# The Devil’s game

I hope that you are familiar of infinity and infinite values.We usually study infinite series in mathematics during the course of our study.Studying these series tends to be abstract and stale.But fortunately, there are a number of cases where such series can be employed producing amazing results.One of these is the Devil’s game.Here is how it works.

The  Devil wants to play a game.He chooses an infinite number of people ( P1, P2, … ) to play with.The game is simple.Each person can say either aye or nay.If a finite number of people say aye the Devil will give gold coins equal to the number of ayes  to everyone but if an infinite number of people say aye the Devil will win and walk away without giving anything .There is also another thing: No one is allowed to talk with the other people before the game starts.This way the people cannot decide upon a game strategy.

Now, suppose that you too are one of the participants.What would YOU do?Would you say aye or nay? Remember that you are independent and no one else can know about your decision.Moreover, your decision has no effect on the decision of other people. (If you say aye then it will result in the addition of a gold coin to the sum.) The rational thing would be to say aye.

Now comes the fun part. The other people are thinking in the same manner. They too, at an individual scale, believe that the rational thing would be to say aye.But if everyone says aye then the Devil will win and this rational thinking will shockingly result in you going away sad, prize-less and confused.

It goes without saying that the devil could lose a lot of money if only finitely many members of the group are fully rational. But the devil was careful to avoid selecting such a group for his game: nothing gives him more pleasure than torturing fully rational people.

This is known as “Collective Tragedy” and it means:
It can happen that a group of people ends up in a sub optimal situation even though every single member of the group behaves in a perfectly rational manner.