Assume an auction with a small and finite number of bidders with discrete values on the aggregate demand curve. Imagine this is a pure common values auction (wikipedia definition):
Some would call this a pure common value auction, using the term common values to describe any auction in which (i) bidders have different information and (ii) one bidder’s information would be informative to another bidder about the latter’s valuation for the good.
Imagine bids are public. Bids are consecutive and the bidder with the highest final bid wins the good. To call upon a basic economic definition, declared prices are signals that reveal information about bidder’s demand curves. The other implication of having common values is that valuations are correlated. In the auction, this implies bidders have dynamic valuations; when a bidder places a bid, the other auction participants are able to gain additional information that allows them to readjust their values for the asset and bid accordingly.
Quick note: can we assume risk-neutral participants? I need to return to that question later, but let’s make that assumption for now.
At this point, let’s bring in some numbers. Imagine an auction with 5 bidders, with bidder valuations being initially uniformly distributed from 0-100, inclusive, which means that bidder 1 values the good at 20, bidder 2 value is 40, bidder 3 has value 60, bidder 4 has value 80, and bidder 5 values the good at 100. The minimum bid increment is 1. This means that bidder 5 wins the auction at some price between 81-100. Where precisely depends on the correlation factor. A higher correlation factor means that the final price is closer to 100; a lower factor means that the final price is closer to 81.
Let’s loosen a parameter. Imagine instead of 5 bidders, there are 100. It’s obvious here that allowing dynamic bidding and (highly) correlated values means that the final price is at least 100; depending on the correlation function. Hypothesis: if you allow the correlation function to be an exponential greater than 1 for values contiguous to the high end of the distribution, you get an asset bubble, where increasing bids inflate exponentially (you need at least two bidders to get into a bidding war).
Can this provide a framework to thinking about bubbles like technology and housing? Does this make any sense to anyone else? The next step is to formulate this mathematically.