There’s a paired optimization problem, where you assign everyone to a room, and the constraint that this assignment be ‘envy-free’; that is, no one looks at someone else’s assignment/rent combo and says “I’d rather have that than my setup!”. There was a calculator that I can’t easily find now which tried to find the centroid of the envy-free region.
There are other approaches that work differently; this one, for example, tries to split surplus evenly between the participants, and shows the comparison to other options.
There’s a paired optimization problem, where you assign everyone to a room, and the constraint that this assignment be ‘envy-free’; that is, no one looks at someone else’s assignment/rent combo and says “I’d rather have that than my setup!”. There was a calculator that I can’t easily find now which tried to find the centroid of the envy-free region.
There are other approaches that work differently; this one, for example, tries to split surplus evenly between the participants, and shows the comparison to other options.
The link no longer works