July 30, 2010

House rental, showers, and auctions

I'm currently in the prologue of the house-rental process. Our sights are set on a four-bedroom house with an interesting property: the room resources are of differing value — not in terms of square-footage, but other, less easily scalable factors.

So how do we dole out the resources of unequal value in a manner that everybody considers fair?

(Talk about first-world problems...)

Proposed solutions

Three systems for deciding the room allocations have been proposed, and one has been rejected:

I'm personally a fan of the simplicity and total lack of competition in the random system, but if the bidding system is more likely to lead to the optimal outcome, it must be considered! (Of course, care must be taken to address possible social ramifications.)

During casual discussion we noted that the bidding system would be strategically interesting. If a person were not really interested in getting a high-value room but didn't care all that much if they did, it is clearly in their favor to drive bids on the early rooms as high as possible — this would entail a decrease in the payment rate for a later room.

I perused the Wikipedia entry on auction theory and realize that we were assuming an open/ascending bid auction, but a first-price/sealed-bid auction might be less socially stressful. [†] My main fear is that open bidding would get carried away (it's exciting, after all) and participants would come to regret their bids.

In any case, it's an interesting problem I thought I would share. Suggestions are welcome; otherwise, I'll write a follow-up entry as to how it turns out.

Footnotes

[*]

This means it has no shower. Stupid terminology, but I suppose it has a nicer ring than "toilet room".

[†]

As an aside, the game theory described on that page also seems to discuss provable equilibrium of a single auction, whereas our auctions have dependent equilibrium values.