One of the nice things about Pittsburgh is that a middle class family like ours can afford to buy a “mansion” very close to CMU and the University of Pittsburgh (where my wife is a Ph.D. student), but the real estate market here is quite peculiar; while some houses languish on the market for years, some fly off the market in a day, and honestly I can’t tell the difference.
Houses in the latter category are essentially sold via a first-price sealed-bid auction: Once it becomes apparent that multiple offers are going to be made, the buyers are told that they need to make their highest and best offer as there will be no negotiation phase; typically some of the offers are above the asking price and the house is sold to the highest bidder (who pays his bid).
I toyed with the idea of suggesting to our real estate broker to conduct a second-price auction instead, but my very informal analysis hit some snags:
- This is actually an online (in the online algorithms sense) auction with dynamic supply and dynamic demand. If I don’t buy a specific house, I’ll probably buy a different one in the future. From the point of view of the seller, new buyers enter and leave the market. OK, we sort of know how to analyze these situations, but:
- There are multiple, heterogeneous goods.
- Buyers have unit demand, which should make things simpler, but interestingly their preferences are definitely not quasi-linear, in the following sense: When I say I’m willing to pay at most $x for a house h, what I mean is that I think I can get a better deal in the future. I don’t mean that my value for h is equal to $x, because I would much rather buy the house h at much more than $x than become homeless. And why would I become homeless? Because:
- Buyers may have deadlines (sellers typically don’t). In our case, we have to move out of the house we’re renting by the end of July, and we’re becoming less picky (i.e., our willingness to pay for houses increases) as the deadline draws nearer. (The house is roughly three times the size we need? At least it’s only 80 years old!)
Admittedly, mechanism design with money hasn’t been my cup of tea so far (some people say that’s why I wrote this paper), so there may be relevant work I’m unaware of. But to me the (Pittsburgh) real estate market seems like a grand challenge for online mechanism design!