Me and my friends decided to rent a 3-bedroom apartment together to save money. The rooms have different areas and we all probably value those areas differently. Rent per month for the whole apartment is fixed. Is there an algorithm to determine who pays how much for his room?
So, there is an apartment with rent per month $x$. It has some common areas and 3 rooms with areas $\alpha x$, $\beta x$, $\gamma x$: $\alpha + \beta + \gamma < 1$. There are Alice, Bob, Jane and Joe. Jane and Joe will live in the same room. Everyone wants his room to have the biggest area but they also want to pay less.