Allocating chores using auctions 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.
Interesting questions. To go through the list of questions you have...


Is there a more efficient mechanism? Will it be better to pay the lowest bidder the amount of the second lowest bid?
According to the revenue equivalence theorem, both types of auctions will result in the same expected revenue to the "cleaner," and will result in the same person doing the cleaning.
Should the amount of funding of each person depend on his/her bid?
This is the same question of choosing first-price or second-price auction. Indeed, any type of auction will depend on the bidders' bids to an extent.
Should the person cleaning also contribute to the funding?
This doesn't make a difference, as the difference would be constant at a factor of $\frac{n}{n-1}$ depending on which "rule" you apply. That is, if you switch the rule to saying that the person cleaning woulnd't have to contribute to the funding, then everyone could just increase their bids by a factor of $\frac{n}{n-1}$.


If your constraint is that someone in your dorm will have to do it, then I'd say this (along with simply keep raising the "price" until someone says, "I'll do it") would be the most efficient. If this is not a constraint, though, an outsider (cleaning company, random guy outside of your dorm) might be willing to do it for less.