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Dividing the cake

Posted by asymptotics under

Game Theory | Tags:

Game Theory |

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Let us consider the following problem which is a popular example in game theory.

A mother wants to divide a cake between her two children. To make both of them happy she has to ensure that each one gets an equal share. That is she has to cut the cake into two equal halves. But the problems is that the cake does not have a regular shape. Hence what is equal to her eyes may not be equal to the eyes of her children. The consequences of an unequal division are imaginable. So how can she make both her kids happy?

The solution is to ask one of the kids to cut the cake into two and the other to choose the piece. It can be verified that this solves the problem. The interesting thing about the solution is that the mother was able to satisfy both the kids even without knowing what will make them happy.

Now if the mother has N kids what will she do?

What will happen if some kids form a collusion and try to get a bigger share for them ?

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December 28, 2008 at 5:12 pm

I never knew the solution to the problem of dividing the cake among two kids… Interesting problem!

April 2, 2010 at 8:47 am

Allow randomly one child out of N to make N cuts. Then again randomly chosen child will pick a piece of cake. This picking of piece by a randomly chosen child from remaining children goes till end. This implements Mechanism in Bayesian Nash Equilibrium sense…

I’m thinking of how to make it in Dominant Strategy Equilibrium Sense…