In my experimental economics class 2 years ago (wow, it’s been that long?) we studied something called the Winner’s Curse. Essentially, what happens is when the winner of an auction (of a common value type) typically overpays for the auction. In some sense it’s a phyrric victory. Of course, the extreme form is by overpaying. Some other forms of the Winner’s Curse, feeling as if one has overpaid is also included (only if you consider independent value auctions as a form common value auctions).
I was involved in one such auction today.
So, as you may have known, I’m moving houses again, to a different state (and I complained about the design problems of the Rock Band guitar). Today I was involved in house inspections for rentals in the new state that I am going to be living and working in. Back in the Old state, looking for houses was a simple thing – there was very little competition. But over in New state1 was the first time I saw 30 people rock up to a tiny apartment and having half of them picking out the forms from the real estate agent. In all my years of finding places to rent, never had I encountered such competition.
In total I visited 6 apartments (and that was before 10 a.m), during which 4 were leased out in less than an hour after inspection. It was at the 5th and 6th apartment, that things got really interesting. The 5th and 6th apartment had significantly fewer people inspecting (only 4 each). The 6th apartment wasn’t even listed on real estate sites yet. At the fifth apartment, everyone went for the forms (me included), and everyone seemed intent on quickly going to the real estate agent’s office as soon as possible. Then suddenly, one fellow suggested to the real estate agent that he was willing to pay more rent in order to secure the location. He had offered to pay $10 more per week to the original listed rental price. His raising of $10 was still within my budget range, so I raised $15 more per week (as I had needed the place urgently, since I start my new work this coming Friday).
The agent looked unsure for a while, and called his boss and the owner of the apartment. After a tense 10 minute conference, he agreed that the the apartment will be rent out to those who can bid the highest. And so the auction quickly went on – the final price was $45 more than the original listed price. I didn’t win it. The guy who won it was happy – let’s call him Hardy (because he looked like a hardy bloke you don’t wanna mess with).
And then came the news – a 6th apartment by the same owner and same agent – previously unlisted – was now available. Same rules, and it was slightly more expensive than the listing price of the 5th apartment (by $10 more a week). And so, the remaining 3 of us went to look at the 6th place. I would be willing to pay the same price Hardy offered in the 5th apartment. And being an economist and all, I was quite confident – I started my bidding slightly below what I valued the place, and once the offer hit what I was willing to pay, I stopped bidding new prices. Instead, I bid other things. I offered to put down 6 weeks rent in advance – something the other 3 were unwilling to do (standard advanced rent is 4 weeks). And I won the bid.
Along the way to the real estate office (the agent actually was gracious enough to drive me there, saving me a train ticket), I calculated my finances – I could afford coughing out 6 weeks in advance, but that in my opinion was a very stupid thing to offer. I had tied up my money in such ways that it would be quite interesting to see how I get by the next 4 weeks, considering I have got tests to pay for and the like. It was the Winner’s Curse.
Immediately after being hit by the Winner’s Curse, I started having doubts about my own valuation of the place, and I kept coming up with justifications for it. I had not seen the other houses (I had planned to inspect 15, and along the way, 3 were leased out before the inspection time had even started, so I only saw half of what was available) – maybe that was an error on judgement that I made. But according to statistics found on realestate.com.au, the last two places I inspected had less than a 100 hits, while the remaining houses had thousands of hits. The odds of me getting a place would be quite slim.
Cognitive dissonance is a bitch, and I hate facing cognitive dissonance. So I sat down and tried my best to work out the valuation. I couldn’t do an objective valuation – I simply do not know the area well enough (you know, quantifiable tacit knowledge2).
One of the main issues is just to figure out if the auction that had taken place was a common value auction – to which I answer, yes. An apartment is an apartment to everyone – it takes care of the first need in Maslow’s heirarchy3- so it’s common to that point, that everyone bidding draws value from the probability distribution that the roof covering their heads are worth X. However, I also contend that there is an element of private values, in that every person could also have an independently drawn value from an independent probability distribution.
So to combine both probability distros, a Bayesian mean is drawn (think of it as a compromise of values drawn between a private value auction and the values drawn from a common value auction – I’m doing this as a just-in-case scenario4). And because I’m a very huge fan of graph theory (think about it, graph theory helps you see situations very clearly), I modelled the auction I had just participated in as a complete graph, where everyone’s bayesian-averaged values affect each other’s values. Again, in this step, Bayes’ theorem comes into play, by incorporating other bidders’ values as priors, the adjusted posterior is one’s value.
Of course, this is an iterative game, but I suppose it should converge to a point of stability. I don’t know, I iterated my model with 3 players (don’t you just love triangle graphs?) twice, and I was happy, that I had bid that amount. What I was unhappy with was, of course my own decision to tie my finances up this way. I have no idea how to model that (maybe discount everything to net present value, and treat it as a one off buying scenario?) yet, and I probably don’t wanna know in the short-run, as it keeps reminding me of my mistake in doing that (yes, I still think it’s a mistake despite that the odds of actually finding a place and moving in a span of one week is actually very low, but I still managed to do it). I believe I could have done better, and I was rash to make that decision. Oh well, live and learn.
Yes I know my blog entry is a little messed up right now, but I’m sitting in a youth hostel typing this. I’ll update it with pictures to illustrate my methods (which in my opinion is kinda dodgy since nobody has ever modelled an auction as a graph before – and I know this because I’m subscribed to game theory journals) when I get back to my home on monday (and yes, as you can or cannot tell, I am indeed frustrated over the stupid decision made)… then it’s moving day on thursday. Sigh.
- I think the capitalization of the term Old and the term New should tell you which was the original state I’m from and where I am moving to – hint, one of them looks like the contraction of the name of the state, and the other one has the term in the name of the state – but if you are too stupid to figure it out I shan’t help you [↩]
- hah, I just stumped you there didn’t I? Tacit knowledge is by definition unquantifiable – what I mean is those gut feelings that can be worked out or proxied as factors [↩]
- you can just tell that I’m name dropping to impress you with the knowledge I have, can’t you? Too bad I’m tons smarter than you, and I am more arrogant than you too [↩]
- as in just in case my assumptions prior to this was wrong, that this situation is either a strictly private value auction or strictly a common value auction [↩]
