SF startup lets would-be tenants bid for apartments
sfgate.com
sfgate.com
On the other hand, this happens already, just much less transparently. I'm a bay area landlord, and had a bidding war for my place last year. I literally had people throwing money at me (take this $20 in my wallet and I'll be back with a cashier's check in 20 minutes!!).
However, since I have a conscience, I ended up renting to the group that I thought would make the best tenants instead of the ones with the most cash. Most landlords I suspect are not like this.
Around here, there's been so much construction at the high end of the market, there's not really a shortage of rentals if you afford the top rents. Landlords won't get bidding wars for that. It's the middle-income folks who are getting the shaft.