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!
Turing's Invisible Hand 
Or you could use the qualitative Vickrey auction if you want to negotiate closing, move-in date, etc. 🙂 One worry in either case is that there are various ways to back out.
The valuation can depend on time so that you can write your valuation for house h at time t as v(h,t) and assume this is increasing in the second argument. That is not a radical difference from standard problems. Another twist to take into account is that these are auctions with option to resell, since one item I really worry about when buying is how much will I get for the house when I sell it.
As far as the Pittsburgh market goes… I had a good time using a linear regression model to predict house prices when we were looking. The model performed pretty well, in that many sellers ended up transacting their house near the predicted price.
Which standard problems/papers do you have in mind? The difficulty is combining these time-dependent valuations with the online setting (some of the online settings have “expiring” buyers, but only in the sense that their value is constant and then they disappear).
Regarding linear regression, was one of your variables the asking price? Even on its own it seems to be a very good estimate of the transaction price.
you’d be surprised… the asking price is not significant once you have size of the house and the address (the only things that really matter). The asking price cannot matter that much, or just by asking for more I could sell for more which sounds unlikely.
I am not that familiar with “online” mechanisms, so I will not comment on those.I was thinking about standard static mechanism design. I meant to address your comment about the valuation being time-dependent. I do not believe that is, per se, the thing that makes the situation hard to analyze. I can write a model in which my value of the object depends on my type *and* an exogenous “state of the world” which captures residual uncertainty about the value of the object (this can be time and other things). This model is not hard to think about; in fact, in the case of one buyer and one seller it is a very simple (monopolistic screening) setup.
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I think its possible to design the online mechanism of the pittsburgh real estate market, ya its quite tough and challenging.
online mechanism of the pittsburgh property valuation is very great idea but its need be done more properly with the safety concern.
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