Instead of arguing for hours about who got which room in a new apartment, I just wrote down my true preference for how much I was willing to pay for each room. Then I automagically got assigned a room that was cheaper than I had been willing to pay for it.
I’m confused by how this second price auction worked. If there was just one room, I see how you’d do a second price auction to figure out who wins and at which price they get it, but how does it work when there are multiple rooms, and each person purchases exactly one room?
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.
I’m confused by how this second price auction worked. If there was just one room, I see how you’d do a second price auction to figure out who wins and at which price they get it, but how does it work when there are multiple rooms, and each person purchases exactly one room?
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