly surprised at the excellence of this game.
The story is simple; you are trying to get out of a test centre with the help of your portal gun. What makes it great is your character interaction; you get betrayed, you have to work with enemies, you get lied to... and all of these happen because of tangible, understandable reasons - something rare in games. And finally what truly sets this game apart is the fantastic voice acting - particularly by Stephen Merchant; with great humour and content I would spend quite some time just listening to what was said, not wanting to miss anything by moving to the next level.
Only two other games have made me feel this connected with the characters before - one was Metal Gear Solid 4 and the other Uncharted 2. Both made use of human characters, this game does without them. Perhaps these 'story' based games are a dying breed - its much safer and more income effective to make mindless shooter games - but for the sake of gamers I hope not. Gamers are seen as dull, counter-productive creatures, and if games were to all dumb down then this assumption would be true enough.

On a lighter note: yeah, portal 2 is a great game - go buy it now :)

UPDATE: It's only now, after finishing the game, that I understand how great a game this is. When you think about it, it's a story about how power corrupts and forgiveness. Really one of the most touching games I have played - really really fantastic.

PS: Portal 2 also has a coop campaign which looks great, although I haven't tried it out yet - the only disadvantage of being an only child