[eru]

Yes, but why care about underpricing at all? Can't you just have a formal auction, where everybody states (legally binding) how many stocks they want at which price level (e.g. for 3$ I'd buy 10 stocks, for 5$ I'd buy only 8 stock, and so on, basically giving your demand function) and then do a simple optimization that finds the highest price at which all shares sell. (Or alternatively, and perhaps better, the lowest price at which everybody who wants to pay at least this price, can buy.)

Why rely on guess work?

Edit: I saw on the linked Wikipedia article that some people have tried auctions. Google seemed a noteworthy example.

[ct4ul4u]

Epoch had an auction equivalent process (which we didn't get to implement because we didn't get to the point of being lead underwriter).