I live in a student dorm with 16 people and we share a kitchen. Every week someone has to clean the kitchen. Right now we just take turns in a way determined by the numbers of our respective rooms. This is obviously not very efficient. I was thinking about the possibility of using auctions to determine who should do the cleaning. One possibility could be a sealed bid type thing where everyone states how much money they want in order to do the cleaning. Then the person who wants least does the cleaning and the other people fund this by contributing an equal amount.
Is there a more efficient mechanism? Some points I am considering: Should the amount of funding of each person depend on his/hers bid? Should the person cleaning also contribute to the funding? Will it be better to pay the lowest bidder the amount of the second lowest bid?
I am well aware that this kind of thing might be socially/morally objectionable. It is more of a thought experiment.